Regents Exam Questions by Topic Page 1 - Yorktown...

2

Regents Exam Questions by Topic PR08ABILlTY Theoretical Probability W I lllaporg Name

The graph below shows the hair colors of all the students in a class

Class Hair Color 1 J

IjJ a

c -y

(1) I

-u 6J

(fj 5 -(5

4 J)

J ~

J Z

Red Blonde Black Brown

Vhat is the probability that a student chosen at random from this class has black hair

The party registration of the voters in Jonesville is shown in the table below

lil

-Party Registration Number of Votes

Registered-Demon1 GOOO

GepJolican 5300 -shy

J r1i~F pendo nI 3700 ~_

If one of the registered Jonesville voters is selected at random what lS the probability that the person selected is not a Democrat (1) 0333 (3) 0600 (2) 0400 (4) 0667

f bull Jl C iCgtL

Regents Exam Questions by Topic Page] POWERS Exponential Functions wwwJlllaporg Name

On the set of axes belov draw the graph of y == 2 over the interval -1 s x S 3 Will this graph ever intersect the x-axis Justify your ansvver

r

2

A radioactive substance has an initial Inass of 100 grams and its mass halves every 4 years Which expression shows the number of grnms remaining after I years

(1) 100(4) 4 (3) 1OO(~)~ 2

(2) IOO(4f2 (4) ]00(~)41

2

lh

A population of wolves in a county is represented by the equation

P(t) = 80(098) where I is the number of years since 1998 Predict the

number of wolves 1n the population in the year 2008

4

(3) 16 (4) 4

The height [(x) of a bouncing ball after x bounces lS represented by

f(x) = 80(05) How many times higher is the first bounce than the fourth

bounce (1) 8 (2) 2

Page 2

Regents Exam Questions by Topic POWERS Exponential Functions -- ~_-_--------~-~--~---__------ -----_--shyName

5 Kathy deposits $25 into an investment account with an annual rate of 5Yo compounded annually The amount in her account can be determined by the

formula A ~ P(I + R) where P is the amount deposited Ii is the annual

interest rate and t is the number of years the money is invested If she makes no other deposits or withdrawals how much money will be in her account at the

end of 15 years (1) $2575 (3) $5197 (2) $4375 (4) $39397

6 The FrankJins inherited $3500 which they want to invest for their childs future collegc expenses If they invest it at 825 with interest compounded monthly detem1ine the value of the account in dollars after 5 years Use the

formula A ~ 1(1 + -) where A = value of the investment atier t years l c n

principal invested r = annual interest rate and n = number of times

cOlnpounded per year

7 The population of Henderson City was 3381000 in 1994 and is growing at an annual rate of 18 If this growth rate continues what will the approximate

population of Henderson City be in the year 20001 (l) 3696000 (3) 3798000 (2) 3763000 (4) 3831000

g On Ianuary 1 1999 the price of gasoline was $139 per gallon 1f the price of gasoline increased by 05 per month what waS the cost of one gallon of

gasoline to the nearest cent on January lone year later

9 Kathy plans to purchase a car that depreciates (loses value) at a rale of 14 per year The initial cosl of the car is $21000 Which equation represents the

value v of the car afier 3 years (1) v = 21000(014)3 (3) v = 21000(114)3

(2) v 21000(086)3 (4) v=21OOO(O86)(3)

10 Daniels Print Shop purchased a new printer for $35000 Each year it depreciates (loses value) at a rate of 5 What will its approximate value be at

the end of the fourth year (1) $3325000 (3) $2850772 (2) $3000813 (4) $2708233

11 A used car was purchased inul y J999 for $ J1900 If the car depreci ates 13 of its value each year what is the value of the car to the nearest

i~ ij dollars in July 2002

Regents Exam Questions by Topic Page I QUADRATICS Factoring Polynomials njlllaporg Name

The greatest com1110n factor of 4a 2h and 6ab] is (1) 2ab (3) 12ab (2) 2ab 2 (4) 24a 3b4

2 If 3x is one factor of 3x 2 - 9x what is the other factor (l)3x (3)x--3

(2) x L -6x (4)x+3

3

]

If one factor of 56x 4y3

(1) 4x 2 - 3y 3

(2) 4x 2 - 3y 2

bull 42x 2y6 is 14x 2 what is the other factor

(3) 4x - 3xy 3

(4) 4x 2y - 3xy

4 Which expression is a factor of x 2 +2x shy 15 (1) (x - 3) (3) (x + IS) (2)(x+3) (4)(x-5)

5 Which expression is a factor of 11 2 + 311 shy

(1) n + 6 (3) n shy 9

(2)n 2 +9 (4)n+9

54

6

Ii

What are the factors of x 2 - 5x + 6

(l) (x + 2) and (x + 3) (3) (x + 6) and (x - 1) (2)(x-2)and(x-3) (4)(x-6)and(x+ I)

7 What are the factors of x 2 - lOx - 24 (l) (x shy 4)(x + 6) (3) (x shy 12)(x + 2) (2) (x shy 4)(x shy 6) (4) (x + 12)(x -- 2)

8 Factored completely the expression 2y2 + 12y shy

(t) 2(y + 9)(y - 3) (3) (y + 6)(2y - 9) (2) 2(y - 3)(y - 9) (4) (2y + 6)(y - 9)

54 is equivalent to

9 Factored con1pletely the expression 2x 2 + lOx shy(1) 2(x - 6)(x + 1) (3) 2(x + 2)(x + 3) (2) 2(x + 6)(x - 1) (4) 2(x - 2)(x - 3)

12 is equivalent to

10 Factor completely 3x 2 + 15x shy 42

Exam Questions by Topic factoring the Difference of Perfect Squares

Name

The expression x 2 - 16 is equivalent to

(1) (x+2)(x-8) (3) (x+4)(x-4)

(2) (x - 2)(x + 8) (4) (x + 8)(x -middot8)

2 What is a common factor of x2 - 9 and x2

- 5x + 6 (l) x + 3 (3) x - 2

(2) x - 3 (4) x~

3 Expressed in factored form the binominaI 4a 2 - 9b 2 is equivalent to (1) (20- 3b)(20-- 3b) (3) (40 -- 3b)(a + 3b) (2) (20 + 3b)(2a - 3b) (4) (20 - 9b)(2a + b)

4 Factored the expression 16x 2 - 25y 2 is equivalent to

(1) (4x - 5y)(4x + 5y) (3) (8x - 5y)(8x + 5y) (2) (4x - 5y)(4x - 5y) (4) (8x - 5y)(8x - 5y)

5 One of the factors of 4x 2 - 9 is

(l) (x + 3) (3) (4x _ 3) II (2)(2x+3) (4) (xmiddotmiddotmiddot 3)

6 One factor of the expression x 2 y2 - 16 is

(1) xy - 4 (3) x2- 4

(2) xy-8 (4) x 2 +8

7 Factor completely 3x 2 - 27

)t I ] ( l~ (1) 3(x-3)2

(2) 3(x 2 - 27)

(3) 3(x + 3)(x --shy

(4) (3x + 3)(x shy

3)

9)

8 Written in simplest factored form the binomial 2x 2 - SOean be expressed as

(1) 2(x - 5)(x - 5) (3) (x - 5)(x + 5) (2) 2(x - 5)(x + 5) (4) 2x(x - 50)

9 Factor completely 5n 2 - 80

10 Factor con1pletely 3ax2 - 270

Regents Exam Questions by Topic Page 1 GRAPHS AND STATISTICS frequency Histograms Bar Graphs and Tables Illaporg Name

The following set of data represents the scores on a mathematics quiz 58798199689276845357 8l 9l 77~GGS~7 ~1 72o~~9

Complete the frequency table below and on the accompanying grid draw and label a frequency histogram of these scores

rut athematics Qu iz Scores

Interval Tally Frequency

50--59

60-69

70-79

80--89

90-99

2

Regents Exam Questiolls by Topic Page 2 GRAPHS AND STATISTICS Frequency Histograms Bar Graphs and Tables W I maporg Name

The scores on a ll1athematics test vere 70 55 61 ~ 80 85~ 72 65 40 74 68 and 84 Complete the accompanying table and use the table to construct a frequency jlisloglam luI dJe~e SCUleS

Score Tally Frequency

40-49

50-59

60-69

70-9

80-89

-- shy - - shy - f--- shy --+-----+---+----+--+--+-+---shy

f---- ~--~-- 1--shy

--- shy --- shy - f-- shy -- shy f---f-- shy ---+--+--+- -+---+-f---+--+-- +---4--+----1

---I----~ f----shy -----I---f--~+-___t__l-- - shy --f---I------f--- shy

- - shy - shy -- --f---- shy --+-+---+--1----+-+-+----+---+---+---+---+- f--- shy

- I- shy r---shy - -- shy - 1---1--shy --I---- --I-t---+---+--+--+---I---- f_

=f-~=1--1~~~f------+~~-~~---+---~-----middott--r----~f---4---r- shy r--------- shy

-- f--f-- shy - --4----cf-----f--+----f-- --- shy -

--l~middotmiddot ~I-= _cLr_~_-----____L-_L__------------___J______L____L__L

(

Regents Exam Questions by Topic GRAPHS AND STATISTICS Frequency Histograms Bar Graphs ane Tables wwJ1l1aporg Name

Page 3

3 Sarahs D1athen1atics grades for on1OO~ 75 86 70 96 and 80

e marking period were 85 72~ 97 8] 77 ~ 93 ~

u CU111pltk the lany ~heet allO frequency laoie oeiow and conSTruct and label a fiequency histogran1 for Sarahs grades using the accompanying grid

n~tetval(grades)

61-70

71-80

81-90

91-100

shy--~-----~

Tally Frequency [

I R

-f---~-----f--~-~

~ -

j

I ~

---+-----I-----+----+-----+---+--+-~--~_r--~--_+_-_+__+_---+-__+_

f------t-----t----+---+-I----+-----t--+----L_~-~---t---t-~-t--

b Which interval contains the 75th percentile (upper quartile)

Regents Exom Questiuns by Topic Page 4 CiRAPHS AND STATISTICS Frequency Histogram~ Bar Graphs and Tables Jlllaporg Name

4 111 tllc l~1l1( trlals for thl FlO Hider nUl ell the SLlk 5(ctiOlII~ f1w [3 nl[IJltr~ lI-(ll) dld tIlt lllllr~ sllo11 ell tlw bbltmiddot bto_

400~Meter Run

Time (sec)

Frequency

I 500~sO9 510-51_9 H

52_0529 JHfI

530-539 HI

54_0-549 HI

ri Ci[l~ Ilw dah Irurn thtgt hC(Ill(([( COlllll)) dLiW a -rcqlHJIV hiltshy(IJpoundUJl) OJ) thp ~rid pnllderJ ()f-ll(w~

I klt pcrc(llt rJf tlw nllllHIS compll-middotted lhl tirnc- tl-ia 1gtt-gtl(Ifl )0 Ind =))q i(Tonds)

1(--

5

Regents Exam Questions by Topic Page 5 GRAPHS AND STA TISTICS Frequency Histograms Bar Graphs and Tables WWJJl1i1porg Name

The foIloyving data consists of the weights in pounds of 30 adults 195 206 10098 ISO 210195106195168180212104195100216195209 11~ ~9~ 2GG~ ~C~ 195 100 142 100 13598160155 Using the data complete the accOlnpanying cU1l1ulative frequency table and construct a cUll1ulative frequency histogran1 on the grid below

Interval Frequency Cumulative Frequency

51-100

101-150

151--200

201-250

I-I ~-+----+----t--f------f_---+-+----+-----+-+---+-----+--+-~--- r---shy -shy f--shy

l =-~~L-+-_r--_-~~_~==_-__I+~------__+f-----+-+_~~_+-_-_-j---_-~f------~+~~--_+__~_f_____==I___=----j----i I~~ --shyf - - ---~~ +---+-+----+---+~+-----+-----+-+--t--------+-----+--j-----shy -- ---shyr~~ -shy-~ -+--+----+---t--r--- -- shy f------ --t---+---+-----+

II ---- -shy r-shy f--- ~

I -I--+----t----+------+-~--+---+-___+_-+__- --+---+--+---+-----+-----+-----+-------1

- shy f---r-------t------t--t---+---+----t---- ------f----- I---~ --1--shy ----f----r-shy

-middot+----+--t---+---+---+~+---_+_---+---f-----_+____+_-_f-+__+__----+--cl------+__---~-

-shy ---- shy - shy ----t--t-----+-----t-- t-----t-- f----- --shy - r-- --r---f------shy - -----shy

---- shy- --+---+---+-+------+---+--- f-shy - -1___- ~-~f___- --1--_+_---+--

I

6

Regents Exam Questions by Topic Page 6 GRAPHS AND STAT1STICS Frequency Histograms Rr Graphs and Tables ww llllap_L)rg Name

The accompanying table shows the weights in pounds for the students in an algebra class


91-100 6

101-110 3

111-120 0

121-130 3

131-140 0

141-150 2

151-160 2

Using the data complete the cumulative frequency table and construct a cumulative frequency histogram on the grid below

( ( )yshy

7

Regents Exam Questions by Topic Page 7 GRAPHS AND STATISTICS Frequency I IiSlOgrams Bar Graphs and Tables WPllilP org Name

Twenty students were surveyed about the number of days they played outside in one week The results of this survey are shown below

r ~ A C A ~ 1 ( 1 1 ~ ~ ~ ~ ~ 1 ~ ~ ~ ~~

UJ~JVlJ~~JLLJL~J~JJj

Complete the frequency table below for these data

Nurn ber of Days Outside


0-1

2-3

4-5

6-7

Complete the cumulative frequency table below using these data

Number of Days Outside

Interval Cumulative Frequency

(-1

0--3

(-5

(-7

On the grid below create a cunlulative frequency histogram based on the table you 111ade

8

Regents Exam Questions by Topic Page 8 CRAPHS AND STATISTICS Frequency Histograms Bar Graphs and Tables ll1ap llrg Name

The accompanying histogram shows the heights of the students in Kyras health class

-------shy

jf-

5

180--169 170-179 180-189 190-199 200-2(19

Height (em

What is the total number of students in the class (1)5 (3)16 (2)15 (4)209

9 The table below shows a cumulative frequency distribution of rUIU1crs i ages

Cumulative Frequency Distribution of Runners Ages

Age Group Total

20-29 8

20-39 18

20-49 25

20-59 31

20-69 35

According to the table how many rmillers are in their fi)rties (1)25 (3)7 (2) ]0 (4) 6

Regents Exam Questions hy Topic Page 9 GRAPHS AND STATISTICS Frequency Histograms Bar Graphs and Tables Jl1laporg Name

10 The test scores for 10 students in Ms Sampsons homeroom were 61 67 81 83 87 88 89 90 98 and 100 Vhich frequency table is accurate for this set of data

Interval Frequency 61-70 2

71-80 2

81-90 7

91-- 00 10

Interval Frequency f-- shy

61-70 2

71-80 0 - shy

81-90 8

91-100 10

(1 ) (3)

Interval Frequency 61-70 )

shy

71-80 2

81-90 8 e---

91-100 10

Interval Frequency

61-70 2

71-80 ()

81-90 6

91-100 2

(2) (4)

1I The prices of seven race cars sold last week are listed in the table helow

Price per NUfnber of Race Car Race Cars

$126000 1

$140000 2

$180000 1

$400000 ) L

$819000 1

What is the 111ean value of these race cars in dollars Vhat is the l11edian value of these race cars in dollars State which of these measures of central tendency best represents the value of the seven race cars Justify your answer

Regents Exam Questions by Topic Page 10 GRAPHS AND STJ TISTICS Frequency Histograms Bar Graphs and Tables Jll1ilp nrg Name

]2 The values of 11 houses on Vashington S1 are shown in the table belov

Value per House

NlImber~ of Houses

-

$ 100 coo

$ 175COI)

$2()O()0

middot1700COO

1 -

c ~I

4 -~

1

Find the 111Can value of these houses in dollars Find the median value of these houses in dollars State which Ineasure of central tendency the mean or the median hesl represents the values of these 11 houses Justify your answer

13 The accompanying table represents the number of cell phone minutes used for one week by 23 users

Number of Number of Minutes Users

71-80 10 61-70 7 51-60 2

41-50 )

)

31-40 1

Which interval contains the median (1) 41-50 (3) 6]-70 (2) 51-60 (4) 71-80

14 What is the luean of the data in the accompanying table

$cl)rts Ftquncy

(X

25

(

3

20 2

11

10 4

(]) 11 (3) 15 (2) 145 (4) 16

Cc

Exam Questions by Topic Page 1 AND STATISTICS

tmiddotp Histograms~ Bar Graphs and Tables Name

15 rVlayken collected data about the size of the honors classes In her building This set of data is shown in the accompanying table

Class Size

Frequency

8 1

10 3

14 2

Which statement about the range of this sample is true (1) range = mean (3) range lt mean (2) rangegt mean (4) range lt standard deviation

Regents Exam Questions by Topic Page I PROBABIUTY Geometric Probability wwmiddotIll1aporg Name

At a school faiL the spilmer represented in the accoolpanying diagram is spun twice

What is the probability that it will land in section G the first time and then in section B the second time

1(l) -- (3) ~

2 8

(2) ~ (4) ~ 4 16

2 The accompanying diagram shows a square dartboard The side of the dartboard measures 30 inches The square shaded region at the center has a side that 111CaSUres 10 inches If darts thrown at the board are cqlwlly likely to land anywhere on the board what is the theoretical probability that a dm1 docs not land in the shaded region

30in

10 in[

L~2

Regents Exam Questions by Topic

PROBABILITY Geometric Probability WWWJ1ll3porg Name

Page 2

3 A square dartboard is represented in the accompanying diagraln The entire dartboard is the first quadrant from x = 0 to 6 and fron1 J = 0 to 6 A triangular region on the dartboard is enclosed by the graphs of the equations y = 2 x = 6

land in the triangular region fanned by the three lines

i

2

Kegents Exam Questions by Topic Page J

LINEA R EQUATIONS Graphing and Writing Linear Equations J1lwporg Name _

Which graph represents the equation x = 2

y y

1 I it it 1~ Which statement describes the graph of xmiddot= 4 (I) It passes through the point (0 4) (2) It has a slope of 4 (3) It is parallel to the y-axis (4) It is parallel to the x-axis

4

Regents Exam Questions by Topic Page 2 LINEAR EQUATIONS Graphing and Writing Linear Equations Jllwporg Name ~_~ _

2 On the accompanying grid draw the graph of the line whose slope is and

1 J

whose y-intercept is -2

--------------------------------shy

Write the equation for the line shown 111 the accOll1panymg graph Explain your answer

(Jt

Regents EaH Questions by Topic Page 3 LINEAR EQUATIONS Graphing and Writing Linear Equations li1l3porg Name _

5 Write an equation that represents the line that passes through the points (5~ 4) and (-5~ 0)

J CJf haL ~i total e~ 16 gallei of g~

miles on 4 gallons of gas If the gas tank is full at the beginning of a trip which graph represents the rate of change in the amount of gas in the tank

y y

~Jbull - 16

f

E-

~ 14 1411 1_1

~-=~ 1 - 12 ~ shy H ~ I-

6 (f)4 4

((j

C (I

J1

~lmiddot r

Distance (miles)

(1) 1

-1S Hmiddot c

G3 14 u 14 VI 0)

12 12 ~ c 11) ~ 11)cc ce r- 8 I- 3

rshy - 6 CfJ 4 if -1cc ~

C 2 lt- -(I I)

Distanceuro (miles Distiince irniI81

) (7--gtshy

7

Regents Exam Questions by Topic Page cl LINEAR EQUATIONS Graphing and Writing Linear Equations wjmaporg Name ~ ~ _

Super Painters charges $100 per square foot plus an additional fee of $2500 to paint a living room If x represents the area of the walls of Franccscas living

l---il r0O111 in square feet and y represents the cost in dollars which graph best ~ ~ 1 _ ~ rmiddot middot 1 _ 1 bull ~ _ n

lCpreSCihgt tile (iJgtl ui pJlllllng ner il v Big 1UU1l1

y 2ro

122200shy

~ (0 1T~

1~O0 V 1)~

1(leiCf) 0 I ~)

U ~U

25- -)~

i I - X -25 2~middot(i

Area (ff) Area (ft2)

1 ( 3 ) j y

250shy225-shy

0 2(I(Jshy

~ 175shy( 1~U-

-s 125shyU) 1tXlshyo Tshy

U shy)L-_J shy

middot-----r-+-----Y-----~_YI----i-r-l- x -2 12E 2~middot(t

Area (ft2) Area (ft2)

( 2 ) 4 )

8 A line with a slope of ~ passes through the point (36) Which point also lies 3

on this line (1) (63) (3) (-3-3) (2)(76) (4)(-63)

9 Line f contains the points (04) and (20) Show that the point (-2581)

does or does not lie on line I

Regents Exam Questions by Topic Page 5 LINEAR EQUA TIONS Graphing and Writing Linear Equations wywjlllap_org Name _

10 The accOlnpanying graph represents the yearly cost of playing 0 to 5 gan1es of golf at the Shadybrook Golf Course What is the total cost of joining the club and playing 10 games during the year

Yearly Total Cost

3-10-

3210

SinO

lj) 0 1(1 lt)

U S 120-E~

(I)

g $(10shy

$60

$J(J

(I

0

Regents Exam Questions by Topic Page 1 INEQUALITIES Linear Inequalities vll11aporg Name

An electronics store sells DVD players and cordless telephones The store 111akes a $75 profit on the sale of each DVD player (d) and a $30 profit on the sale of each cordless telephone (c) The store wants to make a profit of at least $25500 fruw it saks uf DVD players and cordiess poones -Vhich inequality describes this situation (1) 75d+30elt255 (3) 75d + 30e gt 255 (2) 75d + 30e ~ 255 (4) 75d+30C2255

2 Which ordered pair is no in the solution set of y gt 2x + n

(1)(14) (3)(38) (2) (16) (4) (2 cS)

3 In the graph of y s -x ~ which quadrDllt is completely shaded (1)1 (3) III (2) II (4) IV

4 Which inequality is represented by the accornpanying graph

-lt-- - - - - - ~ - -c - - -~ - -

~

bullbull _ cmiddotymiddot~middotmiddot middotmiddotmiddotmiddotmiddotmiddotmiddot

bullbullbullbullbullbullbullbull ~ middotxmiddotmiddot middotmiddot-1middot++-++ -bullraquo ~

(1) ylt3 (3) yS 3

(2) y gt 3 (4) 123

5

6

Regents Exam Questions by Topic Page 2 INEQUALITIES Linear Inequalities I- JlI1ilfJnrg Name

Which inequality is represented by the graph belov

~- t ~

- - )

--

-----+c- shy

)

-- bull

1 (1) y lt 2x +] (3) y lt --x +- 1

2

1(2) y lt -2x + 1 (4) ylt--x+l

2

Which inequality is shown in the accompanying diagrdffi

j (I~~--l y

3 J

(1) ygt-x+2 (3) yzmiddot-x+22 2 3 3

(2) ylt-x+2 (4) yS--x+2 2 2

---- --- - --- ----

2

Page I IRegents Exam Questions by Topic ITOOLS OF GEOMETRY Midpoint

Name -----~----~- ---~ ---- ------shyWJlllaporg

What is the midpoint of the line segment that joins points (4~-2) and (-25)

(1) (I i) (3) (L~)

(2) (~3) (4) (2~) 2

The coordinates of A are (-9~ 2) and the coordinates ofG are (3 14) What are

the coordinates of the midpoint of AG (1) (-3~8) (3)(-616) (2) (-66) (4)(-21-10)

A line segment on the coordinate plane has endpoint5 (24) and (4y) The

l11idpoint of the scgnlent is point (3) What is the value of y (1) 11 (3)5 (2) 10 (4) -2

AI is the midpoint of AR If the coordinates of A are (-15) and the coordinates4 ofl4 are (33) vh3t are the coordinates of B

bullbull( f 1 (1) 04) (3) (71) (2)(28) (4)(-57)

The lnidpoint of AB is (- ]5) and the coordinates of point A are (--32) What5 arc the coordinates of point B (1) (18) (3) (07) (2) (110) (4)(-58)

( J)

6

Regents Exam Questions by Topic Page 2 TOOLS OF GEOMETRY Midpoint Jlllaporg Name

The coordinates of the midpoint of AB are (2A) and the coordinates of point B are (37) What are the coordinates of point 11 [The use of the grid is

I optional]

Regents Exam Questions by Topic Page 3 TOOLS OF GEOMETRY Midpoint wnwjmap org Name

7 The midpoint M of line segment AB has coordinates (-3A) If point A is the origin (OJraquo vhal are the coordinates of point B [The use of the grid is

I optional]

8

Regents ExalT1 Questions by Topic Page 4 TOOLS OF GEOMETRY Midpoint 1 IIII jl11aporg Name

One endpoint of a line segn1ent is (62) The n1idpoint of the segment is (2~O)

Find the coordinates of the other endpoint [The use of the grid is optional]

r-----~-------c-------------------------

----- -middot1

- -jshy

2

Regents Exam Questions by Topic Page j

QUADRATICS Minimum and Maximum of Quadratics Wjllw))org Name _ _

Amy tossed a ball in the air in such a way that the path of the ball was modeled by the

equation y = _x 2 + 6x In the equation y represents the henght of tile ball in feet and

x is the time in seconds

a Graph y = _XL + 6x for 0 ~ x ~ 6 on the grid provided beJow

lV

1middot1

12

~I---

2middot

01 2 J 5 6

b At what time x is the baJJ at its highest point

An architect is designing a museum entranceway in the shape of a paraboiic arch

represented by the equation y = _Xl + 20x where 0 x S 20 and all dimensions

are expressed in feet On the accompanying set of axes sketch a graph of the arch and determine its maximum height in feet

y

o

)

l j

3

4

Regents Exam Questions by Topic Page 2 QUA DRATICS Minimulll and Maximum of Quadratics VVWJlllllporg Name

Tom throws () baJJ into the air The ball travels on a parabolic path represented by

the equation h = -8] +401 where h is the height in feet and I is the time in seconds a On the accompanying set of axes graph the equalion from I = 0 to 1= ) seconus including all integral values of 1 from 0 to 5

11

60t---shy

55

50 -r -+---+-------+----lr--j

I ---+-+---t---j

35shy ~ g 30 - I

----

_j

~ 25 I I ~_--l 20- --i15--)- -- -- -l l~r~r~ --T ~-all -shy _t 0123456

Time (sec)

b What is the value of I at which h has its greatest value

An arch is built so that it is 6 feet wide at the base Its shape can be re presented by

a parabola with the equation y = -2x 2 + 12x where y is the height of the arch

a Graph the parabola from x = 0 to x = 6 on the grid below

I ~-+-+-+-1f-+-+--l-+--i-t--+-+--I-I-t--+--+-+-I

10 15 20

b Determine the maximum height y of the arch

5

I IRegents Exam Questions by Topic Page 3 QUA DRATICS Minimum and Maximum of Quadratics IJnlnporg Name _~__ _~ __ ~ _

The mC111bers of the Lincoln High School Prom Committee are trying to raise money for their senior prom They plan to sell teddy bears The senior advisor

told them that the profit equation for their project is y = -01x 1 + 9x - 50 where

x is the price at which the teddy OeliIS vmiddotill be sold and y is the profit iIi don~-

On the grid below graph this relationship so that 0 x 90 and -50s y S 160

How much profit can the con1n1ittee expect to make if they sell the teddy bears for $20 each What price should they charge for the teddy bears to make the maximum profit possible

Regents Exam Questions by Topic Page ~

OLJADRA TICS Minimum and Maximum of Quadratics lll1ap0rg Name

6 What arc the vertex and the axis of symmetry of the parabola shown in the diagran1 belov

(]) The vertex is (-2-1) and the axis of symmetry is x = -2 (2) The vertex is (-2-3) and the axis of symmetry is y= -2 (3) The veliex is (-3-2) and the axis ofsymn1etry isy= -2 (4) The ve11ex is (-3-2) and the axis of symmetry is x= -2

jet

Regents Exam Questions by Topic Page ) QUADRA TICS Minimum and Maximum of Quadratics WIJl1aporg Name

7 A swim team meInber performs a dive from a l4-foot-high springboard The parabola below shows the path of her dive

y

E 12 2gt OJ

c 8

4

-

4 to

10

Distance from Springboard (feet

Which equation represents the axis of symmetry (l ) x = 3 (3) x = 23 (2)y=-J (4)y=23

8 What is the turning point or vertex of the parabola whose equation IS

y=3x) +6x--l bull 1~~ I - It ~

(1 ) (L8) (3) (-38) (2) (-1-4) (4) (344)

9 What is the In1IIIInUIn point of the graph of the equation

y = 2x 2 +8x+9

(1) (233) (3) (-2-15) (2) (217) (4) (-21)

lOA model rocket is launched 1r0111 ground leveL Its height h meters above the grouncl~ is a function of time seconds after launch and is given by the equation

ii ~-- h = -49 2 + 686 What would be themaximUl11 height to the nearest meter attained by the nlodel (1)243 (3)241 (2)242 (4)240

Regents Exam Questions by Topic Page 6 QUADRATICS Minimum and Maximum of Quadratics wwJmapprg Name

I 1 An archer shoots an arrow into the air such that its height at any tilne L is given

by the function h(l) == --161 2 + kt + 3 If the maxinlum height of the arro

occurs at time t = 4 what is the value of k ~i) 128 (3) 3 (2)64 (4)4

12 The height of an object h(1) is detern1ined by the formula h(1) == -16 2 -+ 2561

where is time in seconds Will the object reach a maxin1un1 or a minin1un1 Explain or show your reasoning

13 Vanessa throws a tennis ball in the aIr The function h(t) == -16r~ + 45 -+ 7

represents the distance in feet that the ball is from the ground at any time 1 At what tin1e to the nearest tenth ofa second is the ball at its maXin1l1111 height

14 The height h in feet a ball will reach when thrown in the air is a function of

tinle I in seconds given by the equation h(t)= -161 1 + 30t + 6 Find to the

nearest tenth the maximum height in feet the ball will reach

15 When a current J flows through a given electrical circuit the power W of the

circuit can be determined by the fonllula W= 1201-1212 Vhat allloun1 of

current 1 supplies the maximum power W

16 The equation W = 1201 - 1212 represents the power (W) in watts of a 120-volt circuit having a resistance of 12 ohms when a current (1) is flowing through the circuit What is the maximum power in watts that can be delivered in this circuit

3((

Regents Exam Questions by Topic Page 7 QUADRATICS Minimum and Maximum of Quadratics )I11lporg Name _~ ~____ ~ __

17 A baseball player throws a ball from the outfield toward home plate The balls

height above the ground is modeled by the equation v = -] 6x 1 + 48x + 6 where

y represents height in feet and x represents tinle in seconds The ball is initIally thrown fron1 a heighl of 6 fed h0Vv iliau) )ecollJ~ a~t(i- ~h( ball i thrown will it again be 6 feet above the ground What is the maximum height in feel that the ball reaches [The use of the grid is optional]

j~glIlIS Lxam Questions by Topic f)llge 8 QUADRATICS Minimum and Maximum of Quadratics II 11 Iilli1p org Name ~__

18 A rock is thrown vertically from the ground with a velocity of 24 meters per second~ and it reaches a height of 2 +24f - 491 1 after seconds Hov many seconds after the rock is thrown will it reach maxin1unl height and vvhat is the maXilTIUlTI heigilt the rucK will icaLli in meters Ho- ill~ny scccnd~ ~f~~r t1~

rock is thrown will it hit the ground Round your answers to the nearesf hundredth [Only an algebraic or graphic solution will be accepted

I 1--- r--- l----r-i-TshyI I

~ --f------shy

I

--f-- shy

-- shy

- shy

- shy

- shy - shy

-- shy

f--- shy -shy

f- shy -

r- shy --

LtJ

19

Regents Exam Questions by Topic Page 9 QUADRATICS Minimum and Maximum of Quadratics 1I11Jp org Name

The path of a rocket fired during a fireworks display is given by the equation

s(f) = 64t - 16t 2 bull where t is the time in scconds~ and s is the height in feet What is the maximum height in feet the rocket will reach 1n how many seconds will the rocket hit the ground fThe use of the grid is optionallmiddot

i I I

i 1--1 middotj-i-F-l -- -i _- L--- 1 +shy-j--- jshy

I Iii-- r-- j--i --- - 1- - -----_I__-----_~------

Regents Exam Questions by Topic Page 10 QUADRATICS Minimum and Maximum of Quadratics wwwjrnaporg Name

20 A laundry owners estimate of her weekly profits p in dollars is gjven by the

equation p = -4112 + 160ft where w represents the nun1her of workers she

hires What is the nun1ber of workers she should hire in order to earn the gredle~l PfuI1l [Tlle USe vi tIle grid i~ oplivilci~]

21

Regents Exam Questions by Topic Page] ] QUADRATICS Minimum and Maximum of Quadratics wwwJmaporg Name

Each yeac the student council at Briarwood High School sponsors a community talent show to raise money In previous years the council has discovered that

~i profit from ticket sales l P( x)c is a function of the amount charged per ticket x

in dollars as modeled by the equation px) = 120x - ] LX vVhat amounL

should the council charge for a ticket to make the greatest profit [The use of the grid is optional]

I C( (

Regents Exam Questions by Topic Page 1 QUADRAT1CS Operations with Polynomials WWJ1naporg Name

What is the product of - Jx 1 y and (5 xy 2+ xy)

(1) -15xy3-3x 3y 2 (3) -15x 2J)-3x 2y

(7) -15xy3 - 3x 3y (4) -15x v3 + xv

2 What is the product of 212 - 5 and 3

(1) 6- - 151 (3) 61 2 - 151 bull l )~

(2) 6r -5 (4) 62 -15

3 What is the product of (c + 8) and (c - 5)

(l) c2 + 3c - 40 (J) c 1

+ 13c - 40

(2) c2 - 3c - 40 (4) c2

- 40

4 The expression (x - 6)2 is equivalent to

(1) X 2

- 36 (3) X 2 - 12x + 36

(2) x 2 + 36 (4) X2 -+ 12x + 36

5 The expression (0 2 + b2 )2 is equivalent to

(1) 0 4 +- b4 (3) a~ + 2a l b2 + b4

4 l b2 4 + b4(2) 0 + a + b4 (4) 0 + 4b 2

6 When 3x 2 - 6x is divided by 3x the result is

(1) -2x (3) x-+2 (2) 2x (4) x - 2

7 What is 6x 3 + 4x 2 + 2x divided by 2x

(1) 3x 2 + 2x (3) 4x 2 + 2x

(2) 3x 2 +2x+l (4) 4x 2 -+-2x+]

8 The expression (50x 3 -- 60x 2 + lOx) 71 Ox is equivalent to

(l) 5x 2 - 6x + 1 (3) 5x 2

- 60x 2 + 1Ox ((--_li

(2) 5x 3 - 6x 2 + x (4) 5x 2

- 6x

1( -)( ~x

Regents Exam Questions by Topic Page] RATIONLS Multiplication and Division of Rationals Wllllaporg Name

x -1 h 4xWhat IS t e product of -- and ---- expressed in simplest fonn x --1 3x + 3

4x l) 4x(1) --- () ---- shy

3( x + 1)

4x 2

(2) --- (4) 4(x~22 l

J J

2 2 1+3What is the product of x -=~ and expressed in snnplest form

x + I 3y - 3 (1) x (3) x + 3

x(2) -- (4) ~+~ )

J J

Perform the indicated operation and express the result in simplest terms3 x 3x

x+3

4 2x 2 + 2x - 24 x 2 + x-- 6 A rectangular prism has a length of ---~~--- a width of ------ and a

4c +x x+4

8x 2 + 2x height of ---)--- for all values of for which it is defillled express in terms of x

xmiddot - 9 the volume of the prism in simplest form

)5 x + i_XIf the length of a rectangular garden is represented by ----- ----- and its width is

x 2 +1x-15 2x- 6

represented by -~-- which expression represents the area of the garden 2x+4

x 2 + 2x (1)x (3) - shy

2(x + 5)

x(2)x+5 (4)-shy

x+5

6 2 2

f f 3x -27 d ) x -7x+12

fi d h( ( t II 1 fI (x)=----- an g(x =) In llxl--g x or a va ues 0 I8x + 30 3x- - 7x - 20

x for which the expression is defined and express your answer in siInplest form

7 4x + 8 2 - X x 2 - 4 Express in simplest form --- -- 2 --

(II)1I X + ] 3x - 15 2x - 8x-l0

8

Regents Exam Questions by Topic Page 2 RATIONALS Multiplication and Division of Rationals wJl11aporg Name

Perforn1 the indicated operations and simplify cOlnpletely

x-4 --- ----- ------ -- shy

x- -)X _ - x - i 2 Xl - 3x -r 1G

Regents Exam Questions by Topic Page 1 PROBABILITY Multiplication Counting Principle wVjrnaporg Name --_-------------- shy

Max goes through the cafeteria line and counts seven different 111eals and difTerent desserts that he can choose Which expression can be used detel111ine hov- many different ways Max can choose a Ineal and a dessert 11 ~_J (1 I ~ J i 7 ~

(2) 7e3 (4) 7 ~

2 Robin has 8 blouses 6 skiIis and 5 scarves Which expression can be used calculate the number of different outfits she can choose if an outfit consists of blouse a skirt and a scarf (1) 8+6+5 (3)8[65

(2) 8-6-5 (4)19C

3 Leo purchased five shirts three pairs of pants and fOUf pairs of shoes Which expression represents how many different outfits consisting of one shirt one pair of pants and one pair of shoes Leo can make

(1) 5-3-4 (3)12 C 3

(2) 5 + 3 +4 (4) 12 P3

4 len and Barrys ice cream stand has three types of cones six flavors of ice creanl and four kinds of sprinkles If a serving consists of a cone one flavor

icc cream and one kind of sprinkles how many different servings are possible

(1)90 (3) uC

(2)72 (4) uP

5 How ll1any different outfits consisting of a hat a pair of slacks and a sweater can be made froIl1 two hats three pairs of slacks and fOUT sweaters

I111 (1)9 (3)24

(2) 12 (4)29

6 Juan has three blue shirts two green shil1S seven red shirts five pairs of denim pants and two pairs of khaki pants How many different outfits consisting

ltI i one shirt and one pair of pants are possible (1) 19 (3) 130 (2) 84 (4) 420

7 Paloma has 3 jackets 6 scarves and 4 hats Determine the nmnbcr of different outfits consisting of a jacket a scarf and a hat that Paloma can wear

8 The school cafeteria offers five sandwich choices four desselis and three beverages How many different meals consisting of one sandwich one dessert

i~IiL1 and one beverage can be ordered (1) 1 (3) 3 (2) 12 (4)60

Regents Exam Questions by Topic Page 2 PROBABILITY Multiplication Counting Principle lIlilpllrg Name

9 A deli has five types of meaL two types of cheese and three types of bread How many different sandwiches consisting of one type of meat one type of cheese and one type of bread does the deli serve f1ln n)iO - I - ~

(2) 25 (4) 75

10 Coles Ice Cream Stand serves sixteen different flavors of ice cream three types of syrup and seven types of sprinkles If an ice cream sundae consists of one navor of ice cream one type of syrup and one type of sprinkles how ll1any different ice cream sundaes can Cole serve (1) lCgt836 (3) 3 (2) 336 (4) 26

11 In a school building there are lO doors that can be used to enter the building and 8 stairways to the second floor How lTIany different routes are there from outside the building to a class on the second floor (l) 1 (3) ] 8 (2) 10 (4) 80

12 It a department store there are six ways to enter the building six ways to get from the first 1100r to the second floor and four ways to get from the second f100r to the third Hoar In how many different ways muld someone enter the building and go to the third loor (l) 16 (3) 120 (2) 24 (4) ]44

13 Jerel11ys bedroOlD has two doors leading into the hallway His house has four doors leading to the outside Using the doorways in how many different ways

can Jeren1Y leave his room and go outside (1)8 (3)5 (2) 6 (4) 4

14 A certain car COilles in three body styles with a choice of two engines a choice of two transmissions~ and a choice of six colors What is the mininlum number

of cars a dealer n1ust stock to have one car of every possible cOlllbination (l) 13 (3) 42 (2) 36 (4) 72

15 Debbie gocs to a diner famous for its express lunch menu The 111CnU has five appetizers three soups seven entrees six vegetables and four desserts How

)1_( many different meals consisting of either an appetizer or a soup one entree one vegetable and one dessert can Debbie order

16

Regents Exam Questions by Topic Page 3 PROBABILlTY Multiplication Counting Principle WWWJm3porg Name

When the Slnith family decided to have their new house built they found that there were 60 different choices involving location style~ and color If they had their choice of 2 locations and 5 styles how nlany choices of color did they hmw

(I) 6 (3) 50 (2) 12 (4) 53

I 7 When Kimberly bought her new car she found that there were 72 different ways her car could be equipped Her choices included tour choices of engine and three choices of transmission If her only other choice vas color how 1113n1 choices of color did she have (1) 6 (3) 60 (2) 12 (4) 65

Regents Exam QUtslions by Topic Page 1 POVERS Operations with Powers WWjlllilporg Name

The expression 3~ middot3gt 31 is equivalent to

(1) 27deg (3) 39

(2) 27~~ (4) 324

2 The expression 2 3 4 2 is equivalent to

(1) 2 (3) 85

(2) i~ (4) 86

3 The expression (xz 3)( xy2Z) is equivalent to

( 1) tV ~ (3) x 3y3z4

(2) ty ~ (4) X 4Y2

4 The product of 2x 3 and 6x 5 is

(1) lOx s (3) lOx s

(2) 12x 8 (4) 12x l5

5 The product of 3x 2y and _4xy 3 is

(1) -12x~ymiddotl (3) _12x 2y l IImiddot l

(2) 12xy4 (4) 12x 2y 3

6 The product of 3x 5 and 2x 4 is (l)5 x J (3)6x9

I Ii

(2) 5x o (4) 6X 2ll

7 The product of 4x 2 y and 2xy 3 is

(1)8x 1 y3 (3)8x 3 y4

(2) 8X 3y 3 (4) 8X 2y4

8 What is the product of 1OX 4 ) and 3xy 3

(1) 30x l y~ (3) 30x 5y5

(2) 30X 4 y 6 (4) 30X 5 y 6

9 What is the product of ~X2 y and ~xy3 3 6

)(ii(lmiddotl 1 2 1 3(l) - x V (3) __ XL y 2 18

(2) --1 x y 4 (4) ~x3y4 9 18

Regents Exam Questions by Topic Page 2 POWERS Operations with Powers YWjl11lt1porg Name

10 The expression (6Xi y6)= is equivalent to

(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2

11 The expression (-40 3b) 2 is equivalent to

(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2

12 Which expression is equivalent to (3X 2)3

(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6

13 Expressed in simplest form (3x 3 )(2y)2 (4x 4 ) is equivalent to

(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl

14 What is half of 2 6

(l) I (3) 2 3

(2) 16 (4) 25

IS When -9xs is divided by - 3x 3 x =I- 0 the quotient is

(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8

1 be quotIent of - -5x2

x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8

bull 1 The expressIOn --42 X =t 0 IS eqUlva ent to

x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6

Regents Exam Questions by Topic Page 1 POWERS Operations vith Powers wlllapl1rg Name

18 6

The expression ~x ~ is equivalent to x y

1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V

The expression ~---S-- is equivalent to 2xy

2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x

20 3 5 11) I (2x )(8x ) bull I fi n V 11C 1 expreSSion represents ~---6~ III Simp est Onl1

4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9

2] If 10k = x then 10Jk is equal to

(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx

The product of (Soh) and (-2a 2b)3 is

(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4

23 If x 0 then (x 2~)3 middot1000 is equivalent to

xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0

(b211+1 )324 The expression ---4- is equivalent tobl1b IIT_

(3) h-311

(4) b-111 1 +

I I

Regents Exam Questions by Topic Page] POWERS Exponential Functions wwwJlllaporg Name

On the set of axes belov draw the graph of y == 2 over the interval -1 s x S 3 Will this graph ever intersect the x-axis Justify your ansvver

r

2

A radioactive substance has an initial Inass of 100 grams and its mass halves every 4 years Which expression shows the number of grnms remaining after I years

(1) 100(4) 4 (3) 1OO(~)~ 2

(2) IOO(4f2 (4) ]00(~)41

2

lh

A population of wolves in a county is represented by the equation

P(t) = 80(098) where I is the number of years since 1998 Predict the

number of wolves 1n the population in the year 2008

4

(3) 16 (4) 4

The height [(x) of a bouncing ball after x bounces lS represented by

f(x) = 80(05) How many times higher is the first bounce than the fourth

bounce (1) 8 (2) 2





end of 15 years (1) $2575 (3) $5197 (2) $4375 (4) $39397











(2) v 21000(086)3 (4) v=21OOO(O86)(3)








(2) x L -6x (4)x+3

3

]


(1) 4x 2 - 3y 3

(2) 4x 2 - 3y 2


(3) 4x - 3xy 3

(4) 4x 2y - 3xy



(1) n + 6 (3) n shy 9

(2)n 2 +9 (4)n+9

54

6

Ii





(t) 2(y + 9)(y - 3) (3) (y + 6)(2y - 9) (2) 2(y - 3)(y - 9) (4) (2y + 6)(y - 9)

54 is equivalent to


12 is equivalent to



Name


(1) (x+2)(x-8) (3) (x+4)(x-4)

(2) (x - 2)(x + 8) (4) (x + 8)(x -middot8)


- 5x + 6 (l) x + 3 (3) x - 2

(2) x - 3 (4) x~







(1) xy - 4 (3) x2- 4

(2) xy-8 (4) x 2 +8


)t I ] ( l~ (1) 3(x-3)2

(2) 3(x 2 - 27)

(3) 3(x + 3)(x --shy

(4) (3x + 3)(x shy

3)

9)


(1) 2(x - 5)(x - 5) (3) (x - 5)(x + 5) (2) 2(x - 5)(x + 5) (4) 2x(x - 50)








50--59

60-69

70-79

80--89

90-99

2




40-49

50-59

60-69

70-9

80-89

-- shy - - shy - f--- shy --+-----+---+----+--+--+-+---shy

f---- ~--~-- 1--shy



- - shy - shy -- --f---- shy --+-+---+--1----+-+-+----+---+---+---+---+- f--- shy



-- f--f-- shy - --4----cf-----f--+----f-- --- shy -


(


Page 3




n~tetval(grades)

61-70

71-80

81-90

91-100

shy--~-----~

Tally Frequency [

I R

-f---~-----f--~-~

~ -

j

I ~

---+-----I-----+----+-----+---+--+-~--~_r--~--_+_-_+__+_---+-__+_

f------t-----t----+---+-I----+-----t--+----L_~-~---t---t-~-t--




400~Meter Run

Time (sec)

Frequency

I 500~sO9 510-51_9 H

52_0529 JHfI

530-539 HI

54_0-549 HI



1(--

5




51-100

101-150

151--200

201-250




I -I--+----t----+------+-~--+---+-___+_-+__- --+---+--+---+-----+-----+-----+-------1


-middot+----+--t---+---+---+~+---_+_---+---f-----_+____+_-_f-+__+__----+--cl------+__---~-


---- shy- --+---+---+-+------+---+--- f-shy - -1___- ~-~f___- --1--_+_---+--

I

6




91-100 6

101-110 3

111-120 0

121-130 3

131-140 0

141-150 2

151-160 2


( ( )yshy

7



r ~ A C A ~ 1 ( 1 1 ~ ~ ~ ~ ~ 1 ~ ~ ~ ~~





0-1

2-3

4-5

6-7




(-1

0--3

(-5

(-7


8



-------shy

jf-

5

180--169 170-179 180-189 190-199 200-2(19

Height (em




Age Group Total

20-29 8

20-39 18

20-49 25

20-59 31

20-69 35





71-80 2

81-90 7

91-- 00 10


61-70 2

71-80 0 - shy

81-90 8

91-100 10

(1 ) (3)


shy

71-80 2

81-90 8 e---

91-100 10

Interval Frequency

61-70 2

71-80 ()

81-90 6

91-100 2

(2) (4)



$126000 1

$140000 2

$180000 1

$400000 ) L

$819000 1




Value per House

NlImber~ of Houses

-

$ 100 coo

$ 175COI)

$2()O()0

middot1700COO

1 -

c ~I

4 -~

1




71-80 10 61-70 7 51-60 2

41-50 )

)

31-40 1



$cl)rts Ftquncy

(X

25

(

3

20 2

11

10 4

(]) 11 (3) 15 (2) 145 (4) 16

Cc




Class Size

Frequency

8 1

10 3

14 2





1(l) -- (3) ~

2 8

(2) ~ (4) ~ 4 16


30in

10 in[

L~2



Page 2



i

2




y y


4



1 J


--------------------------------shy


(Jt





y y

~Jbull - 16

f

E-

~ 14 1411 1_1

~-=~ 1 - 12 ~ shy H ~ I-

6 (f)4 4

((j

C (I

J1

~lmiddot r

Distance (miles)

(1) 1

-1S Hmiddot c

G3 14 u 14 VI 0)

12 12 ~ c 11) ~ 11)cc ce r- 8 I- 3


C 2 lt- -(I I)


) (7--gtshy

7





y 2ro

122200shy

~ (0 1T~

1~O0 V 1)~

1(leiCf) 0 I ~)

U ~U

25- -)~



1 ( 3 ) j y

250shy225-shy

0 2(I(Jshy

~ 175shy( 1~U-


U shy)L-_J shy



( 2 ) 4 )


on this line (1) (63) (3) (-3-3) (2)(76) (4)(-63)





Yearly Total Cost

3-10-

3210

SinO

lj) 0 1(1 lt)

U S 120-E~

(I)

g $(10shy

$60

$J(J

(I

0




(1)(14) (3)(38) (2) (16) (4) (2 cS)



-lt-- - - - - - ~ - -c - - -~ - -

~



(1) ylt3 (3) yS 3

(2) y gt 3 (4) 123

5

6



~- t ~

- - )

--

-----+c- shy

)

-- bull

1 (1) y lt 2x +] (3) y lt --x +- 1

2

1(2) y lt -2x + 1 (4) ylt--x+l

2


j (I~~--l y

3 J

(1) ygt-x+2 (3) yzmiddot-x+22 2 3 3

(2) ylt-x+2 (4) yS--x+2 2 2

---- --- - --- ----

2




(1) (I i) (3) (L~)

(2) (~3) (4) (2~) 2






bullbull( f 1 (1) 04) (3) (71) (2)(28) (4)(-57)


( J)

6



I optional]



I optional]

8




r-----~-------c-------------------------

----- -middot1

- -jshy

2







lV

1middot1

12

~I---

2middot

01 2 J 5 6





y

o

)

l j

3

4




11

60t---shy

55

50 -r -+---+-------+----lr--j

I ---+-+---t---j

35shy ~ g 30 - I

----

_j


Time (sec)





I ~-+-+-+-1f-+-+--l-+--i-t--+-+--I-I-t--+--+-+-I

10 15 20


5











jet



y

E 12 2gt OJ

c 8

4

-

4 to

10




y=3x) +6x--l bull 1~~ I - It ~

(1 ) (L8) (3) (-38) (2) (-1-4) (4) (344)


y = 2x 2 +8x+9

(1) (233) (3) (-2-15) (2) (217) (4) (-21)


















3((








I 1--- r--- l----r-i-TshyI I

~ --f------shy

I

--f-- shy

-- shy

- shy

- shy

- shy - shy

-- shy

f--- shy -shy

f- shy -

r- shy --

LtJ

19




i I I


I Iii-- r-- j--i --- - 1- - -----_I__-----_~------





21






I C( (



(1) -15xy3-3x 3y 2 (3) -15x 2J)-3x 2y

(7) -15xy3 - 3x 3y (4) -15x v3 + xv


(1) 6- - 151 (3) 61 2 - 151 bull l )~

(2) 6r -5 (4) 62 -15


(l) c2 + 3c - 40 (J) c 1

+ 13c - 40

(2) c2 - 3c - 40 (4) c2

- 40


(1) X 2

- 36 (3) X 2 - 12x + 36

(2) x 2 + 36 (4) X2 -+ 12x + 36


(1) 0 4 +- b4 (3) a~ + 2a l b2 + b4

4 l b2 4 + b4(2) 0 + a + b4 (4) 0 + 4b 2


(1) -2x (3) x-+2 (2) 2x (4) x - 2


(1) 3x 2 + 2x (3) 4x 2 + 2x

(2) 3x 2 +2x+l (4) 4x 2 -+-2x+]


(l) 5x 2 - 6x + 1 (3) 5x 2

- 60x 2 + 1Ox ((--_li

(2) 5x 3 - 6x 2 + x (4) 5x 2

- 6x

1( -)( ~x



4x l) 4x(1) --- () ---- shy

3( x + 1)

4x 2

(2) --- (4) 4(x~22 l

J J


x + I 3y - 3 (1) x (3) x + 3

x(2) -- (4) ~+~ )

J J


x+3


4c +x x+4




x 2 +1x-15 2x- 6


x 2 + 2x (1)x (3) - shy

2(x + 5)

x(2)x+5 (4)-shy

x+5

6 2 2

f f 3x -27 d ) x -7x+12




(II)1I X + ] 3x - 15 2x - 8x-l0

8



x-4 --- ----- ------ -- shy

x- -)X _ - x - i 2 Xl - 3x -r 1G



(2) 7e3 (4) 7 ~


(2) 8-6-5 (4)19C


(1) 5-3-4 (3)12 C 3

(2) 5 + 3 +4 (4) 12 P3



(1)90 (3) uC

(2)72 (4) uP


I111 (1)9 (3)24

(2) 12 (4)29








(2) 25 (4) 75










16



(I) 6 (3) 50 (2) 12 (4) 53




(1) 27deg (3) 39

(2) 27~~ (4) 324


(1) 2 (3) 85

(2) i~ (4) 86


( 1) tV ~ (3) x 3y3z4

(2) ty ~ (4) X 4Y2


(1) lOx s (3) lOx s

(2) 12x 8 (4) 12x l5



(2) 12xy4 (4) 12x 2y 3


I Ii

(2) 5x o (4) 6X 2ll


(1)8x 1 y3 (3)8x 3 y4

(2) 8X 3y 3 (4) 8X 2y4


(1) 30x l y~ (3) 30x 5y5

(2) 30X 4 y 6 (4) 30X 5 y 6



(2) --1 x y 4 (4) ~x3y4 9 18



(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2


(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2


(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6


(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl


(l) I (3) 2 3

(2) 16 (4) 25


(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8


x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8


x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

I I





end of 15 years (1) $2575 (3) $5197 (2) $4375 (4) $39397











(2) v 21000(086)3 (4) v=21OOO(O86)(3)








(2) x L -6x (4)x+3

3

]


(1) 4x 2 - 3y 3

(2) 4x 2 - 3y 2


(3) 4x - 3xy 3

(4) 4x 2y - 3xy



(1) n + 6 (3) n shy 9

(2)n 2 +9 (4)n+9

54

6

Ii





(t) 2(y + 9)(y - 3) (3) (y + 6)(2y - 9) (2) 2(y - 3)(y - 9) (4) (2y + 6)(y - 9)

54 is equivalent to


12 is equivalent to



Name


(1) (x+2)(x-8) (3) (x+4)(x-4)

(2) (x - 2)(x + 8) (4) (x + 8)(x -middot8)


- 5x + 6 (l) x + 3 (3) x - 2

(2) x - 3 (4) x~







(1) xy - 4 (3) x2- 4

(2) xy-8 (4) x 2 +8


)t I ] ( l~ (1) 3(x-3)2

(2) 3(x 2 - 27)

(3) 3(x + 3)(x --shy

(4) (3x + 3)(x shy

3)

9)


(1) 2(x - 5)(x - 5) (3) (x - 5)(x + 5) (2) 2(x - 5)(x + 5) (4) 2x(x - 50)








50--59

60-69

70-79

80--89

90-99

2




40-49

50-59

60-69

70-9

80-89

-- shy - - shy - f--- shy --+-----+---+----+--+--+-+---shy

f---- ~--~-- 1--shy



- - shy - shy -- --f---- shy --+-+---+--1----+-+-+----+---+---+---+---+- f--- shy



-- f--f-- shy - --4----cf-----f--+----f-- --- shy -


(





n~tetval(grades)

61-70

71-80

81-90

91-100

shy--~-----~

Tally Frequency [

I R

-f---~-----f--~-~

~ -

j

I ~

---+-----I-----+----+-----+---+--+-~--~_r--~--_+_-_+__+_---+-__+_

f------t-----t----+---+-I----+-----t--+----L_~-~---t---t-~-t--




400~Meter Run

Time (sec)

Frequency

I 500~sO9 510-51_9 H

52_0529 JHfI

530-539 HI

54_0-549 HI



1(--

5




51-100

101-150

151--200

201-250




I -I--+----t----+------+-~--+---+-___+_-+__- --+---+--+---+-----+-----+-----+-------1


-middot+----+--t---+---+---+~+---_+_---+---f-----_+____+_-_f-+__+__----+--cl------+__---~-


---- shy- --+---+---+-+------+---+--- f-shy - -1___- ~-~f___- --1--_+_---+--

I

6




91-100 6

101-110 3

111-120 0

121-130 3

131-140 0

141-150 2

151-160 2


( ( )yshy

7



r ~ A C A ~ 1 ( 1 1 ~ ~ ~ ~ ~ 1 ~ ~ ~ ~~





0-1

2-3

4-5

6-7




(-1

0--3

(-5

(-7


8



-------shy

jf-

5

180--169 170-179 180-189 190-199 200-2(19

Height (em




Age Group Total

20-29 8

20-39 18

20-49 25

20-59 31

20-69 35





71-80 2

81-90 7

91-- 00 10


61-70 2

71-80 0 - shy

81-90 8

91-100 10

(1 ) (3)


shy

71-80 2

81-90 8 e---

91-100 10

Interval Frequency

61-70 2

71-80 ()

81-90 6

91-100 2

(2) (4)



$126000 1

$140000 2

$180000 1

$400000 ) L

$819000 1




Value per House

NlImber~ of Houses

-

$ 100 coo

$ 175COI)

$2()O()0

middot1700COO

1 -

c ~I

4 -~

1




71-80 10 61-70 7 51-60 2

41-50 )

)

31-40 1



$cl)rts Ftquncy

(X

25

(

3

20 2

11

10 4

(]) 11 (3) 15 (2) 145 (4) 16

Cc




Class Size

Frequency

8 1

10 3

14 2





1(l) -- (3) ~

2 8

(2) ~ (4) ~ 4 16


30in

10 in[

L~2



Page 2



i

2




y y


4



1 J


--------------------------------shy


(Jt





y y

~Jbull - 16

f

E-

~ 14 1411 1_1

~-=~ 1 - 12 ~ shy H ~ I-

6 (f)4 4

((j

C (I

J1

~lmiddot r

Distance (miles)

(1) 1

-1S Hmiddot c

G3 14 u 14 VI 0)

12 12 ~ c 11) ~ 11)cc ce r- 8 I- 3


C 2 lt- -(I I)


) (7--gtshy

7





y 2ro

122200shy

~ (0 1T~

1~O0 V 1)~

1(leiCf) 0 I ~)

U ~U

25- -)~



1 ( 3 ) j y

250shy225-shy

0 2(I(Jshy

~ 175shy( 1~U-


U shy)L-_J shy



( 2 ) 4 )


on this line (1) (63) (3) (-3-3) (2)(76) (4)(-63)





Yearly Total Cost

3-10-

3210

SinO

lj) 0 1(1 lt)

U S 120-E~

(I)

g $(10shy

$60

$J(J

(I

0




(1)(14) (3)(38) (2) (16) (4) (2 cS)



-lt-- - - - - - ~ - -c - - -~ - -

~



(1) ylt3 (3) yS 3

(2) y gt 3 (4) 123

5

6



~- t ~

- - )

--

-----+c- shy

)

-- bull

1 (1) y lt 2x +] (3) y lt --x +- 1

2

1(2) y lt -2x + 1 (4) ylt--x+l

2


j (I~~--l y

3 J

(1) ygt-x+2 (3) yzmiddot-x+22 2 3 3

(2) ylt-x+2 (4) yS--x+2 2 2

---- --- - --- ----

2




(1) (I i) (3) (L~)

(2) (~3) (4) (2~) 2






bullbull( f 1 (1) 04) (3) (71) (2)(28) (4)(-57)


( J)

6



I optional]



I optional]

8




r-----~-------c-------------------------

----- -middot1

- -jshy

2







lV

1middot1

12

~I---

2middot

01 2 J 5 6





y

o

)

l j

3

4




11

60t---shy

55

50 -r -+---+-------+----lr--j

I ---+-+---t---j

35shy ~ g 30 - I

----

_j


Time (sec)





I ~-+-+-+-1f-+-+--l-+--i-t--+-+--I-I-t--+--+-+-I

10 15 20


5











jet



y

E 12 2gt OJ

c 8

4

-

4 to

10




y=3x) +6x--l bull 1~~ I - It ~

(1 ) (L8) (3) (-38) (2) (-1-4) (4) (344)


y = 2x 2 +8x+9

(1) (233) (3) (-2-15) (2) (217) (4) (-21)


















3((








I 1--- r--- l----r-i-TshyI I

~ --f------shy

I

--f-- shy

-- shy

- shy

- shy

- shy - shy

-- shy

f--- shy -shy

f- shy -

r- shy --

LtJ

19




i I I


I Iii-- r-- j--i --- - 1- - -----_I__-----_~------





21






I C( (



(1) -15xy3-3x 3y 2 (3) -15x 2J)-3x 2y

(7) -15xy3 - 3x 3y (4) -15x v3 + xv


(1) 6- - 151 (3) 61 2 - 151 bull l )~

(2) 6r -5 (4) 62 -15


(l) c2 + 3c - 40 (J) c 1

+ 13c - 40

(2) c2 - 3c - 40 (4) c2

- 40


(1) X 2

- 36 (3) X 2 - 12x + 36

(2) x 2 + 36 (4) X2 -+ 12x + 36


(1) 0 4 +- b4 (3) a~ + 2a l b2 + b4

4 l b2 4 + b4(2) 0 + a + b4 (4) 0 + 4b 2


(1) -2x (3) x-+2 (2) 2x (4) x - 2


(1) 3x 2 + 2x (3) 4x 2 + 2x

(2) 3x 2 +2x+l (4) 4x 2 -+-2x+]


(l) 5x 2 - 6x + 1 (3) 5x 2

- 60x 2 + 1Ox ((--_li

(2) 5x 3 - 6x 2 + x (4) 5x 2

- 6x

1( -)( ~x



4x l) 4x(1) --- () ---- shy

3( x + 1)

4x 2

(2) --- (4) 4(x~22 l

J J


x + I 3y - 3 (1) x (3) x + 3

x(2) -- (4) ~+~ )

J J


x+3


4c +x x+4




x 2 +1x-15 2x- 6


x 2 + 2x (1)x (3) - shy

2(x + 5)

x(2)x+5 (4)-shy

x+5

6 2 2

f f 3x -27 d ) x -7x+12




(II)1I X + ] 3x - 15 2x - 8x-l0

8



x-4 --- ----- ------ -- shy

x- -)X _ - x - i 2 Xl - 3x -r 1G



(2) 7e3 (4) 7 ~


(2) 8-6-5 (4)19C


(1) 5-3-4 (3)12 C 3

(2) 5 + 3 +4 (4) 12 P3



(1)90 (3) uC

(2)72 (4) uP


I111 (1)9 (3)24

(2) 12 (4)29








(2) 25 (4) 75










16



(I) 6 (3) 50 (2) 12 (4) 53




(1) 27deg (3) 39

(2) 27~~ (4) 324


(1) 2 (3) 85

(2) i~ (4) 86


( 1) tV ~ (3) x 3y3z4

(2) ty ~ (4) X 4Y2


(1) lOx s (3) lOx s

(2) 12x 8 (4) 12x l5



(2) 12xy4 (4) 12x 2y 3


I Ii

(2) 5x o (4) 6X 2ll


(1)8x 1 y3 (3)8x 3 y4

(2) 8X 3y 3 (4) 8X 2y4


(1) 30x l y~ (3) 30x 5y5

(2) 30X 4 y 6 (4) 30X 5 y 6



(2) --1 x y 4 (4) ~x3y4 9 18



(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2


(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2


(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6


(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl


(l) I (3) 2 3

(2) 16 (4) 25


(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8


x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8


x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

I I




(2) x L -6x (4)x+3

3

]


(1) 4x 2 - 3y 3

(2) 4x 2 - 3y 2


(3) 4x - 3xy 3

(4) 4x 2y - 3xy



(1) n + 6 (3) n shy 9

(2)n 2 +9 (4)n+9

54

6

Ii





(t) 2(y + 9)(y - 3) (3) (y + 6)(2y - 9) (2) 2(y - 3)(y - 9) (4) (2y + 6)(y - 9)

54 is equivalent to


12 is equivalent to



Name


(1) (x+2)(x-8) (3) (x+4)(x-4)

(2) (x - 2)(x + 8) (4) (x + 8)(x -middot8)


- 5x + 6 (l) x + 3 (3) x - 2

(2) x - 3 (4) x~







(1) xy - 4 (3) x2- 4

(2) xy-8 (4) x 2 +8


)t I ] ( l~ (1) 3(x-3)2

(2) 3(x 2 - 27)

(3) 3(x + 3)(x --shy

(4) (3x + 3)(x shy

3)

9)


(1) 2(x - 5)(x - 5) (3) (x - 5)(x + 5) (2) 2(x - 5)(x + 5) (4) 2x(x - 50)








50--59

60-69

70-79

80--89

90-99

2




40-49

50-59

60-69

70-9

80-89

-- shy - - shy - f--- shy --+-----+---+----+--+--+-+---shy

f---- ~--~-- 1--shy



- - shy - shy -- --f---- shy --+-+---+--1----+-+-+----+---+---+---+---+- f--- shy



-- f--f-- shy - --4----cf-----f--+----f-- --- shy -


(


Page 3




n~tetval(grades)

61-70

71-80

81-90

91-100

shy--~-----~

Tally Frequency [

I R

-f---~-----f--~-~

~ -

j

I ~

---+-----I-----+----+-----+---+--+-~--~_r--~--_+_-_+__+_---+-__+_

f------t-----t----+---+-I----+-----t--+----L_~-~---t---t-~-t--


Regents Exom Questiuns by Topic CiRAPHS AND STATISTICS Frequency Histogram~ Bar Graphs and Tables Jlllaporg Name


400~Meter Run

Time (sec)

Frequency

I 500~sO9 510-51_9 H

52_0529 JHfI

530-539 HI

54_0-549 HI



1(--

5




51-100

101-150

151--200

201-250




I -I--+----t----+------+-~--+---+-___+_-+__- --+---+--+---+-----+-----+-----+-------1


-middot+----+--t---+---+---+~+---_+_---+---f-----_+____+_-_f-+__+__----+--cl------+__---~-


---- shy- --+---+---+-+------+---+--- f-shy - -1___- ~-~f___- --1--_+_---+--

I

6




91-100 6

101-110 3

111-120 0

121-130 3

131-140 0

141-150 2

151-160 2


( ( )yshy

7



r ~ A C A ~ 1 ( 1 1 ~ ~ ~ ~ ~ 1 ~ ~ ~ ~~





0-1

2-3

4-5

6-7




(-1

0--3

(-5

(-7


8



-------shy

jf-

5

180--169 170-179 180-189 190-199 200-2(19

Height (em




Age Group Total

20-29 8

20-39 18

20-49 25

20-59 31

20-69 35





71-80 2

81-90 7

91-- 00 10


61-70 2

71-80 0 - shy

81-90 8

91-100 10

(1 ) (3)


shy

71-80 2

81-90 8 e---

91-100 10

Interval Frequency

61-70 2

71-80 ()

81-90 6

91-100 2

(2) (4)



$126000 1

$140000 2

$180000 1

$400000 ) L

$819000 1




Value per House

NlImber~ of Houses

-

$ 100 coo

$ 175COI)

$2()O()0

middot1700COO

1 -

c ~I

4 -~

1




71-80 10 61-70 7 51-60 2

41-50 )

)

31-40 1



$cl)rts Ftquncy

(X

25

(

3

20 2

11

10 4

(]) 11 (3) 15 (2) 145 (4) 16

Cc




Class Size

Frequency

8 1

10 3

14 2





1(l) -- (3) ~

2 8

(2) ~ (4) ~ 4 16


30in

10 in[

L~2



Page 2



i

2




y y


4



1 J


--------------------------------shy


(Jt





y y

~Jbull - 16

f

E-

~ 14 1411 1_1

~-=~ 1 - 12 ~ shy H ~ I-

6 (f)4 4

((j

C (I

J1

~lmiddot r

Distance (miles)

(1) 1

-1S Hmiddot c

G3 14 u 14 VI 0)

12 12 ~ c 11) ~ 11)cc ce r- 8 I- 3


C 2 lt- -(I I)


) (7--gtshy

7





y 2ro

122200shy

~ (0 1T~

1~O0 V 1)~

1(leiCf) 0 I ~)

U ~U

25- -)~



1 ( 3 ) j y

250shy225-shy

0 2(I(Jshy

~ 175shy( 1~U-


U shy)L-_J shy



( 2 ) 4 )


on this line (1) (63) (3) (-3-3) (2)(76) (4)(-63)





Yearly Total Cost

3-10-

3210

SinO

lj) 0 1(1 lt)

U S 120-E~

(I)

g $(10shy

$60

$J(J

(I

0




(1)(14) (3)(38) (2) (16) (4) (2 cS)



-lt-- - - - - - ~ - -c - - -~ - -

~



(1) ylt3 (3) yS 3

(2) y gt 3 (4) 123

5

6



~- t ~

- - )

--

-----+c- shy

)

-- bull

1 (1) y lt 2x +] (3) y lt --x +- 1

2

1(2) y lt -2x + 1 (4) ylt--x+l

2


j (I~~--l y

3 J

(1) ygt-x+2 (3) yzmiddot-x+22 2 3 3

(2) ylt-x+2 (4) yS--x+2 2 2

---- --- - --- ----

2




(1) (I i) (3) (L~)

(2) (~3) (4) (2~) 2






bullbull( f 1 (1) 04) (3) (71) (2)(28) (4)(-57)


( J)

6



I optional]



I optional]

8




r-----~-------c-------------------------

----- -middot1

- -jshy

2







lV

1middot1

12

~I---

2middot

01 2 J 5 6





y

o

)

l j

3

4




11

60t---shy

55

50 -r -+---+-------+----lr--j

I ---+-+---t---j

35shy ~ g 30 - I

----

_j


Time (sec)





I ~-+-+-+-1f-+-+--l-+--i-t--+-+--I-I-t--+--+-+-I

10 15 20


5











jet



y

E 12 2gt OJ

c 8

4

-

4 to

10




y=3x) +6x--l bull 1~~ I - It ~

(1 ) (L8) (3) (-38) (2) (-1-4) (4) (344)


y = 2x 2 +8x+9

(1) (233) (3) (-2-15) (2) (217) (4) (-21)


















3((








I 1--- r--- l----r-i-TshyI I

~ --f------shy

I

--f-- shy

-- shy

- shy

- shy

- shy - shy

-- shy

f--- shy -shy

f- shy -

r- shy --

LtJ

19




i I I


I Iii-- r-- j--i --- - 1- - -----_I__-----_~------





21






I C( (



(1) -15xy3-3x 3y 2 (3) -15x 2J)-3x 2y

(7) -15xy3 - 3x 3y (4) -15x v3 + xv


(1) 6- - 151 (3) 61 2 - 151 bull l )~

(2) 6r -5 (4) 62 -15


(l) c2 + 3c - 40 (J) c 1

+ 13c - 40

(2) c2 - 3c - 40 (4) c2

- 40


(1) X 2

- 36 (3) X 2 - 12x + 36

(2) x 2 + 36 (4) X2 -+ 12x + 36


(1) 0 4 +- b4 (3) a~ + 2a l b2 + b4

4 l b2 4 + b4(2) 0 + a + b4 (4) 0 + 4b 2


(1) -2x (3) x-+2 (2) 2x (4) x - 2


(1) 3x 2 + 2x (3) 4x 2 + 2x

(2) 3x 2 +2x+l (4) 4x 2 -+-2x+]


(l) 5x 2 - 6x + 1 (3) 5x 2

- 60x 2 + 1Ox ((--_li

(2) 5x 3 - 6x 2 + x (4) 5x 2

- 6x

1( -)( ~x



4x l) 4x(1) --- () ---- shy

3( x + 1)

4x 2

(2) --- (4) 4(x~22 l

J J


x + I 3y - 3 (1) x (3) x + 3

x(2) -- (4) ~+~ )

J J


x+3


4c +x x+4




x 2 +1x-15 2x- 6


x 2 + 2x (1)x (3) - shy

2(x + 5)

x(2)x+5 (4)-shy

x+5

6 2 2

f f 3x -27 d ) x -7x+12




(II)1I X + ] 3x - 15 2x - 8x-l0

8



x-4 --- ----- ------ -- shy

x- -)X _ - x - i 2 Xl - 3x -r 1G



(2) 7e3 (4) 7 ~


(2) 8-6-5 (4)19C


(1) 5-3-4 (3)12 C 3

(2) 5 + 3 +4 (4) 12 P3



(1)90 (3) uC

(2)72 (4) uP


I111 (1)9 (3)24

(2) 12 (4)29








(2) 25 (4) 75










16



(I) 6 (3) 50 (2) 12 (4) 53




(1) 27deg (3) 39

(2) 27~~ (4) 324


(1) 2 (3) 85

(2) i~ (4) 86


( 1) tV ~ (3) x 3y3z4

(2) ty ~ (4) X 4Y2


(1) lOx s (3) lOx s

(2) 12x 8 (4) 12x l5



(2) 12xy4 (4) 12x 2y 3


I Ii

(2) 5x o (4) 6X 2ll


(1)8x 1 y3 (3)8x 3 y4

(2) 8X 3y 3 (4) 8X 2y4


(1) 30x l y~ (3) 30x 5y5

(2) 30X 4 y 6 (4) 30X 5 y 6



(2) --1 x y 4 (4) ~x3y4 9 18



(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2


(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2


(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6


(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl


(l) I (3) 2 3

(2) 16 (4) 25


(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8


x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8


x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

I I


Name


(1) (x+2)(x-8) (3) (x+4)(x-4)

(2) (x - 2)(x + 8) (4) (x + 8)(x -middot8)


- 5x + 6 (l) x + 3 (3) x - 2

(2) x - 3 (4) x~







(1) xy - 4 (3) x2- 4

(2) xy-8 (4) x 2 +8


)t I ] ( l~ (1) 3(x-3)2

(2) 3(x 2 - 27)

(3) 3(x + 3)(x --shy

(4) (3x + 3)(x shy

3)

9)


(1) 2(x - 5)(x - 5) (3) (x - 5)(x + 5) (2) 2(x - 5)(x + 5) (4) 2x(x - 50)








50--59

60-69

70-79

80--89

90-99

2




40-49

50-59

60-69

70-9

80-89

-- shy - - shy - f--- shy --+-----+---+----+--+--+-+---shy

f---- ~--~-- 1--shy



- - shy - shy -- --f---- shy --+-+---+--1----+-+-+----+---+---+---+---+- f--- shy



-- f--f-- shy - --4----cf-----f--+----f-- --- shy -


(


Page 3




n~tetval(grades)

61-70

71-80

81-90

91-100

shy--~-----~

Tally Frequency [

I R

-f---~-----f--~-~

~ -

j

I ~

---+-----I-----+----+-----+---+--+-~--~_r--~--_+_-_+__+_---+-__+_

f------t-----t----+---+-I----+-----t--+----L_~-~---t---t-~-t--




400~Meter Run

Time (sec)

Frequency

I 500~sO9 510-51_9 H

52_0529 JHfI

530-539 HI

54_0-549 HI



1(--

5

Regents Exam Questions by Topic GRAPHS AND STA TISTICS Frequency Histograms Bar Graphs and Tables WWJJl1i1porg Name



51-100

101-150

151--200

201-250




I -I--+----t----+------+-~--+---+-___+_-+__- --+---+--+---+-----+-----+-----+-------1


-middot+----+--t---+---+---+~+---_+_---+---f-----_+____+_-_f-+__+__----+--cl------+__---~-


---- shy- --+---+---+-+------+---+--- f-shy - -1___- ~-~f___- --1--_+_---+--

I

6




91-100 6

101-110 3

111-120 0

121-130 3

131-140 0

141-150 2

151-160 2


( ( )yshy

7



r ~ A C A ~ 1 ( 1 1 ~ ~ ~ ~ ~ 1 ~ ~ ~ ~~





0-1

2-3

4-5

6-7




(-1

0--3

(-5

(-7


8



-------shy

jf-

5

180--169 170-179 180-189 190-199 200-2(19

Height (em




Age Group Total

20-29 8

20-39 18

20-49 25

20-59 31

20-69 35





71-80 2

81-90 7

91-- 00 10


61-70 2

71-80 0 - shy

81-90 8

91-100 10

(1 ) (3)


shy

71-80 2

81-90 8 e---

91-100 10

Interval Frequency

61-70 2

71-80 ()

81-90 6

91-100 2

(2) (4)



$126000 1

$140000 2

$180000 1

$400000 ) L

$819000 1




Value per House

NlImber~ of Houses

-

$ 100 coo

$ 175COI)

$2()O()0

middot1700COO

1 -

c ~I

4 -~

1




71-80 10 61-70 7 51-60 2

41-50 )

)

31-40 1



$cl)rts Ftquncy

(X

25

(

3

20 2

11

10 4

(]) 11 (3) 15 (2) 145 (4) 16

Cc




Class Size

Frequency

8 1

10 3

14 2





1(l) -- (3) ~

2 8

(2) ~ (4) ~ 4 16


30in

10 in[

L~2



Page 2



i

2




y y


4



1 J


--------------------------------shy


(Jt





y y

~Jbull - 16

f

E-

~ 14 1411 1_1

~-=~ 1 - 12 ~ shy H ~ I-

6 (f)4 4

((j

C (I

J1

~lmiddot r

Distance (miles)

(1) 1

-1S Hmiddot c

G3 14 u 14 VI 0)

12 12 ~ c 11) ~ 11)cc ce r- 8 I- 3


C 2 lt- -(I I)


) (7--gtshy

7





y 2ro

122200shy

~ (0 1T~

1~O0 V 1)~

1(leiCf) 0 I ~)

U ~U

25- -)~



1 ( 3 ) j y

250shy225-shy

0 2(I(Jshy

~ 175shy( 1~U-


U shy)L-_J shy



( 2 ) 4 )


on this line (1) (63) (3) (-3-3) (2)(76) (4)(-63)





Yearly Total Cost

3-10-

3210

SinO

lj) 0 1(1 lt)

U S 120-E~

(I)

g $(10shy

$60

$J(J

(I

0




(1)(14) (3)(38) (2) (16) (4) (2 cS)



-lt-- - - - - - ~ - -c - - -~ - -

~



(1) ylt3 (3) yS 3

(2) y gt 3 (4) 123

5

6



~- t ~

- - )

--

-----+c- shy

)

-- bull

1 (1) y lt 2x +] (3) y lt --x +- 1

2

1(2) y lt -2x + 1 (4) ylt--x+l

2


j (I~~--l y

3 J

(1) ygt-x+2 (3) yzmiddot-x+22 2 3 3

(2) ylt-x+2 (4) yS--x+2 2 2

---- --- - --- ----

2




(1) (I i) (3) (L~)

(2) (~3) (4) (2~) 2






bullbull( f 1 (1) 04) (3) (71) (2)(28) (4)(-57)


( J)

6



I optional]



I optional]

8




r-----~-------c-------------------------

----- -middot1

- -jshy

2







lV

1middot1

12

~I---

2middot

01 2 J 5 6





y

o

)

l j

3

4




11

60t---shy

55

50 -r -+---+-------+----lr--j

I ---+-+---t---j

35shy ~ g 30 - I

----

_j


Time (sec)





I ~-+-+-+-1f-+-+--l-+--i-t--+-+--I-I-t--+--+-+-I

10 15 20


5











jet



y

E 12 2gt OJ

c 8

4

-

4 to

10




y=3x) +6x--l bull 1~~ I - It ~

(1 ) (L8) (3) (-38) (2) (-1-4) (4) (344)


y = 2x 2 +8x+9

(1) (233) (3) (-2-15) (2) (217) (4) (-21)


















3((








I 1--- r--- l----r-i-TshyI I

~ --f------shy

I

--f-- shy

-- shy

- shy

- shy

- shy - shy

-- shy

f--- shy -shy

f- shy -

r- shy --

LtJ

19




i I I


I Iii-- r-- j--i --- - 1- - -----_I__-----_~------





21






I C( (



(1) -15xy3-3x 3y 2 (3) -15x 2J)-3x 2y

(7) -15xy3 - 3x 3y (4) -15x v3 + xv


(1) 6- - 151 (3) 61 2 - 151 bull l )~

(2) 6r -5 (4) 62 -15


(l) c2 + 3c - 40 (J) c 1

+ 13c - 40

(2) c2 - 3c - 40 (4) c2

- 40


(1) X 2

- 36 (3) X 2 - 12x + 36

(2) x 2 + 36 (4) X2 -+ 12x + 36


(1) 0 4 +- b4 (3) a~ + 2a l b2 + b4

4 l b2 4 + b4(2) 0 + a + b4 (4) 0 + 4b 2


(1) -2x (3) x-+2 (2) 2x (4) x - 2


(1) 3x 2 + 2x (3) 4x 2 + 2x

(2) 3x 2 +2x+l (4) 4x 2 -+-2x+]


(l) 5x 2 - 6x + 1 (3) 5x 2

- 60x 2 + 1Ox ((--_li

(2) 5x 3 - 6x 2 + x (4) 5x 2

- 6x

1( -)( ~x



4x l) 4x(1) --- () ---- shy

3( x + 1)

4x 2

(2) --- (4) 4(x~22 l

J J


x + I 3y - 3 (1) x (3) x + 3

x(2) -- (4) ~+~ )

J J


x+3


4c +x x+4




x 2 +1x-15 2x- 6


x 2 + 2x (1)x (3) - shy

2(x + 5)

x(2)x+5 (4)-shy

x+5

6 2 2

f f 3x -27 d ) x -7x+12




(II)1I X + ] 3x - 15 2x - 8x-l0

8



x-4 --- ----- ------ -- shy

x- -)X _ - x - i 2 Xl - 3x -r 1G



(2) 7e3 (4) 7 ~


(2) 8-6-5 (4)19C


(1) 5-3-4 (3)12 C 3

(2) 5 + 3 +4 (4) 12 P3



(1)90 (3) uC

(2)72 (4) uP


I111 (1)9 (3)24

(2) 12 (4)29








(2) 25 (4) 75










16



(I) 6 (3) 50 (2) 12 (4) 53




(1) 27deg (3) 39

(2) 27~~ (4) 324


(1) 2 (3) 85

(2) i~ (4) 86


( 1) tV ~ (3) x 3y3z4

(2) ty ~ (4) X 4Y2


(1) lOx s (3) lOx s

(2) 12x 8 (4) 12x l5



(2) 12xy4 (4) 12x 2y 3


I Ii

(2) 5x o (4) 6X 2ll


(1)8x 1 y3 (3)8x 3 y4

(2) 8X 3y 3 (4) 8X 2y4


(1) 30x l y~ (3) 30x 5y5

(2) 30X 4 y 6 (4) 30X 5 y 6



(2) --1 x y 4 (4) ~x3y4 9 18



(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2


(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2


(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6


(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl


(l) I (3) 2 3

(2) 16 (4) 25


(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8


x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8


x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

I I






50--59

60-69

70-79

80--89

90-99

2




40-49

50-59

60-69

70-9

80-89

-- shy - - shy - f--- shy --+-----+---+----+--+--+-+---shy

f---- ~--~-- 1--shy



- - shy - shy -- --f---- shy --+-+---+--1----+-+-+----+---+---+---+---+- f--- shy



-- f--f-- shy - --4----cf-----f--+----f-- --- shy -


(


Page 3




n~tetval(grades)

61-70

71-80

81-90

91-100

shy--~-----~

Tally Frequency [

I R

-f---~-----f--~-~

~ -

j

I ~

---+-----I-----+----+-----+---+--+-~--~_r--~--_+_-_+__+_---+-__+_

f------t-----t----+---+-I----+-----t--+----L_~-~---t---t-~-t--




400~Meter Run

Time (sec)

Frequency

I 500~sO9 510-51_9 H

52_0529 JHfI

530-539 HI

54_0-549 HI



1(--

5




51-100

101-150

151--200

201-250




I -I--+----t----+------+-~--+---+-___+_-+__- --+---+--+---+-----+-----+-----+-------1


-middot+----+--t---+---+---+~+---_+_---+---f-----_+____+_-_f-+__+__----+--cl------+__---~-


---- shy- --+---+---+-+------+---+--- f-shy - -1___- ~-~f___- --1--_+_---+--

I

6

Regents Exam Questions by Topic GRAPHS AND STAT1STICS Frequency Histograms Rr Graphs and Tables ww llllap_L)rg Name



91-100 6

101-110 3

111-120 0

121-130 3

131-140 0

141-150 2

151-160 2


( ( )yshy

7



r ~ A C A ~ 1 ( 1 1 ~ ~ ~ ~ ~ 1 ~ ~ ~ ~~





0-1

2-3

4-5

6-7




(-1

0--3

(-5

(-7


8



-------shy

jf-

5

180--169 170-179 180-189 190-199 200-2(19

Height (em




Age Group Total

20-29 8

20-39 18

20-49 25

20-59 31

20-69 35





71-80 2

81-90 7

91-- 00 10


61-70 2

71-80 0 - shy

81-90 8

91-100 10

(1 ) (3)


shy

71-80 2

81-90 8 e---

91-100 10

Interval Frequency

61-70 2

71-80 ()

81-90 6

91-100 2

(2) (4)



$126000 1

$140000 2

$180000 1

$400000 ) L

$819000 1




Value per House

NlImber~ of Houses

-

$ 100 coo

$ 175COI)

$2()O()0

middot1700COO

1 -

c ~I

4 -~

1




71-80 10 61-70 7 51-60 2

41-50 )

)

31-40 1



$cl)rts Ftquncy

(X

25

(

3

20 2

11

10 4

(]) 11 (3) 15 (2) 145 (4) 16

Cc




Class Size

Frequency

8 1

10 3

14 2





1(l) -- (3) ~

2 8

(2) ~ (4) ~ 4 16


30in

10 in[

L~2



Page 2



i

2




y y


4



1 J


--------------------------------shy


(Jt





y y

~Jbull - 16

f

E-

~ 14 1411 1_1

~-=~ 1 - 12 ~ shy H ~ I-

6 (f)4 4

((j

C (I

J1

~lmiddot r

Distance (miles)

(1) 1

-1S Hmiddot c

G3 14 u 14 VI 0)

12 12 ~ c 11) ~ 11)cc ce r- 8 I- 3


C 2 lt- -(I I)


) (7--gtshy

7





y 2ro

122200shy

~ (0 1T~

1~O0 V 1)~

1(leiCf) 0 I ~)

U ~U

25- -)~



1 ( 3 ) j y

250shy225-shy

0 2(I(Jshy

~ 175shy( 1~U-


U shy)L-_J shy



( 2 ) 4 )


on this line (1) (63) (3) (-3-3) (2)(76) (4)(-63)





Yearly Total Cost

3-10-

3210

SinO

lj) 0 1(1 lt)

U S 120-E~

(I)

g $(10shy

$60

$J(J

(I

0




(1)(14) (3)(38) (2) (16) (4) (2 cS)



-lt-- - - - - - ~ - -c - - -~ - -

~



(1) ylt3 (3) yS 3

(2) y gt 3 (4) 123

5

6



~- t ~

- - )

--

-----+c- shy

)

-- bull

1 (1) y lt 2x +] (3) y lt --x +- 1

2

1(2) y lt -2x + 1 (4) ylt--x+l

2


j (I~~--l y

3 J

(1) ygt-x+2 (3) yzmiddot-x+22 2 3 3

(2) ylt-x+2 (4) yS--x+2 2 2

---- --- - --- ----

2




(1) (I i) (3) (L~)

(2) (~3) (4) (2~) 2






bullbull( f 1 (1) 04) (3) (71) (2)(28) (4)(-57)


( J)

6



I optional]



I optional]

8




r-----~-------c-------------------------

----- -middot1

- -jshy

2







lV

1middot1

12

~I---

2middot

01 2 J 5 6





y

o

)

l j

3

4




11

60t---shy

55

50 -r -+---+-------+----lr--j

I ---+-+---t---j

35shy ~ g 30 - I

----

_j


Time (sec)





I ~-+-+-+-1f-+-+--l-+--i-t--+-+--I-I-t--+--+-+-I

10 15 20


5











jet



y

E 12 2gt OJ

c 8

4

-

4 to

10




y=3x) +6x--l bull 1~~ I - It ~

(1 ) (L8) (3) (-38) (2) (-1-4) (4) (344)


y = 2x 2 +8x+9

(1) (233) (3) (-2-15) (2) (217) (4) (-21)


















3((








I 1--- r--- l----r-i-TshyI I

~ --f------shy

I

--f-- shy

-- shy

- shy

- shy

- shy - shy

-- shy

f--- shy -shy

f- shy -

r- shy --

LtJ

19




i I I


I Iii-- r-- j--i --- - 1- - -----_I__-----_~------





21






I C( (



(1) -15xy3-3x 3y 2 (3) -15x 2J)-3x 2y

(7) -15xy3 - 3x 3y (4) -15x v3 + xv


(1) 6- - 151 (3) 61 2 - 151 bull l )~

(2) 6r -5 (4) 62 -15


(l) c2 + 3c - 40 (J) c 1

+ 13c - 40

(2) c2 - 3c - 40 (4) c2

- 40


(1) X 2

- 36 (3) X 2 - 12x + 36

(2) x 2 + 36 (4) X2 -+ 12x + 36


(1) 0 4 +- b4 (3) a~ + 2a l b2 + b4

4 l b2 4 + b4(2) 0 + a + b4 (4) 0 + 4b 2


(1) -2x (3) x-+2 (2) 2x (4) x - 2


(1) 3x 2 + 2x (3) 4x 2 + 2x

(2) 3x 2 +2x+l (4) 4x 2 -+-2x+]


(l) 5x 2 - 6x + 1 (3) 5x 2

- 60x 2 + 1Ox ((--_li

(2) 5x 3 - 6x 2 + x (4) 5x 2

- 6x

1( -)( ~x



4x l) 4x(1) --- () ---- shy

3( x + 1)

4x 2

(2) --- (4) 4(x~22 l

J J


x + I 3y - 3 (1) x (3) x + 3

x(2) -- (4) ~+~ )

J J


x+3


4c +x x+4




x 2 +1x-15 2x- 6


x 2 + 2x (1)x (3) - shy

2(x + 5)

x(2)x+5 (4)-shy

x+5

6 2 2

f f 3x -27 d ) x -7x+12




(II)1I X + ] 3x - 15 2x - 8x-l0

8



x-4 --- ----- ------ -- shy

x- -)X _ - x - i 2 Xl - 3x -r 1G



(2) 7e3 (4) 7 ~


(2) 8-6-5 (4)19C


(1) 5-3-4 (3)12 C 3

(2) 5 + 3 +4 (4) 12 P3



(1)90 (3) uC

(2)72 (4) uP


I111 (1)9 (3)24

(2) 12 (4)29








(2) 25 (4) 75










16



(I) 6 (3) 50 (2) 12 (4) 53




(1) 27deg (3) 39

(2) 27~~ (4) 324


(1) 2 (3) 85

(2) i~ (4) 86


( 1) tV ~ (3) x 3y3z4

(2) ty ~ (4) X 4Y2


(1) lOx s (3) lOx s

(2) 12x 8 (4) 12x l5



(2) 12xy4 (4) 12x 2y 3


I Ii

(2) 5x o (4) 6X 2ll


(1)8x 1 y3 (3)8x 3 y4

(2) 8X 3y 3 (4) 8X 2y4


(1) 30x l y~ (3) 30x 5y5

(2) 30X 4 y 6 (4) 30X 5 y 6



(2) --1 x y 4 (4) ~x3y4 9 18



(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2


(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2


(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6


(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl


(l) I (3) 2 3

(2) 16 (4) 25


(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8


x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8


x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

I I

2




40-49

50-59

60-69

70-9

80-89

-- shy - - shy - f--- shy --+-----+---+----+--+--+-+---shy

f---- ~--~-- 1--shy



- - shy - shy -- --f---- shy --+-+---+--1----+-+-+----+---+---+---+---+- f--- shy



-- f--f-- shy - --4----cf-----f--+----f-- --- shy -


(


Page 3




n~tetval(grades)

61-70

71-80

81-90

91-100

shy--~-----~

Tally Frequency [

I R

-f---~-----f--~-~

~ -

j

I ~

---+-----I-----+----+-----+---+--+-~--~_r--~--_+_-_+__+_---+-__+_

f------t-----t----+---+-I----+-----t--+----L_~-~---t---t-~-t--




400~Meter Run

Time (sec)

Frequency

I 500~sO9 510-51_9 H

52_0529 JHfI

530-539 HI

54_0-549 HI



1(--

5




51-100

101-150

151--200

201-250




I -I--+----t----+------+-~--+---+-___+_-+__- --+---+--+---+-----+-----+-----+-------1


-middot+----+--t---+---+---+~+---_+_---+---f-----_+____+_-_f-+__+__----+--cl------+__---~-


---- shy- --+---+---+-+------+---+--- f-shy - -1___- ~-~f___- --1--_+_---+--

I

6




91-100 6

101-110 3

111-120 0

121-130 3

131-140 0

141-150 2

151-160 2


( ( )yshy

7

Regents Exam Questions by Topic GRAPHS AND STATISTICS Frequency I IiSlOgrams Bar Graphs and Tables WPllilP org Name


r ~ A C A ~ 1 ( 1 1 ~ ~ ~ ~ ~ 1 ~ ~ ~ ~~





0-1

2-3

4-5

6-7




(-1

0--3

(-5

(-7


8



-------shy

jf-

5

180--169 170-179 180-189 190-199 200-2(19

Height (em




Age Group Total

20-29 8

20-39 18

20-49 25

20-59 31

20-69 35





71-80 2

81-90 7

91-- 00 10


61-70 2

71-80 0 - shy

81-90 8

91-100 10

(1 ) (3)


shy

71-80 2

81-90 8 e---

91-100 10

Interval Frequency

61-70 2

71-80 ()

81-90 6

91-100 2

(2) (4)



$126000 1

$140000 2

$180000 1

$400000 ) L

$819000 1




Value per House

NlImber~ of Houses

-

$ 100 coo

$ 175COI)

$2()O()0

middot1700COO

1 -

c ~I

4 -~

1




71-80 10 61-70 7 51-60 2

41-50 )

)

31-40 1



$cl)rts Ftquncy

(X

25

(

3

20 2

11

10 4

(]) 11 (3) 15 (2) 145 (4) 16

Cc




Class Size

Frequency

8 1

10 3

14 2





1(l) -- (3) ~

2 8

(2) ~ (4) ~ 4 16


30in

10 in[

L~2



Page 2



i

2




y y


4



1 J


--------------------------------shy


(Jt





y y

~Jbull - 16

f

E-

~ 14 1411 1_1

~-=~ 1 - 12 ~ shy H ~ I-

6 (f)4 4

((j

C (I

J1

~lmiddot r

Distance (miles)

(1) 1

-1S Hmiddot c

G3 14 u 14 VI 0)

12 12 ~ c 11) ~ 11)cc ce r- 8 I- 3


C 2 lt- -(I I)


) (7--gtshy

7





y 2ro

122200shy

~ (0 1T~

1~O0 V 1)~

1(leiCf) 0 I ~)

U ~U

25- -)~



1 ( 3 ) j y

250shy225-shy

0 2(I(Jshy

~ 175shy( 1~U-


U shy)L-_J shy



( 2 ) 4 )


on this line (1) (63) (3) (-3-3) (2)(76) (4)(-63)





Yearly Total Cost

3-10-

3210

SinO

lj) 0 1(1 lt)

U S 120-E~

(I)

g $(10shy

$60

$J(J

(I

0




(1)(14) (3)(38) (2) (16) (4) (2 cS)



-lt-- - - - - - ~ - -c - - -~ - -

~



(1) ylt3 (3) yS 3

(2) y gt 3 (4) 123

5

6



~- t ~

- - )

--

-----+c- shy

)

-- bull

1 (1) y lt 2x +] (3) y lt --x +- 1

2

1(2) y lt -2x + 1 (4) ylt--x+l

2


j (I~~--l y

3 J

(1) ygt-x+2 (3) yzmiddot-x+22 2 3 3

(2) ylt-x+2 (4) yS--x+2 2 2

---- --- - --- ----

2




(1) (I i) (3) (L~)

(2) (~3) (4) (2~) 2






bullbull( f 1 (1) 04) (3) (71) (2)(28) (4)(-57)


( J)

6



I optional]



I optional]

8




r-----~-------c-------------------------

----- -middot1

- -jshy

2







lV

1middot1

12

~I---

2middot

01 2 J 5 6





y

o

)

l j

3

4




11

60t---shy

55

50 -r -+---+-------+----lr--j

I ---+-+---t---j

35shy ~ g 30 - I

----

_j


Time (sec)





I ~-+-+-+-1f-+-+--l-+--i-t--+-+--I-I-t--+--+-+-I

10 15 20


5











jet



y

E 12 2gt OJ

c 8

4

-

4 to

10




y=3x) +6x--l bull 1~~ I - It ~

(1 ) (L8) (3) (-38) (2) (-1-4) (4) (344)


y = 2x 2 +8x+9

(1) (233) (3) (-2-15) (2) (217) (4) (-21)


















3((








I 1--- r--- l----r-i-TshyI I

~ --f------shy

I

--f-- shy

-- shy

- shy

- shy

- shy - shy

-- shy

f--- shy -shy

f- shy -

r- shy --

LtJ

19




i I I


I Iii-- r-- j--i --- - 1- - -----_I__-----_~------





21






I C( (



(1) -15xy3-3x 3y 2 (3) -15x 2J)-3x 2y

(7) -15xy3 - 3x 3y (4) -15x v3 + xv


(1) 6- - 151 (3) 61 2 - 151 bull l )~

(2) 6r -5 (4) 62 -15


(l) c2 + 3c - 40 (J) c 1

+ 13c - 40

(2) c2 - 3c - 40 (4) c2

- 40


(1) X 2

- 36 (3) X 2 - 12x + 36

(2) x 2 + 36 (4) X2 -+ 12x + 36


(1) 0 4 +- b4 (3) a~ + 2a l b2 + b4

4 l b2 4 + b4(2) 0 + a + b4 (4) 0 + 4b 2


(1) -2x (3) x-+2 (2) 2x (4) x - 2


(1) 3x 2 + 2x (3) 4x 2 + 2x

(2) 3x 2 +2x+l (4) 4x 2 -+-2x+]


(l) 5x 2 - 6x + 1 (3) 5x 2

- 60x 2 + 1Ox ((--_li

(2) 5x 3 - 6x 2 + x (4) 5x 2

- 6x

1( -)( ~x



4x l) 4x(1) --- () ---- shy

3( x + 1)

4x 2

(2) --- (4) 4(x~22 l

J J


x + I 3y - 3 (1) x (3) x + 3

x(2) -- (4) ~+~ )

J J


x+3


4c +x x+4




x 2 +1x-15 2x- 6


x 2 + 2x (1)x (3) - shy

2(x + 5)

x(2)x+5 (4)-shy

x+5

6 2 2

f f 3x -27 d ) x -7x+12




(II)1I X + ] 3x - 15 2x - 8x-l0

8



x-4 --- ----- ------ -- shy

x- -)X _ - x - i 2 Xl - 3x -r 1G



(2) 7e3 (4) 7 ~


(2) 8-6-5 (4)19C


(1) 5-3-4 (3)12 C 3

(2) 5 + 3 +4 (4) 12 P3



(1)90 (3) uC

(2)72 (4) uP


I111 (1)9 (3)24

(2) 12 (4)29








(2) 25 (4) 75










16



(I) 6 (3) 50 (2) 12 (4) 53




(1) 27deg (3) 39

(2) 27~~ (4) 324


(1) 2 (3) 85

(2) i~ (4) 86


( 1) tV ~ (3) x 3y3z4

(2) ty ~ (4) X 4Y2


(1) lOx s (3) lOx s

(2) 12x 8 (4) 12x l5



(2) 12xy4 (4) 12x 2y 3


I Ii

(2) 5x o (4) 6X 2ll


(1)8x 1 y3 (3)8x 3 y4

(2) 8X 3y 3 (4) 8X 2y4


(1) 30x l y~ (3) 30x 5y5

(2) 30X 4 y 6 (4) 30X 5 y 6



(2) --1 x y 4 (4) ~x3y4 9 18



(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2


(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2


(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6


(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl


(l) I (3) 2 3

(2) 16 (4) 25


(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8


x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8


x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

I I


Page 3




n~tetval(grades)

61-70

71-80

81-90

91-100

shy--~-----~

Tally Frequency [

I R

-f---~-----f--~-~

~ -

j

I ~

---+-----I-----+----+-----+---+--+-~--~_r--~--_+_-_+__+_---+-__+_

f------t-----t----+---+-I----+-----t--+----L_~-~---t---t-~-t--




400~Meter Run

Time (sec)

Frequency

I 500~sO9 510-51_9 H

52_0529 JHfI

530-539 HI

54_0-549 HI



1(--

5




51-100

101-150

151--200

201-250




I -I--+----t----+------+-~--+---+-___+_-+__- --+---+--+---+-----+-----+-----+-------1


-middot+----+--t---+---+---+~+---_+_---+---f-----_+____+_-_f-+__+__----+--cl------+__---~-


---- shy- --+---+---+-+------+---+--- f-shy - -1___- ~-~f___- --1--_+_---+--

I

6




91-100 6

101-110 3

111-120 0

121-130 3

131-140 0

141-150 2

151-160 2


( ( )yshy

7



r ~ A C A ~ 1 ( 1 1 ~ ~ ~ ~ ~ 1 ~ ~ ~ ~~





0-1

2-3

4-5

6-7




(-1

0--3

(-5

(-7


8

Regents Exam Questions by Topic CRAPHS AND STATISTICS Frequency Histograms Bar Graphs and Tables ll1ap llrg Name


-------shy

jf-

5

180--169 170-179 180-189 190-199 200-2(19

Height (em




Age Group Total

20-29 8

20-39 18

20-49 25

20-59 31

20-69 35





71-80 2

81-90 7

91-- 00 10


61-70 2

71-80 0 - shy

81-90 8

91-100 10

(1 ) (3)


shy

71-80 2

81-90 8 e---

91-100 10

Interval Frequency

61-70 2

71-80 ()

81-90 6

91-100 2

(2) (4)



$126000 1

$140000 2

$180000 1

$400000 ) L

$819000 1




Value per House

NlImber~ of Houses

-

$ 100 coo

$ 175COI)

$2()O()0

middot1700COO

1 -

c ~I

4 -~

1




71-80 10 61-70 7 51-60 2

41-50 )

)

31-40 1



$cl)rts Ftquncy

(X

25

(

3

20 2

11

10 4

(]) 11 (3) 15 (2) 145 (4) 16

Cc




Class Size

Frequency

8 1

10 3

14 2





1(l) -- (3) ~

2 8

(2) ~ (4) ~ 4 16


30in

10 in[

L~2



Page 2



i

2




y y


4



1 J


--------------------------------shy


(Jt





y y

~Jbull - 16

f

E-

~ 14 1411 1_1

~-=~ 1 - 12 ~ shy H ~ I-

6 (f)4 4

((j

C (I

J1

~lmiddot r

Distance (miles)

(1) 1

-1S Hmiddot c

G3 14 u 14 VI 0)

12 12 ~ c 11) ~ 11)cc ce r- 8 I- 3


C 2 lt- -(I I)


) (7--gtshy

7





y 2ro

122200shy

~ (0 1T~

1~O0 V 1)~

1(leiCf) 0 I ~)

U ~U

25- -)~



1 ( 3 ) j y

250shy225-shy

0 2(I(Jshy

~ 175shy( 1~U-


U shy)L-_J shy



( 2 ) 4 )


on this line (1) (63) (3) (-3-3) (2)(76) (4)(-63)





Yearly Total Cost

3-10-

3210

SinO

lj) 0 1(1 lt)

U S 120-E~

(I)

g $(10shy

$60

$J(J

(I

0




(1)(14) (3)(38) (2) (16) (4) (2 cS)



-lt-- - - - - - ~ - -c - - -~ - -

~



(1) ylt3 (3) yS 3

(2) y gt 3 (4) 123

5

6



~- t ~

- - )

--

-----+c- shy

)

-- bull

1 (1) y lt 2x +] (3) y lt --x +- 1

2

1(2) y lt -2x + 1 (4) ylt--x+l

2


j (I~~--l y

3 J

(1) ygt-x+2 (3) yzmiddot-x+22 2 3 3

(2) ylt-x+2 (4) yS--x+2 2 2

---- --- - --- ----

2




(1) (I i) (3) (L~)

(2) (~3) (4) (2~) 2






bullbull( f 1 (1) 04) (3) (71) (2)(28) (4)(-57)


( J)

6



I optional]



I optional]

8




r-----~-------c-------------------------

----- -middot1

- -jshy

2







lV

1middot1

12

~I---

2middot

01 2 J 5 6





y

o

)

l j

3

4




11

60t---shy

55

50 -r -+---+-------+----lr--j

I ---+-+---t---j

35shy ~ g 30 - I

----

_j


Time (sec)





I ~-+-+-+-1f-+-+--l-+--i-t--+-+--I-I-t--+--+-+-I

10 15 20


5











jet



y

E 12 2gt OJ

c 8

4

-

4 to

10




y=3x) +6x--l bull 1~~ I - It ~

(1 ) (L8) (3) (-38) (2) (-1-4) (4) (344)


y = 2x 2 +8x+9

(1) (233) (3) (-2-15) (2) (217) (4) (-21)


















3((








I 1--- r--- l----r-i-TshyI I

~ --f------shy

I

--f-- shy

-- shy

- shy

- shy

- shy - shy

-- shy

f--- shy -shy

f- shy -

r- shy --

LtJ

19




i I I


I Iii-- r-- j--i --- - 1- - -----_I__-----_~------





21






I C( (



(1) -15xy3-3x 3y 2 (3) -15x 2J)-3x 2y

(7) -15xy3 - 3x 3y (4) -15x v3 + xv


(1) 6- - 151 (3) 61 2 - 151 bull l )~

(2) 6r -5 (4) 62 -15


(l) c2 + 3c - 40 (J) c 1

+ 13c - 40

(2) c2 - 3c - 40 (4) c2

- 40


(1) X 2

- 36 (3) X 2 - 12x + 36

(2) x 2 + 36 (4) X2 -+ 12x + 36


(1) 0 4 +- b4 (3) a~ + 2a l b2 + b4

4 l b2 4 + b4(2) 0 + a + b4 (4) 0 + 4b 2


(1) -2x (3) x-+2 (2) 2x (4) x - 2


(1) 3x 2 + 2x (3) 4x 2 + 2x

(2) 3x 2 +2x+l (4) 4x 2 -+-2x+]


(l) 5x 2 - 6x + 1 (3) 5x 2

- 60x 2 + 1Ox ((--_li

(2) 5x 3 - 6x 2 + x (4) 5x 2

- 6x

1( -)( ~x



4x l) 4x(1) --- () ---- shy

3( x + 1)

4x 2

(2) --- (4) 4(x~22 l

J J


x + I 3y - 3 (1) x (3) x + 3

x(2) -- (4) ~+~ )

J J


x+3


4c +x x+4




x 2 +1x-15 2x- 6


x 2 + 2x (1)x (3) - shy

2(x + 5)

x(2)x+5 (4)-shy

x+5

6 2 2

f f 3x -27 d ) x -7x+12




(II)1I X + ] 3x - 15 2x - 8x-l0

8



x-4 --- ----- ------ -- shy

x- -)X _ - x - i 2 Xl - 3x -r 1G



(2) 7e3 (4) 7 ~


(2) 8-6-5 (4)19C


(1) 5-3-4 (3)12 C 3

(2) 5 + 3 +4 (4) 12 P3



(1)90 (3) uC

(2)72 (4) uP


I111 (1)9 (3)24

(2) 12 (4)29








(2) 25 (4) 75










16



(I) 6 (3) 50 (2) 12 (4) 53




(1) 27deg (3) 39

(2) 27~~ (4) 324


(1) 2 (3) 85

(2) i~ (4) 86


( 1) tV ~ (3) x 3y3z4

(2) ty ~ (4) X 4Y2


(1) lOx s (3) lOx s

(2) 12x 8 (4) 12x l5



(2) 12xy4 (4) 12x 2y 3


I Ii

(2) 5x o (4) 6X 2ll


(1)8x 1 y3 (3)8x 3 y4

(2) 8X 3y 3 (4) 8X 2y4


(1) 30x l y~ (3) 30x 5y5

(2) 30X 4 y 6 (4) 30X 5 y 6



(2) --1 x y 4 (4) ~x3y4 9 18



(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2


(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2


(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6


(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl


(l) I (3) 2 3

(2) 16 (4) 25


(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8


x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8


x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

I I



400~Meter Run

Time (sec)

Frequency

I 500~sO9 510-51_9 H

52_0529 JHfI

530-539 HI

54_0-549 HI



1(--

5




51-100

101-150

151--200

201-250




I -I--+----t----+------+-~--+---+-___+_-+__- --+---+--+---+-----+-----+-----+-------1


-middot+----+--t---+---+---+~+---_+_---+---f-----_+____+_-_f-+__+__----+--cl------+__---~-


---- shy- --+---+---+-+------+---+--- f-shy - -1___- ~-~f___- --1--_+_---+--

I

6




91-100 6

101-110 3

111-120 0

121-130 3

131-140 0

141-150 2

151-160 2


( ( )yshy

7



r ~ A C A ~ 1 ( 1 1 ~ ~ ~ ~ ~ 1 ~ ~ ~ ~~





0-1

2-3

4-5

6-7




(-1

0--3

(-5

(-7


8



-------shy

jf-

5

180--169 170-179 180-189 190-199 200-2(19

Height (em




Age Group Total

20-29 8

20-39 18

20-49 25

20-59 31

20-69 35


Regents Exam Questions hy Topic GRAPHS AND STATISTICS Frequency Histograms Bar Graphs and Tables Jl1laporg Name



71-80 2

81-90 7

91-- 00 10


61-70 2

71-80 0 - shy

81-90 8

91-100 10

(1 ) (3)


shy

71-80 2

81-90 8 e---

91-100 10

Interval Frequency

61-70 2

71-80 ()

81-90 6

91-100 2

(2) (4)



$126000 1

$140000 2

$180000 1

$400000 ) L

$819000 1




Value per House

NlImber~ of Houses

-

$ 100 coo

$ 175COI)

$2()O()0

middot1700COO

1 -

c ~I

4 -~

1




71-80 10 61-70 7 51-60 2

41-50 )

)

31-40 1



$cl)rts Ftquncy

(X

25

(

3

20 2

11

10 4

(]) 11 (3) 15 (2) 145 (4) 16

Cc




Class Size

Frequency

8 1

10 3

14 2





1(l) -- (3) ~

2 8

(2) ~ (4) ~ 4 16


30in

10 in[

L~2



Page 2



i

2




y y


4



1 J


--------------------------------shy


(Jt





y y

~Jbull - 16

f

E-

~ 14 1411 1_1

~-=~ 1 - 12 ~ shy H ~ I-

6 (f)4 4

((j

C (I

J1

~lmiddot r

Distance (miles)

(1) 1

-1S Hmiddot c

G3 14 u 14 VI 0)

12 12 ~ c 11) ~ 11)cc ce r- 8 I- 3


C 2 lt- -(I I)


) (7--gtshy

7





y 2ro

122200shy

~ (0 1T~

1~O0 V 1)~

1(leiCf) 0 I ~)

U ~U

25- -)~



1 ( 3 ) j y

250shy225-shy

0 2(I(Jshy

~ 175shy( 1~U-


U shy)L-_J shy



( 2 ) 4 )


on this line (1) (63) (3) (-3-3) (2)(76) (4)(-63)





Yearly Total Cost

3-10-

3210

SinO

lj) 0 1(1 lt)

U S 120-E~

(I)

g $(10shy

$60

$J(J

(I

0




(1)(14) (3)(38) (2) (16) (4) (2 cS)



-lt-- - - - - - ~ - -c - - -~ - -

~



(1) ylt3 (3) yS 3

(2) y gt 3 (4) 123

5

6



~- t ~

- - )

--

-----+c- shy

)

-- bull

1 (1) y lt 2x +] (3) y lt --x +- 1

2

1(2) y lt -2x + 1 (4) ylt--x+l

2


j (I~~--l y

3 J

(1) ygt-x+2 (3) yzmiddot-x+22 2 3 3

(2) ylt-x+2 (4) yS--x+2 2 2

---- --- - --- ----

2




(1) (I i) (3) (L~)

(2) (~3) (4) (2~) 2






bullbull( f 1 (1) 04) (3) (71) (2)(28) (4)(-57)


( J)

6



I optional]



I optional]

8




r-----~-------c-------------------------

----- -middot1

- -jshy

2







lV

1middot1

12

~I---

2middot

01 2 J 5 6





y

o

)

l j

3

4




11

60t---shy

55

50 -r -+---+-------+----lr--j

I ---+-+---t---j

35shy ~ g 30 - I

----

_j


Time (sec)





I ~-+-+-+-1f-+-+--l-+--i-t--+-+--I-I-t--+--+-+-I

10 15 20


5











jet



y

E 12 2gt OJ

c 8

4

-

4 to

10




y=3x) +6x--l bull 1~~ I - It ~

(1 ) (L8) (3) (-38) (2) (-1-4) (4) (344)


y = 2x 2 +8x+9

(1) (233) (3) (-2-15) (2) (217) (4) (-21)


















3((








I 1--- r--- l----r-i-TshyI I

~ --f------shy

I

--f-- shy

-- shy

- shy

- shy

- shy - shy

-- shy

f--- shy -shy

f- shy -

r- shy --

LtJ

19




i I I


I Iii-- r-- j--i --- - 1- - -----_I__-----_~------





21






I C( (



(1) -15xy3-3x 3y 2 (3) -15x 2J)-3x 2y

(7) -15xy3 - 3x 3y (4) -15x v3 + xv


(1) 6- - 151 (3) 61 2 - 151 bull l )~

(2) 6r -5 (4) 62 -15


(l) c2 + 3c - 40 (J) c 1

+ 13c - 40

(2) c2 - 3c - 40 (4) c2

- 40


(1) X 2

- 36 (3) X 2 - 12x + 36

(2) x 2 + 36 (4) X2 -+ 12x + 36


(1) 0 4 +- b4 (3) a~ + 2a l b2 + b4

4 l b2 4 + b4(2) 0 + a + b4 (4) 0 + 4b 2


(1) -2x (3) x-+2 (2) 2x (4) x - 2


(1) 3x 2 + 2x (3) 4x 2 + 2x

(2) 3x 2 +2x+l (4) 4x 2 -+-2x+]


(l) 5x 2 - 6x + 1 (3) 5x 2

- 60x 2 + 1Ox ((--_li

(2) 5x 3 - 6x 2 + x (4) 5x 2

- 6x

1( -)( ~x



4x l) 4x(1) --- () ---- shy

3( x + 1)

4x 2

(2) --- (4) 4(x~22 l

J J


x + I 3y - 3 (1) x (3) x + 3

x(2) -- (4) ~+~ )

J J


x+3


4c +x x+4




x 2 +1x-15 2x- 6


x 2 + 2x (1)x (3) - shy

2(x + 5)

x(2)x+5 (4)-shy

x+5

6 2 2

f f 3x -27 d ) x -7x+12




(II)1I X + ] 3x - 15 2x - 8x-l0

8



x-4 --- ----- ------ -- shy

x- -)X _ - x - i 2 Xl - 3x -r 1G



(2) 7e3 (4) 7 ~


(2) 8-6-5 (4)19C


(1) 5-3-4 (3)12 C 3

(2) 5 + 3 +4 (4) 12 P3



(1)90 (3) uC

(2)72 (4) uP


I111 (1)9 (3)24

(2) 12 (4)29








(2) 25 (4) 75










16



(I) 6 (3) 50 (2) 12 (4) 53




(1) 27deg (3) 39

(2) 27~~ (4) 324


(1) 2 (3) 85

(2) i~ (4) 86


( 1) tV ~ (3) x 3y3z4

(2) ty ~ (4) X 4Y2


(1) lOx s (3) lOx s

(2) 12x 8 (4) 12x l5



(2) 12xy4 (4) 12x 2y 3


I Ii

(2) 5x o (4) 6X 2ll


(1)8x 1 y3 (3)8x 3 y4

(2) 8X 3y 3 (4) 8X 2y4


(1) 30x l y~ (3) 30x 5y5

(2) 30X 4 y 6 (4) 30X 5 y 6



(2) --1 x y 4 (4) ~x3y4 9 18



(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2


(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2


(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6


(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl


(l) I (3) 2 3

(2) 16 (4) 25


(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8


x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8


x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

I I

5




51-100

101-150

151--200

201-250




I -I--+----t----+------+-~--+---+-___+_-+__- --+---+--+---+-----+-----+-----+-------1


-middot+----+--t---+---+---+~+---_+_---+---f-----_+____+_-_f-+__+__----+--cl------+__---~-


---- shy- --+---+---+-+------+---+--- f-shy - -1___- ~-~f___- --1--_+_---+--

I

6




91-100 6

101-110 3

111-120 0

121-130 3

131-140 0

141-150 2

151-160 2


( ( )yshy

7



r ~ A C A ~ 1 ( 1 1 ~ ~ ~ ~ ~ 1 ~ ~ ~ ~~





0-1

2-3

4-5

6-7




(-1

0--3

(-5

(-7


8



-------shy

jf-

5

180--169 170-179 180-189 190-199 200-2(19

Height (em




Age Group Total

20-29 8

20-39 18

20-49 25

20-59 31

20-69 35





71-80 2

81-90 7

91-- 00 10


61-70 2

71-80 0 - shy

81-90 8

91-100 10

(1 ) (3)


shy

71-80 2

81-90 8 e---

91-100 10

Interval Frequency

61-70 2

71-80 ()

81-90 6

91-100 2

(2) (4)



$126000 1

$140000 2

$180000 1

$400000 ) L

$819000 1


Regents Exam Questions by Topic GRAPHS AND STJ TISTICS Frequency Histograms Bar Graphs and Tables Jll1ilp nrg Name


Value per House

NlImber~ of Houses

-

$ 100 coo

$ 175COI)

$2()O()0

middot1700COO

1 -

c ~I

4 -~

1




71-80 10 61-70 7 51-60 2

41-50 )

)

31-40 1



$cl)rts Ftquncy

(X

25

(

3

20 2

11

10 4

(]) 11 (3) 15 (2) 145 (4) 16

Cc




Class Size

Frequency

8 1

10 3

14 2





1(l) -- (3) ~

2 8

(2) ~ (4) ~ 4 16


30in

10 in[

L~2



Page 2



i

2




y y


4



1 J


--------------------------------shy


(Jt





y y

~Jbull - 16

f

E-

~ 14 1411 1_1

~-=~ 1 - 12 ~ shy H ~ I-

6 (f)4 4

((j

C (I

J1

~lmiddot r

Distance (miles)

(1) 1

-1S Hmiddot c

G3 14 u 14 VI 0)

12 12 ~ c 11) ~ 11)cc ce r- 8 I- 3


C 2 lt- -(I I)


) (7--gtshy

7





y 2ro

122200shy

~ (0 1T~

1~O0 V 1)~

1(leiCf) 0 I ~)

U ~U

25- -)~



1 ( 3 ) j y

250shy225-shy

0 2(I(Jshy

~ 175shy( 1~U-


U shy)L-_J shy



( 2 ) 4 )


on this line (1) (63) (3) (-3-3) (2)(76) (4)(-63)





Yearly Total Cost

3-10-

3210

SinO

lj) 0 1(1 lt)

U S 120-E~

(I)

g $(10shy

$60

$J(J

(I

0




(1)(14) (3)(38) (2) (16) (4) (2 cS)



-lt-- - - - - - ~ - -c - - -~ - -

~



(1) ylt3 (3) yS 3

(2) y gt 3 (4) 123

5

6



~- t ~

- - )

--

-----+c- shy

)

-- bull

1 (1) y lt 2x +] (3) y lt --x +- 1

2

1(2) y lt -2x + 1 (4) ylt--x+l

2


j (I~~--l y

3 J

(1) ygt-x+2 (3) yzmiddot-x+22 2 3 3

(2) ylt-x+2 (4) yS--x+2 2 2

---- --- - --- ----

2




(1) (I i) (3) (L~)

(2) (~3) (4) (2~) 2






bullbull( f 1 (1) 04) (3) (71) (2)(28) (4)(-57)


( J)

6



I optional]



I optional]

8




r-----~-------c-------------------------

----- -middot1

- -jshy

2







lV

1middot1

12

~I---

2middot

01 2 J 5 6





y

o

)

l j

3

4




11

60t---shy

55

50 -r -+---+-------+----lr--j

I ---+-+---t---j

35shy ~ g 30 - I

----

_j


Time (sec)





I ~-+-+-+-1f-+-+--l-+--i-t--+-+--I-I-t--+--+-+-I

10 15 20


5











jet



y

E 12 2gt OJ

c 8

4

-

4 to

10




y=3x) +6x--l bull 1~~ I - It ~

(1 ) (L8) (3) (-38) (2) (-1-4) (4) (344)


y = 2x 2 +8x+9

(1) (233) (3) (-2-15) (2) (217) (4) (-21)


















3((








I 1--- r--- l----r-i-TshyI I

~ --f------shy

I

--f-- shy

-- shy

- shy

- shy

- shy - shy

-- shy

f--- shy -shy

f- shy -

r- shy --

LtJ

19




i I I


I Iii-- r-- j--i --- - 1- - -----_I__-----_~------





21






I C( (



(1) -15xy3-3x 3y 2 (3) -15x 2J)-3x 2y

(7) -15xy3 - 3x 3y (4) -15x v3 + xv


(1) 6- - 151 (3) 61 2 - 151 bull l )~

(2) 6r -5 (4) 62 -15


(l) c2 + 3c - 40 (J) c 1

+ 13c - 40

(2) c2 - 3c - 40 (4) c2

- 40


(1) X 2

- 36 (3) X 2 - 12x + 36

(2) x 2 + 36 (4) X2 -+ 12x + 36


(1) 0 4 +- b4 (3) a~ + 2a l b2 + b4

4 l b2 4 + b4(2) 0 + a + b4 (4) 0 + 4b 2


(1) -2x (3) x-+2 (2) 2x (4) x - 2


(1) 3x 2 + 2x (3) 4x 2 + 2x

(2) 3x 2 +2x+l (4) 4x 2 -+-2x+]


(l) 5x 2 - 6x + 1 (3) 5x 2

- 60x 2 + 1Ox ((--_li

(2) 5x 3 - 6x 2 + x (4) 5x 2

- 6x

1( -)( ~x



4x l) 4x(1) --- () ---- shy

3( x + 1)

4x 2

(2) --- (4) 4(x~22 l

J J


x + I 3y - 3 (1) x (3) x + 3

x(2) -- (4) ~+~ )

J J


x+3


4c +x x+4




x 2 +1x-15 2x- 6


x 2 + 2x (1)x (3) - shy

2(x + 5)

x(2)x+5 (4)-shy

x+5

6 2 2

f f 3x -27 d ) x -7x+12




(II)1I X + ] 3x - 15 2x - 8x-l0

8



x-4 --- ----- ------ -- shy

x- -)X _ - x - i 2 Xl - 3x -r 1G



(2) 7e3 (4) 7 ~


(2) 8-6-5 (4)19C


(1) 5-3-4 (3)12 C 3

(2) 5 + 3 +4 (4) 12 P3



(1)90 (3) uC

(2)72 (4) uP


I111 (1)9 (3)24

(2) 12 (4)29








(2) 25 (4) 75










16



(I) 6 (3) 50 (2) 12 (4) 53




(1) 27deg (3) 39

(2) 27~~ (4) 324


(1) 2 (3) 85

(2) i~ (4) 86


( 1) tV ~ (3) x 3y3z4

(2) ty ~ (4) X 4Y2


(1) lOx s (3) lOx s

(2) 12x 8 (4) 12x l5



(2) 12xy4 (4) 12x 2y 3


I Ii

(2) 5x o (4) 6X 2ll


(1)8x 1 y3 (3)8x 3 y4

(2) 8X 3y 3 (4) 8X 2y4


(1) 30x l y~ (3) 30x 5y5

(2) 30X 4 y 6 (4) 30X 5 y 6



(2) --1 x y 4 (4) ~x3y4 9 18



(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2


(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2


(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6


(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl


(l) I (3) 2 3

(2) 16 (4) 25


(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8


x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8


x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

I I

6




91-100 6

101-110 3

111-120 0

121-130 3

131-140 0

141-150 2

151-160 2


( ( )yshy

7



r ~ A C A ~ 1 ( 1 1 ~ ~ ~ ~ ~ 1 ~ ~ ~ ~~





0-1

2-3

4-5

6-7




(-1

0--3

(-5

(-7


8



-------shy

jf-

5

180--169 170-179 180-189 190-199 200-2(19

Height (em




Age Group Total

20-29 8

20-39 18

20-49 25

20-59 31

20-69 35





71-80 2

81-90 7

91-- 00 10


61-70 2

71-80 0 - shy

81-90 8

91-100 10

(1 ) (3)


shy

71-80 2

81-90 8 e---

91-100 10

Interval Frequency

61-70 2

71-80 ()

81-90 6

91-100 2

(2) (4)



$126000 1

$140000 2

$180000 1

$400000 ) L

$819000 1




Value per House

NlImber~ of Houses

-

$ 100 coo

$ 175COI)

$2()O()0

middot1700COO

1 -

c ~I

4 -~

1




71-80 10 61-70 7 51-60 2

41-50 )

)

31-40 1



$cl)rts Ftquncy

(X

25

(

3

20 2

11

10 4

(]) 11 (3) 15 (2) 145 (4) 16

Cc




Class Size

Frequency

8 1

10 3

14 2





1(l) -- (3) ~

2 8

(2) ~ (4) ~ 4 16


30in

10 in[

L~2



Page 2



i

2




y y


4



1 J


--------------------------------shy


(Jt





y y

~Jbull - 16

f

E-

~ 14 1411 1_1

~-=~ 1 - 12 ~ shy H ~ I-

6 (f)4 4

((j

C (I

J1

~lmiddot r

Distance (miles)

(1) 1

-1S Hmiddot c

G3 14 u 14 VI 0)

12 12 ~ c 11) ~ 11)cc ce r- 8 I- 3


C 2 lt- -(I I)


) (7--gtshy

7





y 2ro

122200shy

~ (0 1T~

1~O0 V 1)~

1(leiCf) 0 I ~)

U ~U

25- -)~



1 ( 3 ) j y

250shy225-shy

0 2(I(Jshy

~ 175shy( 1~U-


U shy)L-_J shy



( 2 ) 4 )


on this line (1) (63) (3) (-3-3) (2)(76) (4)(-63)





Yearly Total Cost

3-10-

3210

SinO

lj) 0 1(1 lt)

U S 120-E~

(I)

g $(10shy

$60

$J(J

(I

0




(1)(14) (3)(38) (2) (16) (4) (2 cS)



-lt-- - - - - - ~ - -c - - -~ - -

~



(1) ylt3 (3) yS 3

(2) y gt 3 (4) 123

5

6



~- t ~

- - )

--

-----+c- shy

)

-- bull

1 (1) y lt 2x +] (3) y lt --x +- 1

2

1(2) y lt -2x + 1 (4) ylt--x+l

2


j (I~~--l y

3 J

(1) ygt-x+2 (3) yzmiddot-x+22 2 3 3

(2) ylt-x+2 (4) yS--x+2 2 2

---- --- - --- ----

2




(1) (I i) (3) (L~)

(2) (~3) (4) (2~) 2






bullbull( f 1 (1) 04) (3) (71) (2)(28) (4)(-57)


( J)

6



I optional]



I optional]

8




r-----~-------c-------------------------

----- -middot1

- -jshy

2







lV

1middot1

12

~I---

2middot

01 2 J 5 6





y

o

)

l j

3

4




11

60t---shy

55

50 -r -+---+-------+----lr--j

I ---+-+---t---j

35shy ~ g 30 - I

----

_j


Time (sec)





I ~-+-+-+-1f-+-+--l-+--i-t--+-+--I-I-t--+--+-+-I

10 15 20


5











jet



y

E 12 2gt OJ

c 8

4

-

4 to

10




y=3x) +6x--l bull 1~~ I - It ~

(1 ) (L8) (3) (-38) (2) (-1-4) (4) (344)


y = 2x 2 +8x+9

(1) (233) (3) (-2-15) (2) (217) (4) (-21)


















3((








I 1--- r--- l----r-i-TshyI I

~ --f------shy

I

--f-- shy

-- shy

- shy

- shy

- shy - shy

-- shy

f--- shy -shy

f- shy -

r- shy --

LtJ

19




i I I


I Iii-- r-- j--i --- - 1- - -----_I__-----_~------





21






I C( (



(1) -15xy3-3x 3y 2 (3) -15x 2J)-3x 2y

(7) -15xy3 - 3x 3y (4) -15x v3 + xv


(1) 6- - 151 (3) 61 2 - 151 bull l )~

(2) 6r -5 (4) 62 -15


(l) c2 + 3c - 40 (J) c 1

+ 13c - 40

(2) c2 - 3c - 40 (4) c2

- 40


(1) X 2

- 36 (3) X 2 - 12x + 36

(2) x 2 + 36 (4) X2 -+ 12x + 36


(1) 0 4 +- b4 (3) a~ + 2a l b2 + b4

4 l b2 4 + b4(2) 0 + a + b4 (4) 0 + 4b 2


(1) -2x (3) x-+2 (2) 2x (4) x - 2


(1) 3x 2 + 2x (3) 4x 2 + 2x

(2) 3x 2 +2x+l (4) 4x 2 -+-2x+]


(l) 5x 2 - 6x + 1 (3) 5x 2

- 60x 2 + 1Ox ((--_li

(2) 5x 3 - 6x 2 + x (4) 5x 2

- 6x

1( -)( ~x



4x l) 4x(1) --- () ---- shy

3( x + 1)

4x 2

(2) --- (4) 4(x~22 l

J J


x + I 3y - 3 (1) x (3) x + 3

x(2) -- (4) ~+~ )

J J


x+3


4c +x x+4




x 2 +1x-15 2x- 6


x 2 + 2x (1)x (3) - shy

2(x + 5)

x(2)x+5 (4)-shy

x+5

6 2 2

f f 3x -27 d ) x -7x+12




(II)1I X + ] 3x - 15 2x - 8x-l0

8



x-4 --- ----- ------ -- shy

x- -)X _ - x - i 2 Xl - 3x -r 1G



(2) 7e3 (4) 7 ~


(2) 8-6-5 (4)19C


(1) 5-3-4 (3)12 C 3

(2) 5 + 3 +4 (4) 12 P3



(1)90 (3) uC

(2)72 (4) uP


I111 (1)9 (3)24

(2) 12 (4)29








(2) 25 (4) 75










16



(I) 6 (3) 50 (2) 12 (4) 53




(1) 27deg (3) 39

(2) 27~~ (4) 324


(1) 2 (3) 85

(2) i~ (4) 86


( 1) tV ~ (3) x 3y3z4

(2) ty ~ (4) X 4Y2


(1) lOx s (3) lOx s

(2) 12x 8 (4) 12x l5



(2) 12xy4 (4) 12x 2y 3


I Ii

(2) 5x o (4) 6X 2ll


(1)8x 1 y3 (3)8x 3 y4

(2) 8X 3y 3 (4) 8X 2y4


(1) 30x l y~ (3) 30x 5y5

(2) 30X 4 y 6 (4) 30X 5 y 6



(2) --1 x y 4 (4) ~x3y4 9 18



(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2


(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2


(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6


(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl


(l) I (3) 2 3

(2) 16 (4) 25


(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8


x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8


x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

I I

7



r ~ A C A ~ 1 ( 1 1 ~ ~ ~ ~ ~ 1 ~ ~ ~ ~~





0-1

2-3

4-5

6-7




(-1

0--3

(-5

(-7


8



-------shy

jf-

5

180--169 170-179 180-189 190-199 200-2(19

Height (em




Age Group Total

20-29 8

20-39 18

20-49 25

20-59 31

20-69 35





71-80 2

81-90 7

91-- 00 10


61-70 2

71-80 0 - shy

81-90 8

91-100 10

(1 ) (3)


shy

71-80 2

81-90 8 e---

91-100 10

Interval Frequency

61-70 2

71-80 ()

81-90 6

91-100 2

(2) (4)



$126000 1

$140000 2

$180000 1

$400000 ) L

$819000 1




Value per House

NlImber~ of Houses

-

$ 100 coo

$ 175COI)

$2()O()0

middot1700COO

1 -

c ~I

4 -~

1




71-80 10 61-70 7 51-60 2

41-50 )

)

31-40 1



$cl)rts Ftquncy

(X

25

(

3

20 2

11

10 4

(]) 11 (3) 15 (2) 145 (4) 16

Cc




Class Size

Frequency

8 1

10 3

14 2





1(l) -- (3) ~

2 8

(2) ~ (4) ~ 4 16


30in

10 in[

L~2



Page 2



i

2




y y


4



1 J


--------------------------------shy


(Jt





y y

~Jbull - 16

f

E-

~ 14 1411 1_1

~-=~ 1 - 12 ~ shy H ~ I-

6 (f)4 4

((j

C (I

J1

~lmiddot r

Distance (miles)

(1) 1

-1S Hmiddot c

G3 14 u 14 VI 0)

12 12 ~ c 11) ~ 11)cc ce r- 8 I- 3


C 2 lt- -(I I)


) (7--gtshy

7





y 2ro

122200shy

~ (0 1T~

1~O0 V 1)~

1(leiCf) 0 I ~)

U ~U

25- -)~



1 ( 3 ) j y

250shy225-shy

0 2(I(Jshy

~ 175shy( 1~U-


U shy)L-_J shy



( 2 ) 4 )


on this line (1) (63) (3) (-3-3) (2)(76) (4)(-63)





Yearly Total Cost

3-10-

3210

SinO

lj) 0 1(1 lt)

U S 120-E~

(I)

g $(10shy

$60

$J(J

(I

0




(1)(14) (3)(38) (2) (16) (4) (2 cS)



-lt-- - - - - - ~ - -c - - -~ - -

~



(1) ylt3 (3) yS 3

(2) y gt 3 (4) 123

5

6



~- t ~

- - )

--

-----+c- shy

)

-- bull

1 (1) y lt 2x +] (3) y lt --x +- 1

2

1(2) y lt -2x + 1 (4) ylt--x+l

2


j (I~~--l y

3 J

(1) ygt-x+2 (3) yzmiddot-x+22 2 3 3

(2) ylt-x+2 (4) yS--x+2 2 2

---- --- - --- ----

2




(1) (I i) (3) (L~)

(2) (~3) (4) (2~) 2






bullbull( f 1 (1) 04) (3) (71) (2)(28) (4)(-57)


( J)

6



I optional]



I optional]

8




r-----~-------c-------------------------

----- -middot1

- -jshy

2







lV

1middot1

12

~I---

2middot

01 2 J 5 6





y

o

)

l j

3

4




11

60t---shy

55

50 -r -+---+-------+----lr--j

I ---+-+---t---j

35shy ~ g 30 - I

----

_j


Time (sec)





I ~-+-+-+-1f-+-+--l-+--i-t--+-+--I-I-t--+--+-+-I

10 15 20


5











jet



y

E 12 2gt OJ

c 8

4

-

4 to

10




y=3x) +6x--l bull 1~~ I - It ~

(1 ) (L8) (3) (-38) (2) (-1-4) (4) (344)


y = 2x 2 +8x+9

(1) (233) (3) (-2-15) (2) (217) (4) (-21)


















3((








I 1--- r--- l----r-i-TshyI I

~ --f------shy

I

--f-- shy

-- shy

- shy

- shy

- shy - shy

-- shy

f--- shy -shy

f- shy -

r- shy --

LtJ

19




i I I


I Iii-- r-- j--i --- - 1- - -----_I__-----_~------





21






I C( (



(1) -15xy3-3x 3y 2 (3) -15x 2J)-3x 2y

(7) -15xy3 - 3x 3y (4) -15x v3 + xv


(1) 6- - 151 (3) 61 2 - 151 bull l )~

(2) 6r -5 (4) 62 -15


(l) c2 + 3c - 40 (J) c 1

+ 13c - 40

(2) c2 - 3c - 40 (4) c2

- 40


(1) X 2

- 36 (3) X 2 - 12x + 36

(2) x 2 + 36 (4) X2 -+ 12x + 36


(1) 0 4 +- b4 (3) a~ + 2a l b2 + b4

4 l b2 4 + b4(2) 0 + a + b4 (4) 0 + 4b 2


(1) -2x (3) x-+2 (2) 2x (4) x - 2


(1) 3x 2 + 2x (3) 4x 2 + 2x

(2) 3x 2 +2x+l (4) 4x 2 -+-2x+]


(l) 5x 2 - 6x + 1 (3) 5x 2

- 60x 2 + 1Ox ((--_li

(2) 5x 3 - 6x 2 + x (4) 5x 2

- 6x

1( -)( ~x



4x l) 4x(1) --- () ---- shy

3( x + 1)

4x 2

(2) --- (4) 4(x~22 l

J J


x + I 3y - 3 (1) x (3) x + 3

x(2) -- (4) ~+~ )

J J


x+3


4c +x x+4




x 2 +1x-15 2x- 6


x 2 + 2x (1)x (3) - shy

2(x + 5)

x(2)x+5 (4)-shy

x+5

6 2 2

f f 3x -27 d ) x -7x+12




(II)1I X + ] 3x - 15 2x - 8x-l0

8



x-4 --- ----- ------ -- shy

x- -)X _ - x - i 2 Xl - 3x -r 1G



(2) 7e3 (4) 7 ~


(2) 8-6-5 (4)19C


(1) 5-3-4 (3)12 C 3

(2) 5 + 3 +4 (4) 12 P3



(1)90 (3) uC

(2)72 (4) uP


I111 (1)9 (3)24

(2) 12 (4)29








(2) 25 (4) 75










16



(I) 6 (3) 50 (2) 12 (4) 53




(1) 27deg (3) 39

(2) 27~~ (4) 324


(1) 2 (3) 85

(2) i~ (4) 86


( 1) tV ~ (3) x 3y3z4

(2) ty ~ (4) X 4Y2


(1) lOx s (3) lOx s

(2) 12x 8 (4) 12x l5



(2) 12xy4 (4) 12x 2y 3


I Ii

(2) 5x o (4) 6X 2ll


(1)8x 1 y3 (3)8x 3 y4

(2) 8X 3y 3 (4) 8X 2y4


(1) 30x l y~ (3) 30x 5y5

(2) 30X 4 y 6 (4) 30X 5 y 6



(2) --1 x y 4 (4) ~x3y4 9 18



(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2


(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2


(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6


(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl


(l) I (3) 2 3

(2) 16 (4) 25


(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8


x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8


x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

I I

8



-------shy

jf-

5

180--169 170-179 180-189 190-199 200-2(19

Height (em




Age Group Total

20-29 8

20-39 18

20-49 25

20-59 31

20-69 35





71-80 2

81-90 7

91-- 00 10


61-70 2

71-80 0 - shy

81-90 8

91-100 10

(1 ) (3)


shy

71-80 2

81-90 8 e---

91-100 10

Interval Frequency

61-70 2

71-80 ()

81-90 6

91-100 2

(2) (4)



$126000 1

$140000 2

$180000 1

$400000 ) L

$819000 1




Value per House

NlImber~ of Houses

-

$ 100 coo

$ 175COI)

$2()O()0

middot1700COO

1 -

c ~I

4 -~

1




71-80 10 61-70 7 51-60 2

41-50 )

)

31-40 1



$cl)rts Ftquncy

(X

25

(

3

20 2

11

10 4

(]) 11 (3) 15 (2) 145 (4) 16

Cc




Class Size

Frequency

8 1

10 3

14 2





1(l) -- (3) ~

2 8

(2) ~ (4) ~ 4 16


30in

10 in[

L~2



Page 2



i

2




y y


4



1 J


--------------------------------shy


(Jt





y y

~Jbull - 16

f

E-

~ 14 1411 1_1

~-=~ 1 - 12 ~ shy H ~ I-

6 (f)4 4

((j

C (I

J1

~lmiddot r

Distance (miles)

(1) 1

-1S Hmiddot c

G3 14 u 14 VI 0)

12 12 ~ c 11) ~ 11)cc ce r- 8 I- 3


C 2 lt- -(I I)


) (7--gtshy

7





y 2ro

122200shy

~ (0 1T~

1~O0 V 1)~

1(leiCf) 0 I ~)

U ~U

25- -)~



1 ( 3 ) j y

250shy225-shy

0 2(I(Jshy

~ 175shy( 1~U-


U shy)L-_J shy



( 2 ) 4 )


on this line (1) (63) (3) (-3-3) (2)(76) (4)(-63)





Yearly Total Cost

3-10-

3210

SinO

lj) 0 1(1 lt)

U S 120-E~

(I)

g $(10shy

$60

$J(J

(I

0




(1)(14) (3)(38) (2) (16) (4) (2 cS)



-lt-- - - - - - ~ - -c - - -~ - -

~



(1) ylt3 (3) yS 3

(2) y gt 3 (4) 123

5

6



~- t ~

- - )

--

-----+c- shy

)

-- bull

1 (1) y lt 2x +] (3) y lt --x +- 1

2

1(2) y lt -2x + 1 (4) ylt--x+l

2


j (I~~--l y

3 J

(1) ygt-x+2 (3) yzmiddot-x+22 2 3 3

(2) ylt-x+2 (4) yS--x+2 2 2

---- --- - --- ----

2




(1) (I i) (3) (L~)

(2) (~3) (4) (2~) 2






bullbull( f 1 (1) 04) (3) (71) (2)(28) (4)(-57)


( J)

6



I optional]



I optional]

8




r-----~-------c-------------------------

----- -middot1

- -jshy

2







lV

1middot1

12

~I---

2middot

01 2 J 5 6





y

o

)

l j

3

4




11

60t---shy

55

50 -r -+---+-------+----lr--j

I ---+-+---t---j

35shy ~ g 30 - I

----

_j


Time (sec)





I ~-+-+-+-1f-+-+--l-+--i-t--+-+--I-I-t--+--+-+-I

10 15 20


5











jet



y

E 12 2gt OJ

c 8

4

-

4 to

10




y=3x) +6x--l bull 1~~ I - It ~

(1 ) (L8) (3) (-38) (2) (-1-4) (4) (344)


y = 2x 2 +8x+9

(1) (233) (3) (-2-15) (2) (217) (4) (-21)


















3((








I 1--- r--- l----r-i-TshyI I

~ --f------shy

I

--f-- shy

-- shy

- shy

- shy

- shy - shy

-- shy

f--- shy -shy

f- shy -

r- shy --

LtJ

19




i I I


I Iii-- r-- j--i --- - 1- - -----_I__-----_~------





21






I C( (



(1) -15xy3-3x 3y 2 (3) -15x 2J)-3x 2y

(7) -15xy3 - 3x 3y (4) -15x v3 + xv


(1) 6- - 151 (3) 61 2 - 151 bull l )~

(2) 6r -5 (4) 62 -15


(l) c2 + 3c - 40 (J) c 1

+ 13c - 40

(2) c2 - 3c - 40 (4) c2

- 40


(1) X 2

- 36 (3) X 2 - 12x + 36

(2) x 2 + 36 (4) X2 -+ 12x + 36


(1) 0 4 +- b4 (3) a~ + 2a l b2 + b4

4 l b2 4 + b4(2) 0 + a + b4 (4) 0 + 4b 2


(1) -2x (3) x-+2 (2) 2x (4) x - 2


(1) 3x 2 + 2x (3) 4x 2 + 2x

(2) 3x 2 +2x+l (4) 4x 2 -+-2x+]


(l) 5x 2 - 6x + 1 (3) 5x 2

- 60x 2 + 1Ox ((--_li

(2) 5x 3 - 6x 2 + x (4) 5x 2

- 6x

1( -)( ~x



4x l) 4x(1) --- () ---- shy

3( x + 1)

4x 2

(2) --- (4) 4(x~22 l

J J


x + I 3y - 3 (1) x (3) x + 3

x(2) -- (4) ~+~ )

J J


x+3


4c +x x+4




x 2 +1x-15 2x- 6


x 2 + 2x (1)x (3) - shy

2(x + 5)

x(2)x+5 (4)-shy

x+5

6 2 2

f f 3x -27 d ) x -7x+12




(II)1I X + ] 3x - 15 2x - 8x-l0

8



x-4 --- ----- ------ -- shy

x- -)X _ - x - i 2 Xl - 3x -r 1G



(2) 7e3 (4) 7 ~


(2) 8-6-5 (4)19C


(1) 5-3-4 (3)12 C 3

(2) 5 + 3 +4 (4) 12 P3



(1)90 (3) uC

(2)72 (4) uP


I111 (1)9 (3)24

(2) 12 (4)29








(2) 25 (4) 75










16



(I) 6 (3) 50 (2) 12 (4) 53




(1) 27deg (3) 39

(2) 27~~ (4) 324


(1) 2 (3) 85

(2) i~ (4) 86


( 1) tV ~ (3) x 3y3z4

(2) ty ~ (4) X 4Y2


(1) lOx s (3) lOx s

(2) 12x 8 (4) 12x l5



(2) 12xy4 (4) 12x 2y 3


I Ii

(2) 5x o (4) 6X 2ll


(1)8x 1 y3 (3)8x 3 y4

(2) 8X 3y 3 (4) 8X 2y4


(1) 30x l y~ (3) 30x 5y5

(2) 30X 4 y 6 (4) 30X 5 y 6



(2) --1 x y 4 (4) ~x3y4 9 18



(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2


(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2


(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6


(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl


(l) I (3) 2 3

(2) 16 (4) 25


(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8


x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8


x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

I I




71-80 2

81-90 7

91-- 00 10


61-70 2

71-80 0 - shy

81-90 8

91-100 10

(1 ) (3)


shy

71-80 2

81-90 8 e---

91-100 10

Interval Frequency

61-70 2

71-80 ()

81-90 6

91-100 2

(2) (4)



$126000 1

$140000 2

$180000 1

$400000 ) L

$819000 1




Value per House

NlImber~ of Houses

-

$ 100 coo

$ 175COI)

$2()O()0

middot1700COO

1 -

c ~I

4 -~

1




71-80 10 61-70 7 51-60 2

41-50 )

)

31-40 1



$cl)rts Ftquncy

(X

25

(

3

20 2

11

10 4

(]) 11 (3) 15 (2) 145 (4) 16

Cc




Class Size

Frequency

8 1

10 3

14 2





1(l) -- (3) ~

2 8

(2) ~ (4) ~ 4 16


30in

10 in[

L~2



Page 2



i

2




y y


4



1 J


--------------------------------shy


(Jt





y y

~Jbull - 16

f

E-

~ 14 1411 1_1

~-=~ 1 - 12 ~ shy H ~ I-

6 (f)4 4

((j

C (I

J1

~lmiddot r

Distance (miles)

(1) 1

-1S Hmiddot c

G3 14 u 14 VI 0)

12 12 ~ c 11) ~ 11)cc ce r- 8 I- 3


C 2 lt- -(I I)


) (7--gtshy

7





y 2ro

122200shy

~ (0 1T~

1~O0 V 1)~

1(leiCf) 0 I ~)

U ~U

25- -)~



1 ( 3 ) j y

250shy225-shy

0 2(I(Jshy

~ 175shy( 1~U-


U shy)L-_J shy



( 2 ) 4 )


on this line (1) (63) (3) (-3-3) (2)(76) (4)(-63)





Yearly Total Cost

3-10-

3210

SinO

lj) 0 1(1 lt)

U S 120-E~

(I)

g $(10shy

$60

$J(J

(I

0




(1)(14) (3)(38) (2) (16) (4) (2 cS)



-lt-- - - - - - ~ - -c - - -~ - -

~



(1) ylt3 (3) yS 3

(2) y gt 3 (4) 123

5

6



~- t ~

- - )

--

-----+c- shy

)

-- bull

1 (1) y lt 2x +] (3) y lt --x +- 1

2

1(2) y lt -2x + 1 (4) ylt--x+l

2


j (I~~--l y

3 J

(1) ygt-x+2 (3) yzmiddot-x+22 2 3 3

(2) ylt-x+2 (4) yS--x+2 2 2

---- --- - --- ----

2




(1) (I i) (3) (L~)

(2) (~3) (4) (2~) 2






bullbull( f 1 (1) 04) (3) (71) (2)(28) (4)(-57)


( J)

6



I optional]



I optional]

8




r-----~-------c-------------------------

----- -middot1

- -jshy

2







lV

1middot1

12

~I---

2middot

01 2 J 5 6





y

o

)

l j

3

4




11

60t---shy

55

50 -r -+---+-------+----lr--j

I ---+-+---t---j

35shy ~ g 30 - I

----

_j


Time (sec)





I ~-+-+-+-1f-+-+--l-+--i-t--+-+--I-I-t--+--+-+-I

10 15 20


5











jet



y

E 12 2gt OJ

c 8

4

-

4 to

10




y=3x) +6x--l bull 1~~ I - It ~

(1 ) (L8) (3) (-38) (2) (-1-4) (4) (344)


y = 2x 2 +8x+9

(1) (233) (3) (-2-15) (2) (217) (4) (-21)


















3((








I 1--- r--- l----r-i-TshyI I

~ --f------shy

I

--f-- shy

-- shy

- shy

- shy

- shy - shy

-- shy

f--- shy -shy

f- shy -

r- shy --

LtJ

19




i I I


I Iii-- r-- j--i --- - 1- - -----_I__-----_~------





21






I C( (



(1) -15xy3-3x 3y 2 (3) -15x 2J)-3x 2y

(7) -15xy3 - 3x 3y (4) -15x v3 + xv


(1) 6- - 151 (3) 61 2 - 151 bull l )~

(2) 6r -5 (4) 62 -15


(l) c2 + 3c - 40 (J) c 1

+ 13c - 40

(2) c2 - 3c - 40 (4) c2

- 40


(1) X 2

- 36 (3) X 2 - 12x + 36

(2) x 2 + 36 (4) X2 -+ 12x + 36


(1) 0 4 +- b4 (3) a~ + 2a l b2 + b4

4 l b2 4 + b4(2) 0 + a + b4 (4) 0 + 4b 2


(1) -2x (3) x-+2 (2) 2x (4) x - 2


(1) 3x 2 + 2x (3) 4x 2 + 2x

(2) 3x 2 +2x+l (4) 4x 2 -+-2x+]


(l) 5x 2 - 6x + 1 (3) 5x 2

- 60x 2 + 1Ox ((--_li

(2) 5x 3 - 6x 2 + x (4) 5x 2

- 6x

1( -)( ~x



4x l) 4x(1) --- () ---- shy

3( x + 1)

4x 2

(2) --- (4) 4(x~22 l

J J


x + I 3y - 3 (1) x (3) x + 3

x(2) -- (4) ~+~ )

J J


x+3


4c +x x+4




x 2 +1x-15 2x- 6


x 2 + 2x (1)x (3) - shy

2(x + 5)

x(2)x+5 (4)-shy

x+5

6 2 2

f f 3x -27 d ) x -7x+12




(II)1I X + ] 3x - 15 2x - 8x-l0

8



x-4 --- ----- ------ -- shy

x- -)X _ - x - i 2 Xl - 3x -r 1G



(2) 7e3 (4) 7 ~


(2) 8-6-5 (4)19C


(1) 5-3-4 (3)12 C 3

(2) 5 + 3 +4 (4) 12 P3



(1)90 (3) uC

(2)72 (4) uP


I111 (1)9 (3)24

(2) 12 (4)29








(2) 25 (4) 75










16



(I) 6 (3) 50 (2) 12 (4) 53




(1) 27deg (3) 39

(2) 27~~ (4) 324


(1) 2 (3) 85

(2) i~ (4) 86


( 1) tV ~ (3) x 3y3z4

(2) ty ~ (4) X 4Y2


(1) lOx s (3) lOx s

(2) 12x 8 (4) 12x l5



(2) 12xy4 (4) 12x 2y 3


I Ii

(2) 5x o (4) 6X 2ll


(1)8x 1 y3 (3)8x 3 y4

(2) 8X 3y 3 (4) 8X 2y4


(1) 30x l y~ (3) 30x 5y5

(2) 30X 4 y 6 (4) 30X 5 y 6



(2) --1 x y 4 (4) ~x3y4 9 18



(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2


(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2


(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6


(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl


(l) I (3) 2 3

(2) 16 (4) 25


(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8


x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8


x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

I I



Value per House

NlImber~ of Houses

-

$ 100 coo

$ 175COI)

$2()O()0

middot1700COO

1 -

c ~I

4 -~

1




71-80 10 61-70 7 51-60 2

41-50 )

)

31-40 1



$cl)rts Ftquncy

(X

25

(

3

20 2

11

10 4

(]) 11 (3) 15 (2) 145 (4) 16

Cc




Class Size

Frequency

8 1

10 3

14 2





1(l) -- (3) ~

2 8

(2) ~ (4) ~ 4 16


30in

10 in[

L~2



Page 2



i

2




y y


4



1 J


--------------------------------shy


(Jt





y y

~Jbull - 16

f

E-

~ 14 1411 1_1

~-=~ 1 - 12 ~ shy H ~ I-

6 (f)4 4

((j

C (I

J1

~lmiddot r

Distance (miles)

(1) 1

-1S Hmiddot c

G3 14 u 14 VI 0)

12 12 ~ c 11) ~ 11)cc ce r- 8 I- 3


C 2 lt- -(I I)


) (7--gtshy

7





y 2ro

122200shy

~ (0 1T~

1~O0 V 1)~

1(leiCf) 0 I ~)

U ~U

25- -)~



1 ( 3 ) j y

250shy225-shy

0 2(I(Jshy

~ 175shy( 1~U-


U shy)L-_J shy



( 2 ) 4 )


on this line (1) (63) (3) (-3-3) (2)(76) (4)(-63)





Yearly Total Cost

3-10-

3210

SinO

lj) 0 1(1 lt)

U S 120-E~

(I)

g $(10shy

$60

$J(J

(I

0




(1)(14) (3)(38) (2) (16) (4) (2 cS)



-lt-- - - - - - ~ - -c - - -~ - -

~



(1) ylt3 (3) yS 3

(2) y gt 3 (4) 123

5

6



~- t ~

- - )

--

-----+c- shy

)

-- bull

1 (1) y lt 2x +] (3) y lt --x +- 1

2

1(2) y lt -2x + 1 (4) ylt--x+l

2


j (I~~--l y

3 J

(1) ygt-x+2 (3) yzmiddot-x+22 2 3 3

(2) ylt-x+2 (4) yS--x+2 2 2

---- --- - --- ----

2




(1) (I i) (3) (L~)

(2) (~3) (4) (2~) 2






bullbull( f 1 (1) 04) (3) (71) (2)(28) (4)(-57)


( J)

6



I optional]



I optional]

8




r-----~-------c-------------------------

----- -middot1

- -jshy

2







lV

1middot1

12

~I---

2middot

01 2 J 5 6





y

o

)

l j

3

4




11

60t---shy

55

50 -r -+---+-------+----lr--j

I ---+-+---t---j

35shy ~ g 30 - I

----

_j


Time (sec)





I ~-+-+-+-1f-+-+--l-+--i-t--+-+--I-I-t--+--+-+-I

10 15 20


5











jet



y

E 12 2gt OJ

c 8

4

-

4 to

10




y=3x) +6x--l bull 1~~ I - It ~

(1 ) (L8) (3) (-38) (2) (-1-4) (4) (344)


y = 2x 2 +8x+9

(1) (233) (3) (-2-15) (2) (217) (4) (-21)


















3((








I 1--- r--- l----r-i-TshyI I

~ --f------shy

I

--f-- shy

-- shy

- shy

- shy

- shy - shy

-- shy

f--- shy -shy

f- shy -

r- shy --

LtJ

19




i I I


I Iii-- r-- j--i --- - 1- - -----_I__-----_~------





21






I C( (



(1) -15xy3-3x 3y 2 (3) -15x 2J)-3x 2y

(7) -15xy3 - 3x 3y (4) -15x v3 + xv


(1) 6- - 151 (3) 61 2 - 151 bull l )~

(2) 6r -5 (4) 62 -15


(l) c2 + 3c - 40 (J) c 1

+ 13c - 40

(2) c2 - 3c - 40 (4) c2

- 40


(1) X 2

- 36 (3) X 2 - 12x + 36

(2) x 2 + 36 (4) X2 -+ 12x + 36


(1) 0 4 +- b4 (3) a~ + 2a l b2 + b4

4 l b2 4 + b4(2) 0 + a + b4 (4) 0 + 4b 2


(1) -2x (3) x-+2 (2) 2x (4) x - 2


(1) 3x 2 + 2x (3) 4x 2 + 2x

(2) 3x 2 +2x+l (4) 4x 2 -+-2x+]


(l) 5x 2 - 6x + 1 (3) 5x 2

- 60x 2 + 1Ox ((--_li

(2) 5x 3 - 6x 2 + x (4) 5x 2

- 6x

1( -)( ~x



4x l) 4x(1) --- () ---- shy

3( x + 1)

4x 2

(2) --- (4) 4(x~22 l

J J


x + I 3y - 3 (1) x (3) x + 3

x(2) -- (4) ~+~ )

J J


x+3


4c +x x+4




x 2 +1x-15 2x- 6


x 2 + 2x (1)x (3) - shy

2(x + 5)

x(2)x+5 (4)-shy

x+5

6 2 2

f f 3x -27 d ) x -7x+12




(II)1I X + ] 3x - 15 2x - 8x-l0

8



x-4 --- ----- ------ -- shy

x- -)X _ - x - i 2 Xl - 3x -r 1G



(2) 7e3 (4) 7 ~


(2) 8-6-5 (4)19C


(1) 5-3-4 (3)12 C 3

(2) 5 + 3 +4 (4) 12 P3



(1)90 (3) uC

(2)72 (4) uP


I111 (1)9 (3)24

(2) 12 (4)29








(2) 25 (4) 75










16



(I) 6 (3) 50 (2) 12 (4) 53




(1) 27deg (3) 39

(2) 27~~ (4) 324


(1) 2 (3) 85

(2) i~ (4) 86


( 1) tV ~ (3) x 3y3z4

(2) ty ~ (4) X 4Y2


(1) lOx s (3) lOx s

(2) 12x 8 (4) 12x l5



(2) 12xy4 (4) 12x 2y 3


I Ii

(2) 5x o (4) 6X 2ll


(1)8x 1 y3 (3)8x 3 y4

(2) 8X 3y 3 (4) 8X 2y4


(1) 30x l y~ (3) 30x 5y5

(2) 30X 4 y 6 (4) 30X 5 y 6



(2) --1 x y 4 (4) ~x3y4 9 18



(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2


(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2


(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6


(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl


(l) I (3) 2 3

(2) 16 (4) 25


(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8


x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8


x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

I I




Class Size

Frequency

8 1

10 3

14 2





1(l) -- (3) ~

2 8

(2) ~ (4) ~ 4 16


30in

10 in[

L~2



Page 2



i

2




y y


4



1 J


--------------------------------shy


(Jt





y y

~Jbull - 16

f

E-

~ 14 1411 1_1

~-=~ 1 - 12 ~ shy H ~ I-

6 (f)4 4

((j

C (I

J1

~lmiddot r

Distance (miles)

(1) 1

-1S Hmiddot c

G3 14 u 14 VI 0)

12 12 ~ c 11) ~ 11)cc ce r- 8 I- 3


C 2 lt- -(I I)


) (7--gtshy

7





y 2ro

122200shy

~ (0 1T~

1~O0 V 1)~

1(leiCf) 0 I ~)

U ~U

25- -)~



1 ( 3 ) j y

250shy225-shy

0 2(I(Jshy

~ 175shy( 1~U-


U shy)L-_J shy



( 2 ) 4 )


on this line (1) (63) (3) (-3-3) (2)(76) (4)(-63)





Yearly Total Cost

3-10-

3210

SinO

lj) 0 1(1 lt)

U S 120-E~

(I)

g $(10shy

$60

$J(J

(I

0




(1)(14) (3)(38) (2) (16) (4) (2 cS)



-lt-- - - - - - ~ - -c - - -~ - -

~



(1) ylt3 (3) yS 3

(2) y gt 3 (4) 123

5

6



~- t ~

- - )

--

-----+c- shy

)

-- bull

1 (1) y lt 2x +] (3) y lt --x +- 1

2

1(2) y lt -2x + 1 (4) ylt--x+l

2


j (I~~--l y

3 J

(1) ygt-x+2 (3) yzmiddot-x+22 2 3 3

(2) ylt-x+2 (4) yS--x+2 2 2

---- --- - --- ----

2




(1) (I i) (3) (L~)

(2) (~3) (4) (2~) 2






bullbull( f 1 (1) 04) (3) (71) (2)(28) (4)(-57)


( J)

6



I optional]



I optional]

8




r-----~-------c-------------------------

----- -middot1

- -jshy

2







lV

1middot1

12

~I---

2middot

01 2 J 5 6





y

o

)

l j

3

4




11

60t---shy

55

50 -r -+---+-------+----lr--j

I ---+-+---t---j

35shy ~ g 30 - I

----

_j


Time (sec)





I ~-+-+-+-1f-+-+--l-+--i-t--+-+--I-I-t--+--+-+-I

10 15 20


5











jet



y

E 12 2gt OJ

c 8

4

-

4 to

10




y=3x) +6x--l bull 1~~ I - It ~

(1 ) (L8) (3) (-38) (2) (-1-4) (4) (344)


y = 2x 2 +8x+9

(1) (233) (3) (-2-15) (2) (217) (4) (-21)


















3((








I 1--- r--- l----r-i-TshyI I

~ --f------shy

I

--f-- shy

-- shy

- shy

- shy

- shy - shy

-- shy

f--- shy -shy

f- shy -

r- shy --

LtJ

19




i I I


I Iii-- r-- j--i --- - 1- - -----_I__-----_~------





21






I C( (



(1) -15xy3-3x 3y 2 (3) -15x 2J)-3x 2y

(7) -15xy3 - 3x 3y (4) -15x v3 + xv


(1) 6- - 151 (3) 61 2 - 151 bull l )~

(2) 6r -5 (4) 62 -15


(l) c2 + 3c - 40 (J) c 1

+ 13c - 40

(2) c2 - 3c - 40 (4) c2

- 40


(1) X 2

- 36 (3) X 2 - 12x + 36

(2) x 2 + 36 (4) X2 -+ 12x + 36


(1) 0 4 +- b4 (3) a~ + 2a l b2 + b4

4 l b2 4 + b4(2) 0 + a + b4 (4) 0 + 4b 2


(1) -2x (3) x-+2 (2) 2x (4) x - 2


(1) 3x 2 + 2x (3) 4x 2 + 2x

(2) 3x 2 +2x+l (4) 4x 2 -+-2x+]


(l) 5x 2 - 6x + 1 (3) 5x 2

- 60x 2 + 1Ox ((--_li

(2) 5x 3 - 6x 2 + x (4) 5x 2

- 6x

1( -)( ~x



4x l) 4x(1) --- () ---- shy

3( x + 1)

4x 2

(2) --- (4) 4(x~22 l

J J


x + I 3y - 3 (1) x (3) x + 3

x(2) -- (4) ~+~ )

J J


x+3


4c +x x+4




x 2 +1x-15 2x- 6


x 2 + 2x (1)x (3) - shy

2(x + 5)

x(2)x+5 (4)-shy

x+5

6 2 2

f f 3x -27 d ) x -7x+12




(II)1I X + ] 3x - 15 2x - 8x-l0

8



x-4 --- ----- ------ -- shy

x- -)X _ - x - i 2 Xl - 3x -r 1G



(2) 7e3 (4) 7 ~


(2) 8-6-5 (4)19C


(1) 5-3-4 (3)12 C 3

(2) 5 + 3 +4 (4) 12 P3



(1)90 (3) uC

(2)72 (4) uP


I111 (1)9 (3)24

(2) 12 (4)29








(2) 25 (4) 75










16



(I) 6 (3) 50 (2) 12 (4) 53




(1) 27deg (3) 39

(2) 27~~ (4) 324


(1) 2 (3) 85

(2) i~ (4) 86


( 1) tV ~ (3) x 3y3z4

(2) ty ~ (4) X 4Y2


(1) lOx s (3) lOx s

(2) 12x 8 (4) 12x l5



(2) 12xy4 (4) 12x 2y 3


I Ii

(2) 5x o (4) 6X 2ll


(1)8x 1 y3 (3)8x 3 y4

(2) 8X 3y 3 (4) 8X 2y4


(1) 30x l y~ (3) 30x 5y5

(2) 30X 4 y 6 (4) 30X 5 y 6



(2) --1 x y 4 (4) ~x3y4 9 18



(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2


(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2


(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6


(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl


(l) I (3) 2 3

(2) 16 (4) 25


(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8


x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8


x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

I I




1(l) -- (3) ~

2 8

(2) ~ (4) ~ 4 16


30in

10 in[

L~2



Page 2



i

2




y y


4



1 J


--------------------------------shy


(Jt





y y

~Jbull - 16

f

E-

~ 14 1411 1_1

~-=~ 1 - 12 ~ shy H ~ I-

6 (f)4 4

((j

C (I

J1

~lmiddot r

Distance (miles)

(1) 1

-1S Hmiddot c

G3 14 u 14 VI 0)

12 12 ~ c 11) ~ 11)cc ce r- 8 I- 3


C 2 lt- -(I I)


) (7--gtshy

7





y 2ro

122200shy

~ (0 1T~

1~O0 V 1)~

1(leiCf) 0 I ~)

U ~U

25- -)~



1 ( 3 ) j y

250shy225-shy

0 2(I(Jshy

~ 175shy( 1~U-


U shy)L-_J shy



( 2 ) 4 )


on this line (1) (63) (3) (-3-3) (2)(76) (4)(-63)





Yearly Total Cost

3-10-

3210

SinO

lj) 0 1(1 lt)

U S 120-E~

(I)

g $(10shy

$60

$J(J

(I

0




(1)(14) (3)(38) (2) (16) (4) (2 cS)



-lt-- - - - - - ~ - -c - - -~ - -

~



(1) ylt3 (3) yS 3

(2) y gt 3 (4) 123

5

6



~- t ~

- - )

--

-----+c- shy

)

-- bull

1 (1) y lt 2x +] (3) y lt --x +- 1

2

1(2) y lt -2x + 1 (4) ylt--x+l

2


j (I~~--l y

3 J

(1) ygt-x+2 (3) yzmiddot-x+22 2 3 3

(2) ylt-x+2 (4) yS--x+2 2 2

---- --- - --- ----

2




(1) (I i) (3) (L~)

(2) (~3) (4) (2~) 2






bullbull( f 1 (1) 04) (3) (71) (2)(28) (4)(-57)


( J)

6



I optional]



I optional]

8




r-----~-------c-------------------------

----- -middot1

- -jshy

2







lV

1middot1

12

~I---

2middot

01 2 J 5 6





y

o

)

l j

3

4




11

60t---shy

55

50 -r -+---+-------+----lr--j

I ---+-+---t---j

35shy ~ g 30 - I

----

_j


Time (sec)





I ~-+-+-+-1f-+-+--l-+--i-t--+-+--I-I-t--+--+-+-I

10 15 20


5











jet



y

E 12 2gt OJ

c 8

4

-

4 to

10




y=3x) +6x--l bull 1~~ I - It ~

(1 ) (L8) (3) (-38) (2) (-1-4) (4) (344)


y = 2x 2 +8x+9

(1) (233) (3) (-2-15) (2) (217) (4) (-21)


















3((








I 1--- r--- l----r-i-TshyI I

~ --f------shy

I

--f-- shy

-- shy

- shy

- shy

- shy - shy

-- shy

f--- shy -shy

f- shy -

r- shy --

LtJ

19




i I I


I Iii-- r-- j--i --- - 1- - -----_I__-----_~------





21






I C( (



(1) -15xy3-3x 3y 2 (3) -15x 2J)-3x 2y

(7) -15xy3 - 3x 3y (4) -15x v3 + xv


(1) 6- - 151 (3) 61 2 - 151 bull l )~

(2) 6r -5 (4) 62 -15


(l) c2 + 3c - 40 (J) c 1

+ 13c - 40

(2) c2 - 3c - 40 (4) c2

- 40


(1) X 2

- 36 (3) X 2 - 12x + 36

(2) x 2 + 36 (4) X2 -+ 12x + 36


(1) 0 4 +- b4 (3) a~ + 2a l b2 + b4

4 l b2 4 + b4(2) 0 + a + b4 (4) 0 + 4b 2


(1) -2x (3) x-+2 (2) 2x (4) x - 2


(1) 3x 2 + 2x (3) 4x 2 + 2x

(2) 3x 2 +2x+l (4) 4x 2 -+-2x+]


(l) 5x 2 - 6x + 1 (3) 5x 2

- 60x 2 + 1Ox ((--_li

(2) 5x 3 - 6x 2 + x (4) 5x 2

- 6x

1( -)( ~x



4x l) 4x(1) --- () ---- shy

3( x + 1)

4x 2

(2) --- (4) 4(x~22 l

J J


x + I 3y - 3 (1) x (3) x + 3

x(2) -- (4) ~+~ )

J J


x+3


4c +x x+4




x 2 +1x-15 2x- 6


x 2 + 2x (1)x (3) - shy

2(x + 5)

x(2)x+5 (4)-shy

x+5

6 2 2

f f 3x -27 d ) x -7x+12




(II)1I X + ] 3x - 15 2x - 8x-l0

8



x-4 --- ----- ------ -- shy

x- -)X _ - x - i 2 Xl - 3x -r 1G



(2) 7e3 (4) 7 ~


(2) 8-6-5 (4)19C


(1) 5-3-4 (3)12 C 3

(2) 5 + 3 +4 (4) 12 P3



(1)90 (3) uC

(2)72 (4) uP


I111 (1)9 (3)24

(2) 12 (4)29








(2) 25 (4) 75










16



(I) 6 (3) 50 (2) 12 (4) 53




(1) 27deg (3) 39

(2) 27~~ (4) 324


(1) 2 (3) 85

(2) i~ (4) 86


( 1) tV ~ (3) x 3y3z4

(2) ty ~ (4) X 4Y2


(1) lOx s (3) lOx s

(2) 12x 8 (4) 12x l5



(2) 12xy4 (4) 12x 2y 3


I Ii

(2) 5x o (4) 6X 2ll


(1)8x 1 y3 (3)8x 3 y4

(2) 8X 3y 3 (4) 8X 2y4


(1) 30x l y~ (3) 30x 5y5

(2) 30X 4 y 6 (4) 30X 5 y 6



(2) --1 x y 4 (4) ~x3y4 9 18



(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2


(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2


(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6


(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl


(l) I (3) 2 3

(2) 16 (4) 25


(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8


x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8


x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

I I



Page 2



i

2




y y


4



1 J


--------------------------------shy


(Jt





y y

~Jbull - 16

f

E-

~ 14 1411 1_1

~-=~ 1 - 12 ~ shy H ~ I-

6 (f)4 4

((j

C (I

J1

~lmiddot r

Distance (miles)

(1) 1

-1S Hmiddot c

G3 14 u 14 VI 0)

12 12 ~ c 11) ~ 11)cc ce r- 8 I- 3


C 2 lt- -(I I)


) (7--gtshy

7





y 2ro

122200shy

~ (0 1T~

1~O0 V 1)~

1(leiCf) 0 I ~)

U ~U

25- -)~



1 ( 3 ) j y

250shy225-shy

0 2(I(Jshy

~ 175shy( 1~U-


U shy)L-_J shy



( 2 ) 4 )


on this line (1) (63) (3) (-3-3) (2)(76) (4)(-63)





Yearly Total Cost

3-10-

3210

SinO

lj) 0 1(1 lt)

U S 120-E~

(I)

g $(10shy

$60

$J(J

(I

0




(1)(14) (3)(38) (2) (16) (4) (2 cS)



-lt-- - - - - - ~ - -c - - -~ - -

~



(1) ylt3 (3) yS 3

(2) y gt 3 (4) 123

5

6



~- t ~

- - )

--

-----+c- shy

)

-- bull

1 (1) y lt 2x +] (3) y lt --x +- 1

2

1(2) y lt -2x + 1 (4) ylt--x+l

2


j (I~~--l y

3 J

(1) ygt-x+2 (3) yzmiddot-x+22 2 3 3

(2) ylt-x+2 (4) yS--x+2 2 2

---- --- - --- ----

2




(1) (I i) (3) (L~)

(2) (~3) (4) (2~) 2






bullbull( f 1 (1) 04) (3) (71) (2)(28) (4)(-57)


( J)

6



I optional]



I optional]

8




r-----~-------c-------------------------

----- -middot1

- -jshy

2







lV

1middot1

12

~I---

2middot

01 2 J 5 6





y

o

)

l j

3

4




11

60t---shy

55

50 -r -+---+-------+----lr--j

I ---+-+---t---j

35shy ~ g 30 - I

----

_j


Time (sec)





I ~-+-+-+-1f-+-+--l-+--i-t--+-+--I-I-t--+--+-+-I

10 15 20


5











jet



y

E 12 2gt OJ

c 8

4

-

4 to

10




y=3x) +6x--l bull 1~~ I - It ~

(1 ) (L8) (3) (-38) (2) (-1-4) (4) (344)


y = 2x 2 +8x+9

(1) (233) (3) (-2-15) (2) (217) (4) (-21)


















3((








I 1--- r--- l----r-i-TshyI I

~ --f------shy

I

--f-- shy

-- shy

- shy

- shy

- shy - shy

-- shy

f--- shy -shy

f- shy -

r- shy --

LtJ

19




i I I


I Iii-- r-- j--i --- - 1- - -----_I__-----_~------





21






I C( (



(1) -15xy3-3x 3y 2 (3) -15x 2J)-3x 2y

(7) -15xy3 - 3x 3y (4) -15x v3 + xv


(1) 6- - 151 (3) 61 2 - 151 bull l )~

(2) 6r -5 (4) 62 -15


(l) c2 + 3c - 40 (J) c 1

+ 13c - 40

(2) c2 - 3c - 40 (4) c2

- 40


(1) X 2

- 36 (3) X 2 - 12x + 36

(2) x 2 + 36 (4) X2 -+ 12x + 36


(1) 0 4 +- b4 (3) a~ + 2a l b2 + b4

4 l b2 4 + b4(2) 0 + a + b4 (4) 0 + 4b 2


(1) -2x (3) x-+2 (2) 2x (4) x - 2


(1) 3x 2 + 2x (3) 4x 2 + 2x

(2) 3x 2 +2x+l (4) 4x 2 -+-2x+]


(l) 5x 2 - 6x + 1 (3) 5x 2

- 60x 2 + 1Ox ((--_li

(2) 5x 3 - 6x 2 + x (4) 5x 2

- 6x

1( -)( ~x



4x l) 4x(1) --- () ---- shy

3( x + 1)

4x 2

(2) --- (4) 4(x~22 l

J J


x + I 3y - 3 (1) x (3) x + 3

x(2) -- (4) ~+~ )

J J


x+3


4c +x x+4




x 2 +1x-15 2x- 6


x 2 + 2x (1)x (3) - shy

2(x + 5)

x(2)x+5 (4)-shy

x+5

6 2 2

f f 3x -27 d ) x -7x+12




(II)1I X + ] 3x - 15 2x - 8x-l0

8



x-4 --- ----- ------ -- shy

x- -)X _ - x - i 2 Xl - 3x -r 1G



(2) 7e3 (4) 7 ~


(2) 8-6-5 (4)19C


(1) 5-3-4 (3)12 C 3

(2) 5 + 3 +4 (4) 12 P3



(1)90 (3) uC

(2)72 (4) uP


I111 (1)9 (3)24

(2) 12 (4)29








(2) 25 (4) 75










16



(I) 6 (3) 50 (2) 12 (4) 53




(1) 27deg (3) 39

(2) 27~~ (4) 324


(1) 2 (3) 85

(2) i~ (4) 86


( 1) tV ~ (3) x 3y3z4

(2) ty ~ (4) X 4Y2


(1) lOx s (3) lOx s

(2) 12x 8 (4) 12x l5



(2) 12xy4 (4) 12x 2y 3


I Ii

(2) 5x o (4) 6X 2ll


(1)8x 1 y3 (3)8x 3 y4

(2) 8X 3y 3 (4) 8X 2y4


(1) 30x l y~ (3) 30x 5y5

(2) 30X 4 y 6 (4) 30X 5 y 6



(2) --1 x y 4 (4) ~x3y4 9 18



(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2


(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2


(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6


(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl


(l) I (3) 2 3

(2) 16 (4) 25


(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8


x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8


x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

I I

i

2




y y


4



1 J


--------------------------------shy


(Jt





y y

~Jbull - 16

f

E-

~ 14 1411 1_1

~-=~ 1 - 12 ~ shy H ~ I-

6 (f)4 4

((j

C (I

J1

~lmiddot r

Distance (miles)

(1) 1

-1S Hmiddot c

G3 14 u 14 VI 0)

12 12 ~ c 11) ~ 11)cc ce r- 8 I- 3


C 2 lt- -(I I)


) (7--gtshy

7





y 2ro

122200shy

~ (0 1T~

1~O0 V 1)~

1(leiCf) 0 I ~)

U ~U

25- -)~



1 ( 3 ) j y

250shy225-shy

0 2(I(Jshy

~ 175shy( 1~U-


U shy)L-_J shy



( 2 ) 4 )


on this line (1) (63) (3) (-3-3) (2)(76) (4)(-63)





Yearly Total Cost

3-10-

3210

SinO

lj) 0 1(1 lt)

U S 120-E~

(I)

g $(10shy

$60

$J(J

(I

0




(1)(14) (3)(38) (2) (16) (4) (2 cS)



-lt-- - - - - - ~ - -c - - -~ - -

~



(1) ylt3 (3) yS 3

(2) y gt 3 (4) 123

5

6



~- t ~

- - )

--

-----+c- shy

)

-- bull

1 (1) y lt 2x +] (3) y lt --x +- 1

2

1(2) y lt -2x + 1 (4) ylt--x+l

2


j (I~~--l y

3 J

(1) ygt-x+2 (3) yzmiddot-x+22 2 3 3

(2) ylt-x+2 (4) yS--x+2 2 2

---- --- - --- ----

2




(1) (I i) (3) (L~)

(2) (~3) (4) (2~) 2






bullbull( f 1 (1) 04) (3) (71) (2)(28) (4)(-57)


( J)

6



I optional]



I optional]

8




r-----~-------c-------------------------

----- -middot1

- -jshy

2







lV

1middot1

12

~I---

2middot

01 2 J 5 6





y

o

)

l j

3

4




11

60t---shy

55

50 -r -+---+-------+----lr--j

I ---+-+---t---j

35shy ~ g 30 - I

----

_j


Time (sec)





I ~-+-+-+-1f-+-+--l-+--i-t--+-+--I-I-t--+--+-+-I

10 15 20


5











jet



y

E 12 2gt OJ

c 8

4

-

4 to

10




y=3x) +6x--l bull 1~~ I - It ~

(1 ) (L8) (3) (-38) (2) (-1-4) (4) (344)


y = 2x 2 +8x+9

(1) (233) (3) (-2-15) (2) (217) (4) (-21)


















3((








I 1--- r--- l----r-i-TshyI I

~ --f------shy

I

--f-- shy

-- shy

- shy

- shy

- shy - shy

-- shy

f--- shy -shy

f- shy -

r- shy --

LtJ

19




i I I


I Iii-- r-- j--i --- - 1- - -----_I__-----_~------





21






I C( (



(1) -15xy3-3x 3y 2 (3) -15x 2J)-3x 2y

(7) -15xy3 - 3x 3y (4) -15x v3 + xv


(1) 6- - 151 (3) 61 2 - 151 bull l )~

(2) 6r -5 (4) 62 -15


(l) c2 + 3c - 40 (J) c 1

+ 13c - 40

(2) c2 - 3c - 40 (4) c2

- 40


(1) X 2

- 36 (3) X 2 - 12x + 36

(2) x 2 + 36 (4) X2 -+ 12x + 36


(1) 0 4 +- b4 (3) a~ + 2a l b2 + b4

4 l b2 4 + b4(2) 0 + a + b4 (4) 0 + 4b 2


(1) -2x (3) x-+2 (2) 2x (4) x - 2


(1) 3x 2 + 2x (3) 4x 2 + 2x

(2) 3x 2 +2x+l (4) 4x 2 -+-2x+]


(l) 5x 2 - 6x + 1 (3) 5x 2

- 60x 2 + 1Ox ((--_li

(2) 5x 3 - 6x 2 + x (4) 5x 2

- 6x

1( -)( ~x



4x l) 4x(1) --- () ---- shy

3( x + 1)

4x 2

(2) --- (4) 4(x~22 l

J J


x + I 3y - 3 (1) x (3) x + 3

x(2) -- (4) ~+~ )

J J


x+3


4c +x x+4




x 2 +1x-15 2x- 6


x 2 + 2x (1)x (3) - shy

2(x + 5)

x(2)x+5 (4)-shy

x+5

6 2 2

f f 3x -27 d ) x -7x+12




(II)1I X + ] 3x - 15 2x - 8x-l0

8



x-4 --- ----- ------ -- shy

x- -)X _ - x - i 2 Xl - 3x -r 1G



(2) 7e3 (4) 7 ~


(2) 8-6-5 (4)19C


(1) 5-3-4 (3)12 C 3

(2) 5 + 3 +4 (4) 12 P3



(1)90 (3) uC

(2)72 (4) uP


I111 (1)9 (3)24

(2) 12 (4)29








(2) 25 (4) 75










16



(I) 6 (3) 50 (2) 12 (4) 53




(1) 27deg (3) 39

(2) 27~~ (4) 324


(1) 2 (3) 85

(2) i~ (4) 86


( 1) tV ~ (3) x 3y3z4

(2) ty ~ (4) X 4Y2


(1) lOx s (3) lOx s

(2) 12x 8 (4) 12x l5



(2) 12xy4 (4) 12x 2y 3


I Ii

(2) 5x o (4) 6X 2ll


(1)8x 1 y3 (3)8x 3 y4

(2) 8X 3y 3 (4) 8X 2y4


(1) 30x l y~ (3) 30x 5y5

(2) 30X 4 y 6 (4) 30X 5 y 6



(2) --1 x y 4 (4) ~x3y4 9 18



(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2


(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2


(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6


(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl


(l) I (3) 2 3

(2) 16 (4) 25


(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8


x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8


x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

I I

4



1 J


--------------------------------shy


(Jt





y y

~Jbull - 16

f

E-

~ 14 1411 1_1

~-=~ 1 - 12 ~ shy H ~ I-

6 (f)4 4

((j

C (I

J1

~lmiddot r

Distance (miles)

(1) 1

-1S Hmiddot c

G3 14 u 14 VI 0)

12 12 ~ c 11) ~ 11)cc ce r- 8 I- 3


C 2 lt- -(I I)


) (7--gtshy

7





y 2ro

122200shy

~ (0 1T~

1~O0 V 1)~

1(leiCf) 0 I ~)

U ~U

25- -)~



1 ( 3 ) j y

250shy225-shy

0 2(I(Jshy

~ 175shy( 1~U-


U shy)L-_J shy



( 2 ) 4 )


on this line (1) (63) (3) (-3-3) (2)(76) (4)(-63)





Yearly Total Cost

3-10-

3210

SinO

lj) 0 1(1 lt)

U S 120-E~

(I)

g $(10shy

$60

$J(J

(I

0




(1)(14) (3)(38) (2) (16) (4) (2 cS)



-lt-- - - - - - ~ - -c - - -~ - -

~



(1) ylt3 (3) yS 3

(2) y gt 3 (4) 123

5

6



~- t ~

- - )

--

-----+c- shy

)

-- bull

1 (1) y lt 2x +] (3) y lt --x +- 1

2

1(2) y lt -2x + 1 (4) ylt--x+l

2


j (I~~--l y

3 J

(1) ygt-x+2 (3) yzmiddot-x+22 2 3 3

(2) ylt-x+2 (4) yS--x+2 2 2

---- --- - --- ----

2




(1) (I i) (3) (L~)

(2) (~3) (4) (2~) 2






bullbull( f 1 (1) 04) (3) (71) (2)(28) (4)(-57)


( J)

6



I optional]



I optional]

8




r-----~-------c-------------------------

----- -middot1

- -jshy

2







lV

1middot1

12

~I---

2middot

01 2 J 5 6





y

o

)

l j

3

4




11

60t---shy

55

50 -r -+---+-------+----lr--j

I ---+-+---t---j

35shy ~ g 30 - I

----

_j


Time (sec)





I ~-+-+-+-1f-+-+--l-+--i-t--+-+--I-I-t--+--+-+-I

10 15 20


5











jet



y

E 12 2gt OJ

c 8

4

-

4 to

10




y=3x) +6x--l bull 1~~ I - It ~

(1 ) (L8) (3) (-38) (2) (-1-4) (4) (344)


y = 2x 2 +8x+9

(1) (233) (3) (-2-15) (2) (217) (4) (-21)


















3((








I 1--- r--- l----r-i-TshyI I

~ --f------shy

I

--f-- shy

-- shy

- shy

- shy

- shy - shy

-- shy

f--- shy -shy

f- shy -

r- shy --

LtJ

19




i I I


I Iii-- r-- j--i --- - 1- - -----_I__-----_~------





21






I C( (



(1) -15xy3-3x 3y 2 (3) -15x 2J)-3x 2y

(7) -15xy3 - 3x 3y (4) -15x v3 + xv


(1) 6- - 151 (3) 61 2 - 151 bull l )~

(2) 6r -5 (4) 62 -15


(l) c2 + 3c - 40 (J) c 1

+ 13c - 40

(2) c2 - 3c - 40 (4) c2

- 40


(1) X 2

- 36 (3) X 2 - 12x + 36

(2) x 2 + 36 (4) X2 -+ 12x + 36


(1) 0 4 +- b4 (3) a~ + 2a l b2 + b4

4 l b2 4 + b4(2) 0 + a + b4 (4) 0 + 4b 2


(1) -2x (3) x-+2 (2) 2x (4) x - 2


(1) 3x 2 + 2x (3) 4x 2 + 2x

(2) 3x 2 +2x+l (4) 4x 2 -+-2x+]


(l) 5x 2 - 6x + 1 (3) 5x 2

- 60x 2 + 1Ox ((--_li

(2) 5x 3 - 6x 2 + x (4) 5x 2

- 6x

1( -)( ~x



4x l) 4x(1) --- () ---- shy

3( x + 1)

4x 2

(2) --- (4) 4(x~22 l

J J


x + I 3y - 3 (1) x (3) x + 3

x(2) -- (4) ~+~ )

J J


x+3


4c +x x+4




x 2 +1x-15 2x- 6


x 2 + 2x (1)x (3) - shy

2(x + 5)

x(2)x+5 (4)-shy

x+5

6 2 2

f f 3x -27 d ) x -7x+12




(II)1I X + ] 3x - 15 2x - 8x-l0

8



x-4 --- ----- ------ -- shy

x- -)X _ - x - i 2 Xl - 3x -r 1G



(2) 7e3 (4) 7 ~


(2) 8-6-5 (4)19C


(1) 5-3-4 (3)12 C 3

(2) 5 + 3 +4 (4) 12 P3



(1)90 (3) uC

(2)72 (4) uP


I111 (1)9 (3)24

(2) 12 (4)29








(2) 25 (4) 75










16



(I) 6 (3) 50 (2) 12 (4) 53




(1) 27deg (3) 39

(2) 27~~ (4) 324


(1) 2 (3) 85

(2) i~ (4) 86


( 1) tV ~ (3) x 3y3z4

(2) ty ~ (4) X 4Y2


(1) lOx s (3) lOx s

(2) 12x 8 (4) 12x l5



(2) 12xy4 (4) 12x 2y 3


I Ii

(2) 5x o (4) 6X 2ll


(1)8x 1 y3 (3)8x 3 y4

(2) 8X 3y 3 (4) 8X 2y4


(1) 30x l y~ (3) 30x 5y5

(2) 30X 4 y 6 (4) 30X 5 y 6



(2) --1 x y 4 (4) ~x3y4 9 18



(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2


(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2


(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6


(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl


(l) I (3) 2 3

(2) 16 (4) 25


(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8


x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8


x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

I I





y y

~Jbull - 16

f

E-

~ 14 1411 1_1

~-=~ 1 - 12 ~ shy H ~ I-

6 (f)4 4

((j

C (I

J1

~lmiddot r

Distance (miles)

(1) 1

-1S Hmiddot c

G3 14 u 14 VI 0)

12 12 ~ c 11) ~ 11)cc ce r- 8 I- 3


C 2 lt- -(I I)


) (7--gtshy

7





y 2ro

122200shy

~ (0 1T~

1~O0 V 1)~

1(leiCf) 0 I ~)

U ~U

25- -)~



1 ( 3 ) j y

250shy225-shy

0 2(I(Jshy

~ 175shy( 1~U-


U shy)L-_J shy



( 2 ) 4 )


on this line (1) (63) (3) (-3-3) (2)(76) (4)(-63)





Yearly Total Cost

3-10-

3210

SinO

lj) 0 1(1 lt)

U S 120-E~

(I)

g $(10shy

$60

$J(J

(I

0




(1)(14) (3)(38) (2) (16) (4) (2 cS)



-lt-- - - - - - ~ - -c - - -~ - -

~



(1) ylt3 (3) yS 3

(2) y gt 3 (4) 123

5

6



~- t ~

- - )

--

-----+c- shy

)

-- bull

1 (1) y lt 2x +] (3) y lt --x +- 1

2

1(2) y lt -2x + 1 (4) ylt--x+l

2


j (I~~--l y

3 J

(1) ygt-x+2 (3) yzmiddot-x+22 2 3 3

(2) ylt-x+2 (4) yS--x+2 2 2

---- --- - --- ----

2




(1) (I i) (3) (L~)

(2) (~3) (4) (2~) 2






bullbull( f 1 (1) 04) (3) (71) (2)(28) (4)(-57)


( J)

6



I optional]



I optional]

8




r-----~-------c-------------------------

----- -middot1

- -jshy

2







lV

1middot1

12

~I---

2middot

01 2 J 5 6





y

o

)

l j

3

4




11

60t---shy

55

50 -r -+---+-------+----lr--j

I ---+-+---t---j

35shy ~ g 30 - I

----

_j


Time (sec)





I ~-+-+-+-1f-+-+--l-+--i-t--+-+--I-I-t--+--+-+-I

10 15 20


5











jet



y

E 12 2gt OJ

c 8

4

-

4 to

10




y=3x) +6x--l bull 1~~ I - It ~

(1 ) (L8) (3) (-38) (2) (-1-4) (4) (344)


y = 2x 2 +8x+9

(1) (233) (3) (-2-15) (2) (217) (4) (-21)


















3((








I 1--- r--- l----r-i-TshyI I

~ --f------shy

I

--f-- shy

-- shy

- shy

- shy

- shy - shy

-- shy

f--- shy -shy

f- shy -

r- shy --

LtJ

19




i I I


I Iii-- r-- j--i --- - 1- - -----_I__-----_~------





21






I C( (



(1) -15xy3-3x 3y 2 (3) -15x 2J)-3x 2y

(7) -15xy3 - 3x 3y (4) -15x v3 + xv


(1) 6- - 151 (3) 61 2 - 151 bull l )~

(2) 6r -5 (4) 62 -15


(l) c2 + 3c - 40 (J) c 1

+ 13c - 40

(2) c2 - 3c - 40 (4) c2

- 40


(1) X 2

- 36 (3) X 2 - 12x + 36

(2) x 2 + 36 (4) X2 -+ 12x + 36


(1) 0 4 +- b4 (3) a~ + 2a l b2 + b4

4 l b2 4 + b4(2) 0 + a + b4 (4) 0 + 4b 2


(1) -2x (3) x-+2 (2) 2x (4) x - 2


(1) 3x 2 + 2x (3) 4x 2 + 2x

(2) 3x 2 +2x+l (4) 4x 2 -+-2x+]


(l) 5x 2 - 6x + 1 (3) 5x 2

- 60x 2 + 1Ox ((--_li

(2) 5x 3 - 6x 2 + x (4) 5x 2

- 6x

1( -)( ~x



4x l) 4x(1) --- () ---- shy

3( x + 1)

4x 2

(2) --- (4) 4(x~22 l

J J


x + I 3y - 3 (1) x (3) x + 3

x(2) -- (4) ~+~ )

J J


x+3


4c +x x+4




x 2 +1x-15 2x- 6


x 2 + 2x (1)x (3) - shy

2(x + 5)

x(2)x+5 (4)-shy

x+5

6 2 2

f f 3x -27 d ) x -7x+12




(II)1I X + ] 3x - 15 2x - 8x-l0

8



x-4 --- ----- ------ -- shy

x- -)X _ - x - i 2 Xl - 3x -r 1G



(2) 7e3 (4) 7 ~


(2) 8-6-5 (4)19C


(1) 5-3-4 (3)12 C 3

(2) 5 + 3 +4 (4) 12 P3



(1)90 (3) uC

(2)72 (4) uP


I111 (1)9 (3)24

(2) 12 (4)29








(2) 25 (4) 75










16



(I) 6 (3) 50 (2) 12 (4) 53




(1) 27deg (3) 39

(2) 27~~ (4) 324


(1) 2 (3) 85

(2) i~ (4) 86


( 1) tV ~ (3) x 3y3z4

(2) ty ~ (4) X 4Y2


(1) lOx s (3) lOx s

(2) 12x 8 (4) 12x l5



(2) 12xy4 (4) 12x 2y 3


I Ii

(2) 5x o (4) 6X 2ll


(1)8x 1 y3 (3)8x 3 y4

(2) 8X 3y 3 (4) 8X 2y4


(1) 30x l y~ (3) 30x 5y5

(2) 30X 4 y 6 (4) 30X 5 y 6



(2) --1 x y 4 (4) ~x3y4 9 18



(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2


(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2


(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6


(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl


(l) I (3) 2 3

(2) 16 (4) 25


(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8


x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8


x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

I I

7





y 2ro

122200shy

~ (0 1T~

1~O0 V 1)~

1(leiCf) 0 I ~)

U ~U

25- -)~



1 ( 3 ) j y

250shy225-shy

0 2(I(Jshy

~ 175shy( 1~U-


U shy)L-_J shy



( 2 ) 4 )


on this line (1) (63) (3) (-3-3) (2)(76) (4)(-63)





Yearly Total Cost

3-10-

3210

SinO

lj) 0 1(1 lt)

U S 120-E~

(I)

g $(10shy

$60

$J(J

(I

0




(1)(14) (3)(38) (2) (16) (4) (2 cS)



-lt-- - - - - - ~ - -c - - -~ - -

~



(1) ylt3 (3) yS 3

(2) y gt 3 (4) 123

5

6



~- t ~

- - )

--

-----+c- shy

)

-- bull

1 (1) y lt 2x +] (3) y lt --x +- 1

2

1(2) y lt -2x + 1 (4) ylt--x+l

2


j (I~~--l y

3 J

(1) ygt-x+2 (3) yzmiddot-x+22 2 3 3

(2) ylt-x+2 (4) yS--x+2 2 2

---- --- - --- ----

2




(1) (I i) (3) (L~)

(2) (~3) (4) (2~) 2






bullbull( f 1 (1) 04) (3) (71) (2)(28) (4)(-57)


( J)

6



I optional]



I optional]

8




r-----~-------c-------------------------

----- -middot1

- -jshy

2







lV

1middot1

12

~I---

2middot

01 2 J 5 6





y

o

)

l j

3

4




11

60t---shy

55

50 -r -+---+-------+----lr--j

I ---+-+---t---j

35shy ~ g 30 - I

----

_j


Time (sec)





I ~-+-+-+-1f-+-+--l-+--i-t--+-+--I-I-t--+--+-+-I

10 15 20


5











jet



y

E 12 2gt OJ

c 8

4

-

4 to

10




y=3x) +6x--l bull 1~~ I - It ~

(1 ) (L8) (3) (-38) (2) (-1-4) (4) (344)


y = 2x 2 +8x+9

(1) (233) (3) (-2-15) (2) (217) (4) (-21)


















3((








I 1--- r--- l----r-i-TshyI I

~ --f------shy

I

--f-- shy

-- shy

- shy

- shy

- shy - shy

-- shy

f--- shy -shy

f- shy -

r- shy --

LtJ

19




i I I


I Iii-- r-- j--i --- - 1- - -----_I__-----_~------





21






I C( (



(1) -15xy3-3x 3y 2 (3) -15x 2J)-3x 2y

(7) -15xy3 - 3x 3y (4) -15x v3 + xv


(1) 6- - 151 (3) 61 2 - 151 bull l )~

(2) 6r -5 (4) 62 -15


(l) c2 + 3c - 40 (J) c 1

+ 13c - 40

(2) c2 - 3c - 40 (4) c2

- 40


(1) X 2

- 36 (3) X 2 - 12x + 36

(2) x 2 + 36 (4) X2 -+ 12x + 36


(1) 0 4 +- b4 (3) a~ + 2a l b2 + b4

4 l b2 4 + b4(2) 0 + a + b4 (4) 0 + 4b 2


(1) -2x (3) x-+2 (2) 2x (4) x - 2


(1) 3x 2 + 2x (3) 4x 2 + 2x

(2) 3x 2 +2x+l (4) 4x 2 -+-2x+]


(l) 5x 2 - 6x + 1 (3) 5x 2

- 60x 2 + 1Ox ((--_li

(2) 5x 3 - 6x 2 + x (4) 5x 2

- 6x

1( -)( ~x



4x l) 4x(1) --- () ---- shy

3( x + 1)

4x 2

(2) --- (4) 4(x~22 l

J J


x + I 3y - 3 (1) x (3) x + 3

x(2) -- (4) ~+~ )

J J


x+3


4c +x x+4




x 2 +1x-15 2x- 6


x 2 + 2x (1)x (3) - shy

2(x + 5)

x(2)x+5 (4)-shy

x+5

6 2 2

f f 3x -27 d ) x -7x+12




(II)1I X + ] 3x - 15 2x - 8x-l0

8



x-4 --- ----- ------ -- shy

x- -)X _ - x - i 2 Xl - 3x -r 1G



(2) 7e3 (4) 7 ~


(2) 8-6-5 (4)19C


(1) 5-3-4 (3)12 C 3

(2) 5 + 3 +4 (4) 12 P3



(1)90 (3) uC

(2)72 (4) uP


I111 (1)9 (3)24

(2) 12 (4)29








(2) 25 (4) 75










16



(I) 6 (3) 50 (2) 12 (4) 53




(1) 27deg (3) 39

(2) 27~~ (4) 324


(1) 2 (3) 85

(2) i~ (4) 86


( 1) tV ~ (3) x 3y3z4

(2) ty ~ (4) X 4Y2


(1) lOx s (3) lOx s

(2) 12x 8 (4) 12x l5



(2) 12xy4 (4) 12x 2y 3


I Ii

(2) 5x o (4) 6X 2ll


(1)8x 1 y3 (3)8x 3 y4

(2) 8X 3y 3 (4) 8X 2y4


(1) 30x l y~ (3) 30x 5y5

(2) 30X 4 y 6 (4) 30X 5 y 6



(2) --1 x y 4 (4) ~x3y4 9 18



(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2


(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2


(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6


(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl


(l) I (3) 2 3

(2) 16 (4) 25


(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8


x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8


x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

I I



Yearly Total Cost

3-10-

3210

SinO

lj) 0 1(1 lt)

U S 120-E~

(I)

g $(10shy

$60

$J(J

(I

0




(1)(14) (3)(38) (2) (16) (4) (2 cS)



-lt-- - - - - - ~ - -c - - -~ - -

~



(1) ylt3 (3) yS 3

(2) y gt 3 (4) 123

5

6



~- t ~

- - )

--

-----+c- shy

)

-- bull

1 (1) y lt 2x +] (3) y lt --x +- 1

2

1(2) y lt -2x + 1 (4) ylt--x+l

2


j (I~~--l y

3 J

(1) ygt-x+2 (3) yzmiddot-x+22 2 3 3

(2) ylt-x+2 (4) yS--x+2 2 2

---- --- - --- ----

2




(1) (I i) (3) (L~)

(2) (~3) (4) (2~) 2






bullbull( f 1 (1) 04) (3) (71) (2)(28) (4)(-57)


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6



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8




r-----~-------c-------------------------

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2







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12

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3

4




11

60t---shy

55

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I ---+-+---t---j

35shy ~ g 30 - I

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Time (sec)





I ~-+-+-+-1f-+-+--l-+--i-t--+-+--I-I-t--+--+-+-I

10 15 20


5











jet



y

E 12 2gt OJ

c 8

4

-

4 to

10




y=3x) +6x--l bull 1~~ I - It ~

(1 ) (L8) (3) (-38) (2) (-1-4) (4) (344)


y = 2x 2 +8x+9

(1) (233) (3) (-2-15) (2) (217) (4) (-21)


















3((








I 1--- r--- l----r-i-TshyI I

~ --f------shy

I

--f-- shy

-- shy

- shy

- shy

- shy - shy

-- shy

f--- shy -shy

f- shy -

r- shy --

LtJ

19




i I I


I Iii-- r-- j--i --- - 1- - -----_I__-----_~------





21






I C( (



(1) -15xy3-3x 3y 2 (3) -15x 2J)-3x 2y

(7) -15xy3 - 3x 3y (4) -15x v3 + xv


(1) 6- - 151 (3) 61 2 - 151 bull l )~

(2) 6r -5 (4) 62 -15


(l) c2 + 3c - 40 (J) c 1

+ 13c - 40

(2) c2 - 3c - 40 (4) c2

- 40


(1) X 2

- 36 (3) X 2 - 12x + 36

(2) x 2 + 36 (4) X2 -+ 12x + 36


(1) 0 4 +- b4 (3) a~ + 2a l b2 + b4

4 l b2 4 + b4(2) 0 + a + b4 (4) 0 + 4b 2


(1) -2x (3) x-+2 (2) 2x (4) x - 2


(1) 3x 2 + 2x (3) 4x 2 + 2x

(2) 3x 2 +2x+l (4) 4x 2 -+-2x+]


(l) 5x 2 - 6x + 1 (3) 5x 2

- 60x 2 + 1Ox ((--_li

(2) 5x 3 - 6x 2 + x (4) 5x 2

- 6x

1( -)( ~x



4x l) 4x(1) --- () ---- shy

3( x + 1)

4x 2

(2) --- (4) 4(x~22 l

J J


x + I 3y - 3 (1) x (3) x + 3

x(2) -- (4) ~+~ )

J J


x+3


4c +x x+4




x 2 +1x-15 2x- 6


x 2 + 2x (1)x (3) - shy

2(x + 5)

x(2)x+5 (4)-shy

x+5

6 2 2

f f 3x -27 d ) x -7x+12




(II)1I X + ] 3x - 15 2x - 8x-l0

8



x-4 --- ----- ------ -- shy

x- -)X _ - x - i 2 Xl - 3x -r 1G



(2) 7e3 (4) 7 ~


(2) 8-6-5 (4)19C


(1) 5-3-4 (3)12 C 3

(2) 5 + 3 +4 (4) 12 P3



(1)90 (3) uC

(2)72 (4) uP


I111 (1)9 (3)24

(2) 12 (4)29








(2) 25 (4) 75










16



(I) 6 (3) 50 (2) 12 (4) 53




(1) 27deg (3) 39

(2) 27~~ (4) 324


(1) 2 (3) 85

(2) i~ (4) 86


( 1) tV ~ (3) x 3y3z4

(2) ty ~ (4) X 4Y2


(1) lOx s (3) lOx s

(2) 12x 8 (4) 12x l5



(2) 12xy4 (4) 12x 2y 3


I Ii

(2) 5x o (4) 6X 2ll


(1)8x 1 y3 (3)8x 3 y4

(2) 8X 3y 3 (4) 8X 2y4


(1) 30x l y~ (3) 30x 5y5

(2) 30X 4 y 6 (4) 30X 5 y 6



(2) --1 x y 4 (4) ~x3y4 9 18



(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2


(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2


(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6


(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl


(l) I (3) 2 3

(2) 16 (4) 25


(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8


x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8


x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

I I




(1)(14) (3)(38) (2) (16) (4) (2 cS)



-lt-- - - - - - ~ - -c - - -~ - -

~



(1) ylt3 (3) yS 3

(2) y gt 3 (4) 123

5

6



~- t ~

- - )

--

-----+c- shy

)

-- bull

1 (1) y lt 2x +] (3) y lt --x +- 1

2

1(2) y lt -2x + 1 (4) ylt--x+l

2


j (I~~--l y

3 J

(1) ygt-x+2 (3) yzmiddot-x+22 2 3 3

(2) ylt-x+2 (4) yS--x+2 2 2

---- --- - --- ----

2




(1) (I i) (3) (L~)

(2) (~3) (4) (2~) 2






bullbull( f 1 (1) 04) (3) (71) (2)(28) (4)(-57)


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6



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8




r-----~-------c-------------------------

----- -middot1

- -jshy

2







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1middot1

12

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2middot

01 2 J 5 6





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3

4




11

60t---shy

55

50 -r -+---+-------+----lr--j

I ---+-+---t---j

35shy ~ g 30 - I

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Time (sec)





I ~-+-+-+-1f-+-+--l-+--i-t--+-+--I-I-t--+--+-+-I

10 15 20


5











jet



y

E 12 2gt OJ

c 8

4

-

4 to

10




y=3x) +6x--l bull 1~~ I - It ~

(1 ) (L8) (3) (-38) (2) (-1-4) (4) (344)


y = 2x 2 +8x+9

(1) (233) (3) (-2-15) (2) (217) (4) (-21)


















3((








I 1--- r--- l----r-i-TshyI I

~ --f------shy

I

--f-- shy

-- shy

- shy

- shy

- shy - shy

-- shy

f--- shy -shy

f- shy -

r- shy --

LtJ

19




i I I


I Iii-- r-- j--i --- - 1- - -----_I__-----_~------





21






I C( (



(1) -15xy3-3x 3y 2 (3) -15x 2J)-3x 2y

(7) -15xy3 - 3x 3y (4) -15x v3 + xv


(1) 6- - 151 (3) 61 2 - 151 bull l )~

(2) 6r -5 (4) 62 -15


(l) c2 + 3c - 40 (J) c 1

+ 13c - 40

(2) c2 - 3c - 40 (4) c2

- 40


(1) X 2

- 36 (3) X 2 - 12x + 36

(2) x 2 + 36 (4) X2 -+ 12x + 36


(1) 0 4 +- b4 (3) a~ + 2a l b2 + b4

4 l b2 4 + b4(2) 0 + a + b4 (4) 0 + 4b 2


(1) -2x (3) x-+2 (2) 2x (4) x - 2


(1) 3x 2 + 2x (3) 4x 2 + 2x

(2) 3x 2 +2x+l (4) 4x 2 -+-2x+]


(l) 5x 2 - 6x + 1 (3) 5x 2

- 60x 2 + 1Ox ((--_li

(2) 5x 3 - 6x 2 + x (4) 5x 2

- 6x

1( -)( ~x



4x l) 4x(1) --- () ---- shy

3( x + 1)

4x 2

(2) --- (4) 4(x~22 l

J J


x + I 3y - 3 (1) x (3) x + 3

x(2) -- (4) ~+~ )

J J


x+3


4c +x x+4




x 2 +1x-15 2x- 6


x 2 + 2x (1)x (3) - shy

2(x + 5)

x(2)x+5 (4)-shy

x+5

6 2 2

f f 3x -27 d ) x -7x+12




(II)1I X + ] 3x - 15 2x - 8x-l0

8



x-4 --- ----- ------ -- shy

x- -)X _ - x - i 2 Xl - 3x -r 1G



(2) 7e3 (4) 7 ~


(2) 8-6-5 (4)19C


(1) 5-3-4 (3)12 C 3

(2) 5 + 3 +4 (4) 12 P3



(1)90 (3) uC

(2)72 (4) uP


I111 (1)9 (3)24

(2) 12 (4)29








(2) 25 (4) 75










16



(I) 6 (3) 50 (2) 12 (4) 53




(1) 27deg (3) 39

(2) 27~~ (4) 324


(1) 2 (3) 85

(2) i~ (4) 86


( 1) tV ~ (3) x 3y3z4

(2) ty ~ (4) X 4Y2


(1) lOx s (3) lOx s

(2) 12x 8 (4) 12x l5



(2) 12xy4 (4) 12x 2y 3


I Ii

(2) 5x o (4) 6X 2ll


(1)8x 1 y3 (3)8x 3 y4

(2) 8X 3y 3 (4) 8X 2y4


(1) 30x l y~ (3) 30x 5y5

(2) 30X 4 y 6 (4) 30X 5 y 6



(2) --1 x y 4 (4) ~x3y4 9 18



(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2


(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2


(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6


(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl


(l) I (3) 2 3

(2) 16 (4) 25


(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8


x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8


x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

I I

5

6



~- t ~

- - )

--

-----+c- shy

)

-- bull

1 (1) y lt 2x +] (3) y lt --x +- 1

2

1(2) y lt -2x + 1 (4) ylt--x+l

2


j (I~~--l y

3 J

(1) ygt-x+2 (3) yzmiddot-x+22 2 3 3

(2) ylt-x+2 (4) yS--x+2 2 2

---- --- - --- ----

2




(1) (I i) (3) (L~)

(2) (~3) (4) (2~) 2






bullbull( f 1 (1) 04) (3) (71) (2)(28) (4)(-57)


( J)

6



I optional]



I optional]

8




r-----~-------c-------------------------

----- -middot1

- -jshy

2







lV

1middot1

12

~I---

2middot

01 2 J 5 6





y

o

)

l j

3

4




11

60t---shy

55

50 -r -+---+-------+----lr--j

I ---+-+---t---j

35shy ~ g 30 - I

----

_j


Time (sec)





I ~-+-+-+-1f-+-+--l-+--i-t--+-+--I-I-t--+--+-+-I

10 15 20


5











jet



y

E 12 2gt OJ

c 8

4

-

4 to

10




y=3x) +6x--l bull 1~~ I - It ~

(1 ) (L8) (3) (-38) (2) (-1-4) (4) (344)


y = 2x 2 +8x+9

(1) (233) (3) (-2-15) (2) (217) (4) (-21)


















3((








I 1--- r--- l----r-i-TshyI I

~ --f------shy

I

--f-- shy

-- shy

- shy

- shy

- shy - shy

-- shy

f--- shy -shy

f- shy -

r- shy --

LtJ

19




i I I


I Iii-- r-- j--i --- - 1- - -----_I__-----_~------





21






I C( (



(1) -15xy3-3x 3y 2 (3) -15x 2J)-3x 2y

(7) -15xy3 - 3x 3y (4) -15x v3 + xv


(1) 6- - 151 (3) 61 2 - 151 bull l )~

(2) 6r -5 (4) 62 -15


(l) c2 + 3c - 40 (J) c 1

+ 13c - 40

(2) c2 - 3c - 40 (4) c2

- 40


(1) X 2

- 36 (3) X 2 - 12x + 36

(2) x 2 + 36 (4) X2 -+ 12x + 36


(1) 0 4 +- b4 (3) a~ + 2a l b2 + b4

4 l b2 4 + b4(2) 0 + a + b4 (4) 0 + 4b 2


(1) -2x (3) x-+2 (2) 2x (4) x - 2


(1) 3x 2 + 2x (3) 4x 2 + 2x

(2) 3x 2 +2x+l (4) 4x 2 -+-2x+]


(l) 5x 2 - 6x + 1 (3) 5x 2

- 60x 2 + 1Ox ((--_li

(2) 5x 3 - 6x 2 + x (4) 5x 2

- 6x

1( -)( ~x



4x l) 4x(1) --- () ---- shy

3( x + 1)

4x 2

(2) --- (4) 4(x~22 l

J J


x + I 3y - 3 (1) x (3) x + 3

x(2) -- (4) ~+~ )

J J


x+3


4c +x x+4




x 2 +1x-15 2x- 6


x 2 + 2x (1)x (3) - shy

2(x + 5)

x(2)x+5 (4)-shy

x+5

6 2 2

f f 3x -27 d ) x -7x+12




(II)1I X + ] 3x - 15 2x - 8x-l0

8



x-4 --- ----- ------ -- shy

x- -)X _ - x - i 2 Xl - 3x -r 1G



(2) 7e3 (4) 7 ~


(2) 8-6-5 (4)19C


(1) 5-3-4 (3)12 C 3

(2) 5 + 3 +4 (4) 12 P3



(1)90 (3) uC

(2)72 (4) uP


I111 (1)9 (3)24

(2) 12 (4)29








(2) 25 (4) 75










16



(I) 6 (3) 50 (2) 12 (4) 53




(1) 27deg (3) 39

(2) 27~~ (4) 324


(1) 2 (3) 85

(2) i~ (4) 86


( 1) tV ~ (3) x 3y3z4

(2) ty ~ (4) X 4Y2


(1) lOx s (3) lOx s

(2) 12x 8 (4) 12x l5



(2) 12xy4 (4) 12x 2y 3


I Ii

(2) 5x o (4) 6X 2ll


(1)8x 1 y3 (3)8x 3 y4

(2) 8X 3y 3 (4) 8X 2y4


(1) 30x l y~ (3) 30x 5y5

(2) 30X 4 y 6 (4) 30X 5 y 6



(2) --1 x y 4 (4) ~x3y4 9 18



(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2


(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2


(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6


(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl


(l) I (3) 2 3

(2) 16 (4) 25


(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8


x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8


x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

I I

---- --- - --- ----

2




(1) (I i) (3) (L~)

(2) (~3) (4) (2~) 2






bullbull( f 1 (1) 04) (3) (71) (2)(28) (4)(-57)


( J)

6



I optional]



I optional]

8




r-----~-------c-------------------------

----- -middot1

- -jshy

2







lV

1middot1

12

~I---

2middot

01 2 J 5 6





y

o

)

l j

3

4




11

60t---shy

55

50 -r -+---+-------+----lr--j

I ---+-+---t---j

35shy ~ g 30 - I

----

_j


Time (sec)





I ~-+-+-+-1f-+-+--l-+--i-t--+-+--I-I-t--+--+-+-I

10 15 20


5











jet



y

E 12 2gt OJ

c 8

4

-

4 to

10




y=3x) +6x--l bull 1~~ I - It ~

(1 ) (L8) (3) (-38) (2) (-1-4) (4) (344)


y = 2x 2 +8x+9

(1) (233) (3) (-2-15) (2) (217) (4) (-21)


















3((








I 1--- r--- l----r-i-TshyI I

~ --f------shy

I

--f-- shy

-- shy

- shy

- shy

- shy - shy

-- shy

f--- shy -shy

f- shy -

r- shy --

LtJ

19




i I I


I Iii-- r-- j--i --- - 1- - -----_I__-----_~------





21






I C( (



(1) -15xy3-3x 3y 2 (3) -15x 2J)-3x 2y

(7) -15xy3 - 3x 3y (4) -15x v3 + xv


(1) 6- - 151 (3) 61 2 - 151 bull l )~

(2) 6r -5 (4) 62 -15


(l) c2 + 3c - 40 (J) c 1

+ 13c - 40

(2) c2 - 3c - 40 (4) c2

- 40


(1) X 2

- 36 (3) X 2 - 12x + 36

(2) x 2 + 36 (4) X2 -+ 12x + 36


(1) 0 4 +- b4 (3) a~ + 2a l b2 + b4

4 l b2 4 + b4(2) 0 + a + b4 (4) 0 + 4b 2


(1) -2x (3) x-+2 (2) 2x (4) x - 2


(1) 3x 2 + 2x (3) 4x 2 + 2x

(2) 3x 2 +2x+l (4) 4x 2 -+-2x+]


(l) 5x 2 - 6x + 1 (3) 5x 2

- 60x 2 + 1Ox ((--_li

(2) 5x 3 - 6x 2 + x (4) 5x 2

- 6x

1( -)( ~x



4x l) 4x(1) --- () ---- shy

3( x + 1)

4x 2

(2) --- (4) 4(x~22 l

J J


x + I 3y - 3 (1) x (3) x + 3

x(2) -- (4) ~+~ )

J J


x+3


4c +x x+4




x 2 +1x-15 2x- 6


x 2 + 2x (1)x (3) - shy

2(x + 5)

x(2)x+5 (4)-shy

x+5

6 2 2

f f 3x -27 d ) x -7x+12




(II)1I X + ] 3x - 15 2x - 8x-l0

8



x-4 --- ----- ------ -- shy

x- -)X _ - x - i 2 Xl - 3x -r 1G



(2) 7e3 (4) 7 ~


(2) 8-6-5 (4)19C


(1) 5-3-4 (3)12 C 3

(2) 5 + 3 +4 (4) 12 P3



(1)90 (3) uC

(2)72 (4) uP


I111 (1)9 (3)24

(2) 12 (4)29








(2) 25 (4) 75










16



(I) 6 (3) 50 (2) 12 (4) 53




(1) 27deg (3) 39

(2) 27~~ (4) 324


(1) 2 (3) 85

(2) i~ (4) 86


( 1) tV ~ (3) x 3y3z4

(2) ty ~ (4) X 4Y2


(1) lOx s (3) lOx s

(2) 12x 8 (4) 12x l5



(2) 12xy4 (4) 12x 2y 3


I Ii

(2) 5x o (4) 6X 2ll


(1)8x 1 y3 (3)8x 3 y4

(2) 8X 3y 3 (4) 8X 2y4


(1) 30x l y~ (3) 30x 5y5

(2) 30X 4 y 6 (4) 30X 5 y 6



(2) --1 x y 4 (4) ~x3y4 9 18



(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2


(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2


(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6


(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl


(l) I (3) 2 3

(2) 16 (4) 25


(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8


x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8


x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

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Time (sec)





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10 15 20


5











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y=3x) +6x--l bull 1~~ I - It ~

(1 ) (L8) (3) (-38) (2) (-1-4) (4) (344)


y = 2x 2 +8x+9

(1) (233) (3) (-2-15) (2) (217) (4) (-21)


















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19




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21






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(1) -15xy3-3x 3y 2 (3) -15x 2J)-3x 2y

(7) -15xy3 - 3x 3y (4) -15x v3 + xv


(1) 6- - 151 (3) 61 2 - 151 bull l )~

(2) 6r -5 (4) 62 -15


(l) c2 + 3c - 40 (J) c 1

+ 13c - 40

(2) c2 - 3c - 40 (4) c2

- 40


(1) X 2

- 36 (3) X 2 - 12x + 36

(2) x 2 + 36 (4) X2 -+ 12x + 36


(1) 0 4 +- b4 (3) a~ + 2a l b2 + b4

4 l b2 4 + b4(2) 0 + a + b4 (4) 0 + 4b 2


(1) -2x (3) x-+2 (2) 2x (4) x - 2


(1) 3x 2 + 2x (3) 4x 2 + 2x

(2) 3x 2 +2x+l (4) 4x 2 -+-2x+]


(l) 5x 2 - 6x + 1 (3) 5x 2

- 60x 2 + 1Ox ((--_li

(2) 5x 3 - 6x 2 + x (4) 5x 2

- 6x

1( -)( ~x



4x l) 4x(1) --- () ---- shy

3( x + 1)

4x 2

(2) --- (4) 4(x~22 l

J J


x + I 3y - 3 (1) x (3) x + 3

x(2) -- (4) ~+~ )

J J


x+3


4c +x x+4




x 2 +1x-15 2x- 6


x 2 + 2x (1)x (3) - shy

2(x + 5)

x(2)x+5 (4)-shy

x+5

6 2 2

f f 3x -27 d ) x -7x+12




(II)1I X + ] 3x - 15 2x - 8x-l0

8



x-4 --- ----- ------ -- shy

x- -)X _ - x - i 2 Xl - 3x -r 1G



(2) 7e3 (4) 7 ~


(2) 8-6-5 (4)19C


(1) 5-3-4 (3)12 C 3

(2) 5 + 3 +4 (4) 12 P3



(1)90 (3) uC

(2)72 (4) uP


I111 (1)9 (3)24

(2) 12 (4)29








(2) 25 (4) 75










16



(I) 6 (3) 50 (2) 12 (4) 53




(1) 27deg (3) 39

(2) 27~~ (4) 324


(1) 2 (3) 85

(2) i~ (4) 86


( 1) tV ~ (3) x 3y3z4

(2) ty ~ (4) X 4Y2


(1) lOx s (3) lOx s

(2) 12x 8 (4) 12x l5



(2) 12xy4 (4) 12x 2y 3


I Ii

(2) 5x o (4) 6X 2ll


(1)8x 1 y3 (3)8x 3 y4

(2) 8X 3y 3 (4) 8X 2y4


(1) 30x l y~ (3) 30x 5y5

(2) 30X 4 y 6 (4) 30X 5 y 6



(2) --1 x y 4 (4) ~x3y4 9 18



(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2


(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2


(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6


(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl


(l) I (3) 2 3

(2) 16 (4) 25


(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8


x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8


x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

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Time (sec)





I ~-+-+-+-1f-+-+--l-+--i-t--+-+--I-I-t--+--+-+-I

10 15 20


5











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y=3x) +6x--l bull 1~~ I - It ~

(1 ) (L8) (3) (-38) (2) (-1-4) (4) (344)


y = 2x 2 +8x+9

(1) (233) (3) (-2-15) (2) (217) (4) (-21)


















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19




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(1) -15xy3-3x 3y 2 (3) -15x 2J)-3x 2y

(7) -15xy3 - 3x 3y (4) -15x v3 + xv


(1) 6- - 151 (3) 61 2 - 151 bull l )~

(2) 6r -5 (4) 62 -15


(l) c2 + 3c - 40 (J) c 1

+ 13c - 40

(2) c2 - 3c - 40 (4) c2

- 40


(1) X 2

- 36 (3) X 2 - 12x + 36

(2) x 2 + 36 (4) X2 -+ 12x + 36


(1) 0 4 +- b4 (3) a~ + 2a l b2 + b4

4 l b2 4 + b4(2) 0 + a + b4 (4) 0 + 4b 2


(1) -2x (3) x-+2 (2) 2x (4) x - 2


(1) 3x 2 + 2x (3) 4x 2 + 2x

(2) 3x 2 +2x+l (4) 4x 2 -+-2x+]


(l) 5x 2 - 6x + 1 (3) 5x 2

- 60x 2 + 1Ox ((--_li

(2) 5x 3 - 6x 2 + x (4) 5x 2

- 6x

1( -)( ~x



4x l) 4x(1) --- () ---- shy

3( x + 1)

4x 2

(2) --- (4) 4(x~22 l

J J


x + I 3y - 3 (1) x (3) x + 3

x(2) -- (4) ~+~ )

J J


x+3


4c +x x+4




x 2 +1x-15 2x- 6


x 2 + 2x (1)x (3) - shy

2(x + 5)

x(2)x+5 (4)-shy

x+5

6 2 2

f f 3x -27 d ) x -7x+12




(II)1I X + ] 3x - 15 2x - 8x-l0

8



x-4 --- ----- ------ -- shy

x- -)X _ - x - i 2 Xl - 3x -r 1G



(2) 7e3 (4) 7 ~


(2) 8-6-5 (4)19C


(1) 5-3-4 (3)12 C 3

(2) 5 + 3 +4 (4) 12 P3



(1)90 (3) uC

(2)72 (4) uP


I111 (1)9 (3)24

(2) 12 (4)29








(2) 25 (4) 75










16



(I) 6 (3) 50 (2) 12 (4) 53




(1) 27deg (3) 39

(2) 27~~ (4) 324


(1) 2 (3) 85

(2) i~ (4) 86


( 1) tV ~ (3) x 3y3z4

(2) ty ~ (4) X 4Y2


(1) lOx s (3) lOx s

(2) 12x 8 (4) 12x l5



(2) 12xy4 (4) 12x 2y 3


I Ii

(2) 5x o (4) 6X 2ll


(1)8x 1 y3 (3)8x 3 y4

(2) 8X 3y 3 (4) 8X 2y4


(1) 30x l y~ (3) 30x 5y5

(2) 30X 4 y 6 (4) 30X 5 y 6



(2) --1 x y 4 (4) ~x3y4 9 18



(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2


(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2


(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6


(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl


(l) I (3) 2 3

(2) 16 (4) 25


(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8


x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8


x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

I I

8




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35shy ~ g 30 - I

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Time (sec)





I ~-+-+-+-1f-+-+--l-+--i-t--+-+--I-I-t--+--+-+-I

10 15 20


5











jet



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4

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10




y=3x) +6x--l bull 1~~ I - It ~

(1 ) (L8) (3) (-38) (2) (-1-4) (4) (344)


y = 2x 2 +8x+9

(1) (233) (3) (-2-15) (2) (217) (4) (-21)


















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19




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21






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(1) -15xy3-3x 3y 2 (3) -15x 2J)-3x 2y

(7) -15xy3 - 3x 3y (4) -15x v3 + xv


(1) 6- - 151 (3) 61 2 - 151 bull l )~

(2) 6r -5 (4) 62 -15


(l) c2 + 3c - 40 (J) c 1

+ 13c - 40

(2) c2 - 3c - 40 (4) c2

- 40


(1) X 2

- 36 (3) X 2 - 12x + 36

(2) x 2 + 36 (4) X2 -+ 12x + 36


(1) 0 4 +- b4 (3) a~ + 2a l b2 + b4

4 l b2 4 + b4(2) 0 + a + b4 (4) 0 + 4b 2


(1) -2x (3) x-+2 (2) 2x (4) x - 2


(1) 3x 2 + 2x (3) 4x 2 + 2x

(2) 3x 2 +2x+l (4) 4x 2 -+-2x+]


(l) 5x 2 - 6x + 1 (3) 5x 2

- 60x 2 + 1Ox ((--_li

(2) 5x 3 - 6x 2 + x (4) 5x 2

- 6x

1( -)( ~x



4x l) 4x(1) --- () ---- shy

3( x + 1)

4x 2

(2) --- (4) 4(x~22 l

J J


x + I 3y - 3 (1) x (3) x + 3

x(2) -- (4) ~+~ )

J J


x+3


4c +x x+4




x 2 +1x-15 2x- 6


x 2 + 2x (1)x (3) - shy

2(x + 5)

x(2)x+5 (4)-shy

x+5

6 2 2

f f 3x -27 d ) x -7x+12




(II)1I X + ] 3x - 15 2x - 8x-l0

8



x-4 --- ----- ------ -- shy

x- -)X _ - x - i 2 Xl - 3x -r 1G



(2) 7e3 (4) 7 ~


(2) 8-6-5 (4)19C


(1) 5-3-4 (3)12 C 3

(2) 5 + 3 +4 (4) 12 P3



(1)90 (3) uC

(2)72 (4) uP


I111 (1)9 (3)24

(2) 12 (4)29








(2) 25 (4) 75










16



(I) 6 (3) 50 (2) 12 (4) 53




(1) 27deg (3) 39

(2) 27~~ (4) 324


(1) 2 (3) 85

(2) i~ (4) 86


( 1) tV ~ (3) x 3y3z4

(2) ty ~ (4) X 4Y2


(1) lOx s (3) lOx s

(2) 12x 8 (4) 12x l5



(2) 12xy4 (4) 12x 2y 3


I Ii

(2) 5x o (4) 6X 2ll


(1)8x 1 y3 (3)8x 3 y4

(2) 8X 3y 3 (4) 8X 2y4


(1) 30x l y~ (3) 30x 5y5

(2) 30X 4 y 6 (4) 30X 5 y 6



(2) --1 x y 4 (4) ~x3y4 9 18



(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2


(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2


(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6


(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl


(l) I (3) 2 3

(2) 16 (4) 25


(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8


x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8


x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

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35shy ~ g 30 - I

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Time (sec)





I ~-+-+-+-1f-+-+--l-+--i-t--+-+--I-I-t--+--+-+-I

10 15 20


5











jet



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c 8

4

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10




y=3x) +6x--l bull 1~~ I - It ~

(1 ) (L8) (3) (-38) (2) (-1-4) (4) (344)


y = 2x 2 +8x+9

(1) (233) (3) (-2-15) (2) (217) (4) (-21)


















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19




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21






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(1) -15xy3-3x 3y 2 (3) -15x 2J)-3x 2y

(7) -15xy3 - 3x 3y (4) -15x v3 + xv


(1) 6- - 151 (3) 61 2 - 151 bull l )~

(2) 6r -5 (4) 62 -15


(l) c2 + 3c - 40 (J) c 1

+ 13c - 40

(2) c2 - 3c - 40 (4) c2

- 40


(1) X 2

- 36 (3) X 2 - 12x + 36

(2) x 2 + 36 (4) X2 -+ 12x + 36


(1) 0 4 +- b4 (3) a~ + 2a l b2 + b4

4 l b2 4 + b4(2) 0 + a + b4 (4) 0 + 4b 2


(1) -2x (3) x-+2 (2) 2x (4) x - 2


(1) 3x 2 + 2x (3) 4x 2 + 2x

(2) 3x 2 +2x+l (4) 4x 2 -+-2x+]


(l) 5x 2 - 6x + 1 (3) 5x 2

- 60x 2 + 1Ox ((--_li

(2) 5x 3 - 6x 2 + x (4) 5x 2

- 6x

1( -)( ~x



4x l) 4x(1) --- () ---- shy

3( x + 1)

4x 2

(2) --- (4) 4(x~22 l

J J


x + I 3y - 3 (1) x (3) x + 3

x(2) -- (4) ~+~ )

J J


x+3


4c +x x+4




x 2 +1x-15 2x- 6


x 2 + 2x (1)x (3) - shy

2(x + 5)

x(2)x+5 (4)-shy

x+5

6 2 2

f f 3x -27 d ) x -7x+12




(II)1I X + ] 3x - 15 2x - 8x-l0

8



x-4 --- ----- ------ -- shy

x- -)X _ - x - i 2 Xl - 3x -r 1G



(2) 7e3 (4) 7 ~


(2) 8-6-5 (4)19C


(1) 5-3-4 (3)12 C 3

(2) 5 + 3 +4 (4) 12 P3



(1)90 (3) uC

(2)72 (4) uP


I111 (1)9 (3)24

(2) 12 (4)29








(2) 25 (4) 75










16



(I) 6 (3) 50 (2) 12 (4) 53




(1) 27deg (3) 39

(2) 27~~ (4) 324


(1) 2 (3) 85

(2) i~ (4) 86


( 1) tV ~ (3) x 3y3z4

(2) ty ~ (4) X 4Y2


(1) lOx s (3) lOx s

(2) 12x 8 (4) 12x l5



(2) 12xy4 (4) 12x 2y 3


I Ii

(2) 5x o (4) 6X 2ll


(1)8x 1 y3 (3)8x 3 y4

(2) 8X 3y 3 (4) 8X 2y4


(1) 30x l y~ (3) 30x 5y5

(2) 30X 4 y 6 (4) 30X 5 y 6



(2) --1 x y 4 (4) ~x3y4 9 18



(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2


(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2


(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6


(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl


(l) I (3) 2 3

(2) 16 (4) 25


(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8


x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8


x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

I I

3

4




11

60t---shy

55

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I ---+-+---t---j

35shy ~ g 30 - I

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Time (sec)





I ~-+-+-+-1f-+-+--l-+--i-t--+-+--I-I-t--+--+-+-I

10 15 20


5











jet



y

E 12 2gt OJ

c 8

4

-

4 to

10




y=3x) +6x--l bull 1~~ I - It ~

(1 ) (L8) (3) (-38) (2) (-1-4) (4) (344)


y = 2x 2 +8x+9

(1) (233) (3) (-2-15) (2) (217) (4) (-21)


















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19




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21






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(1) -15xy3-3x 3y 2 (3) -15x 2J)-3x 2y

(7) -15xy3 - 3x 3y (4) -15x v3 + xv


(1) 6- - 151 (3) 61 2 - 151 bull l )~

(2) 6r -5 (4) 62 -15


(l) c2 + 3c - 40 (J) c 1

+ 13c - 40

(2) c2 - 3c - 40 (4) c2

- 40


(1) X 2

- 36 (3) X 2 - 12x + 36

(2) x 2 + 36 (4) X2 -+ 12x + 36


(1) 0 4 +- b4 (3) a~ + 2a l b2 + b4

4 l b2 4 + b4(2) 0 + a + b4 (4) 0 + 4b 2


(1) -2x (3) x-+2 (2) 2x (4) x - 2


(1) 3x 2 + 2x (3) 4x 2 + 2x

(2) 3x 2 +2x+l (4) 4x 2 -+-2x+]


(l) 5x 2 - 6x + 1 (3) 5x 2

- 60x 2 + 1Ox ((--_li

(2) 5x 3 - 6x 2 + x (4) 5x 2

- 6x

1( -)( ~x



4x l) 4x(1) --- () ---- shy

3( x + 1)

4x 2

(2) --- (4) 4(x~22 l

J J


x + I 3y - 3 (1) x (3) x + 3

x(2) -- (4) ~+~ )

J J


x+3


4c +x x+4




x 2 +1x-15 2x- 6


x 2 + 2x (1)x (3) - shy

2(x + 5)

x(2)x+5 (4)-shy

x+5

6 2 2

f f 3x -27 d ) x -7x+12




(II)1I X + ] 3x - 15 2x - 8x-l0

8



x-4 --- ----- ------ -- shy

x- -)X _ - x - i 2 Xl - 3x -r 1G



(2) 7e3 (4) 7 ~


(2) 8-6-5 (4)19C


(1) 5-3-4 (3)12 C 3

(2) 5 + 3 +4 (4) 12 P3



(1)90 (3) uC

(2)72 (4) uP


I111 (1)9 (3)24

(2) 12 (4)29








(2) 25 (4) 75










16



(I) 6 (3) 50 (2) 12 (4) 53




(1) 27deg (3) 39

(2) 27~~ (4) 324


(1) 2 (3) 85

(2) i~ (4) 86


( 1) tV ~ (3) x 3y3z4

(2) ty ~ (4) X 4Y2


(1) lOx s (3) lOx s

(2) 12x 8 (4) 12x l5



(2) 12xy4 (4) 12x 2y 3


I Ii

(2) 5x o (4) 6X 2ll


(1)8x 1 y3 (3)8x 3 y4

(2) 8X 3y 3 (4) 8X 2y4


(1) 30x l y~ (3) 30x 5y5

(2) 30X 4 y 6 (4) 30X 5 y 6



(2) --1 x y 4 (4) ~x3y4 9 18



(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2


(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2


(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6


(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl


(l) I (3) 2 3

(2) 16 (4) 25


(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8


x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8


x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

I I

5











jet



y

E 12 2gt OJ

c 8

4

-

4 to

10




y=3x) +6x--l bull 1~~ I - It ~

(1 ) (L8) (3) (-38) (2) (-1-4) (4) (344)


y = 2x 2 +8x+9

(1) (233) (3) (-2-15) (2) (217) (4) (-21)


















3((








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~ --f------shy

I

--f-- shy

-- shy

- shy

- shy

- shy - shy

-- shy

f--- shy -shy

f- shy -

r- shy --

LtJ

19




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I Iii-- r-- j--i --- - 1- - -----_I__-----_~------





21






I C( (



(1) -15xy3-3x 3y 2 (3) -15x 2J)-3x 2y

(7) -15xy3 - 3x 3y (4) -15x v3 + xv


(1) 6- - 151 (3) 61 2 - 151 bull l )~

(2) 6r -5 (4) 62 -15


(l) c2 + 3c - 40 (J) c 1

+ 13c - 40

(2) c2 - 3c - 40 (4) c2

- 40


(1) X 2

- 36 (3) X 2 - 12x + 36

(2) x 2 + 36 (4) X2 -+ 12x + 36


(1) 0 4 +- b4 (3) a~ + 2a l b2 + b4

4 l b2 4 + b4(2) 0 + a + b4 (4) 0 + 4b 2


(1) -2x (3) x-+2 (2) 2x (4) x - 2


(1) 3x 2 + 2x (3) 4x 2 + 2x

(2) 3x 2 +2x+l (4) 4x 2 -+-2x+]


(l) 5x 2 - 6x + 1 (3) 5x 2

- 60x 2 + 1Ox ((--_li

(2) 5x 3 - 6x 2 + x (4) 5x 2

- 6x

1( -)( ~x



4x l) 4x(1) --- () ---- shy

3( x + 1)

4x 2

(2) --- (4) 4(x~22 l

J J


x + I 3y - 3 (1) x (3) x + 3

x(2) -- (4) ~+~ )

J J


x+3


4c +x x+4




x 2 +1x-15 2x- 6


x 2 + 2x (1)x (3) - shy

2(x + 5)

x(2)x+5 (4)-shy

x+5

6 2 2

f f 3x -27 d ) x -7x+12




(II)1I X + ] 3x - 15 2x - 8x-l0

8



x-4 --- ----- ------ -- shy

x- -)X _ - x - i 2 Xl - 3x -r 1G



(2) 7e3 (4) 7 ~


(2) 8-6-5 (4)19C


(1) 5-3-4 (3)12 C 3

(2) 5 + 3 +4 (4) 12 P3



(1)90 (3) uC

(2)72 (4) uP


I111 (1)9 (3)24

(2) 12 (4)29








(2) 25 (4) 75










16



(I) 6 (3) 50 (2) 12 (4) 53




(1) 27deg (3) 39

(2) 27~~ (4) 324


(1) 2 (3) 85

(2) i~ (4) 86


( 1) tV ~ (3) x 3y3z4

(2) ty ~ (4) X 4Y2


(1) lOx s (3) lOx s

(2) 12x 8 (4) 12x l5



(2) 12xy4 (4) 12x 2y 3


I Ii

(2) 5x o (4) 6X 2ll


(1)8x 1 y3 (3)8x 3 y4

(2) 8X 3y 3 (4) 8X 2y4


(1) 30x l y~ (3) 30x 5y5

(2) 30X 4 y 6 (4) 30X 5 y 6



(2) --1 x y 4 (4) ~x3y4 9 18



(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2


(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2


(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6


(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl


(l) I (3) 2 3

(2) 16 (4) 25


(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8


x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8


x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

I I





jet



y

E 12 2gt OJ

c 8

4

-

4 to

10




y=3x) +6x--l bull 1~~ I - It ~

(1 ) (L8) (3) (-38) (2) (-1-4) (4) (344)


y = 2x 2 +8x+9

(1) (233) (3) (-2-15) (2) (217) (4) (-21)


















3((








I 1--- r--- l----r-i-TshyI I

~ --f------shy

I

--f-- shy

-- shy

- shy

- shy

- shy - shy

-- shy

f--- shy -shy

f- shy -

r- shy --

LtJ

19




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I Iii-- r-- j--i --- - 1- - -----_I__-----_~------





21






I C( (



(1) -15xy3-3x 3y 2 (3) -15x 2J)-3x 2y

(7) -15xy3 - 3x 3y (4) -15x v3 + xv


(1) 6- - 151 (3) 61 2 - 151 bull l )~

(2) 6r -5 (4) 62 -15


(l) c2 + 3c - 40 (J) c 1

+ 13c - 40

(2) c2 - 3c - 40 (4) c2

- 40


(1) X 2

- 36 (3) X 2 - 12x + 36

(2) x 2 + 36 (4) X2 -+ 12x + 36


(1) 0 4 +- b4 (3) a~ + 2a l b2 + b4

4 l b2 4 + b4(2) 0 + a + b4 (4) 0 + 4b 2


(1) -2x (3) x-+2 (2) 2x (4) x - 2


(1) 3x 2 + 2x (3) 4x 2 + 2x

(2) 3x 2 +2x+l (4) 4x 2 -+-2x+]


(l) 5x 2 - 6x + 1 (3) 5x 2

- 60x 2 + 1Ox ((--_li

(2) 5x 3 - 6x 2 + x (4) 5x 2

- 6x

1( -)( ~x



4x l) 4x(1) --- () ---- shy

3( x + 1)

4x 2

(2) --- (4) 4(x~22 l

J J


x + I 3y - 3 (1) x (3) x + 3

x(2) -- (4) ~+~ )

J J


x+3


4c +x x+4




x 2 +1x-15 2x- 6


x 2 + 2x (1)x (3) - shy

2(x + 5)

x(2)x+5 (4)-shy

x+5

6 2 2

f f 3x -27 d ) x -7x+12




(II)1I X + ] 3x - 15 2x - 8x-l0

8



x-4 --- ----- ------ -- shy

x- -)X _ - x - i 2 Xl - 3x -r 1G



(2) 7e3 (4) 7 ~


(2) 8-6-5 (4)19C


(1) 5-3-4 (3)12 C 3

(2) 5 + 3 +4 (4) 12 P3



(1)90 (3) uC

(2)72 (4) uP


I111 (1)9 (3)24

(2) 12 (4)29








(2) 25 (4) 75










16



(I) 6 (3) 50 (2) 12 (4) 53




(1) 27deg (3) 39

(2) 27~~ (4) 324


(1) 2 (3) 85

(2) i~ (4) 86


( 1) tV ~ (3) x 3y3z4

(2) ty ~ (4) X 4Y2


(1) lOx s (3) lOx s

(2) 12x 8 (4) 12x l5



(2) 12xy4 (4) 12x 2y 3


I Ii

(2) 5x o (4) 6X 2ll


(1)8x 1 y3 (3)8x 3 y4

(2) 8X 3y 3 (4) 8X 2y4


(1) 30x l y~ (3) 30x 5y5

(2) 30X 4 y 6 (4) 30X 5 y 6



(2) --1 x y 4 (4) ~x3y4 9 18



(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2


(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2


(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6


(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl


(l) I (3) 2 3

(2) 16 (4) 25


(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8


x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8


x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

I I



y

E 12 2gt OJ

c 8

4

-

4 to

10




y=3x) +6x--l bull 1~~ I - It ~

(1 ) (L8) (3) (-38) (2) (-1-4) (4) (344)


y = 2x 2 +8x+9

(1) (233) (3) (-2-15) (2) (217) (4) (-21)


















3((








I 1--- r--- l----r-i-TshyI I

~ --f------shy

I

--f-- shy

-- shy

- shy

- shy

- shy - shy

-- shy

f--- shy -shy

f- shy -

r- shy --

LtJ

19




i I I


I Iii-- r-- j--i --- - 1- - -----_I__-----_~------





21






I C( (



(1) -15xy3-3x 3y 2 (3) -15x 2J)-3x 2y

(7) -15xy3 - 3x 3y (4) -15x v3 + xv


(1) 6- - 151 (3) 61 2 - 151 bull l )~

(2) 6r -5 (4) 62 -15


(l) c2 + 3c - 40 (J) c 1

+ 13c - 40

(2) c2 - 3c - 40 (4) c2

- 40


(1) X 2

- 36 (3) X 2 - 12x + 36

(2) x 2 + 36 (4) X2 -+ 12x + 36


(1) 0 4 +- b4 (3) a~ + 2a l b2 + b4

4 l b2 4 + b4(2) 0 + a + b4 (4) 0 + 4b 2


(1) -2x (3) x-+2 (2) 2x (4) x - 2


(1) 3x 2 + 2x (3) 4x 2 + 2x

(2) 3x 2 +2x+l (4) 4x 2 -+-2x+]


(l) 5x 2 - 6x + 1 (3) 5x 2

- 60x 2 + 1Ox ((--_li

(2) 5x 3 - 6x 2 + x (4) 5x 2

- 6x

1( -)( ~x



4x l) 4x(1) --- () ---- shy

3( x + 1)

4x 2

(2) --- (4) 4(x~22 l

J J


x + I 3y - 3 (1) x (3) x + 3

x(2) -- (4) ~+~ )

J J


x+3


4c +x x+4




x 2 +1x-15 2x- 6


x 2 + 2x (1)x (3) - shy

2(x + 5)

x(2)x+5 (4)-shy

x+5

6 2 2

f f 3x -27 d ) x -7x+12




(II)1I X + ] 3x - 15 2x - 8x-l0

8



x-4 --- ----- ------ -- shy

x- -)X _ - x - i 2 Xl - 3x -r 1G



(2) 7e3 (4) 7 ~


(2) 8-6-5 (4)19C


(1) 5-3-4 (3)12 C 3

(2) 5 + 3 +4 (4) 12 P3



(1)90 (3) uC

(2)72 (4) uP


I111 (1)9 (3)24

(2) 12 (4)29








(2) 25 (4) 75










16



(I) 6 (3) 50 (2) 12 (4) 53




(1) 27deg (3) 39

(2) 27~~ (4) 324


(1) 2 (3) 85

(2) i~ (4) 86


( 1) tV ~ (3) x 3y3z4

(2) ty ~ (4) X 4Y2


(1) lOx s (3) lOx s

(2) 12x 8 (4) 12x l5



(2) 12xy4 (4) 12x 2y 3


I Ii

(2) 5x o (4) 6X 2ll


(1)8x 1 y3 (3)8x 3 y4

(2) 8X 3y 3 (4) 8X 2y4


(1) 30x l y~ (3) 30x 5y5

(2) 30X 4 y 6 (4) 30X 5 y 6



(2) --1 x y 4 (4) ~x3y4 9 18



(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2


(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2


(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6


(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl


(l) I (3) 2 3

(2) 16 (4) 25


(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8


x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8


x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

I I
















3((








I 1--- r--- l----r-i-TshyI I

~ --f------shy

I

--f-- shy

-- shy

- shy

- shy

- shy - shy

-- shy

f--- shy -shy

f- shy -

r- shy --

LtJ

19




i I I


I Iii-- r-- j--i --- - 1- - -----_I__-----_~------





21






I C( (



(1) -15xy3-3x 3y 2 (3) -15x 2J)-3x 2y

(7) -15xy3 - 3x 3y (4) -15x v3 + xv


(1) 6- - 151 (3) 61 2 - 151 bull l )~

(2) 6r -5 (4) 62 -15


(l) c2 + 3c - 40 (J) c 1

+ 13c - 40

(2) c2 - 3c - 40 (4) c2

- 40


(1) X 2

- 36 (3) X 2 - 12x + 36

(2) x 2 + 36 (4) X2 -+ 12x + 36


(1) 0 4 +- b4 (3) a~ + 2a l b2 + b4

4 l b2 4 + b4(2) 0 + a + b4 (4) 0 + 4b 2


(1) -2x (3) x-+2 (2) 2x (4) x - 2


(1) 3x 2 + 2x (3) 4x 2 + 2x

(2) 3x 2 +2x+l (4) 4x 2 -+-2x+]


(l) 5x 2 - 6x + 1 (3) 5x 2

- 60x 2 + 1Ox ((--_li

(2) 5x 3 - 6x 2 + x (4) 5x 2

- 6x

1( -)( ~x



4x l) 4x(1) --- () ---- shy

3( x + 1)

4x 2

(2) --- (4) 4(x~22 l

J J


x + I 3y - 3 (1) x (3) x + 3

x(2) -- (4) ~+~ )

J J


x+3


4c +x x+4




x 2 +1x-15 2x- 6


x 2 + 2x (1)x (3) - shy

2(x + 5)

x(2)x+5 (4)-shy

x+5

6 2 2

f f 3x -27 d ) x -7x+12




(II)1I X + ] 3x - 15 2x - 8x-l0

8



x-4 --- ----- ------ -- shy

x- -)X _ - x - i 2 Xl - 3x -r 1G



(2) 7e3 (4) 7 ~


(2) 8-6-5 (4)19C


(1) 5-3-4 (3)12 C 3

(2) 5 + 3 +4 (4) 12 P3



(1)90 (3) uC

(2)72 (4) uP


I111 (1)9 (3)24

(2) 12 (4)29








(2) 25 (4) 75










16



(I) 6 (3) 50 (2) 12 (4) 53




(1) 27deg (3) 39

(2) 27~~ (4) 324


(1) 2 (3) 85

(2) i~ (4) 86


( 1) tV ~ (3) x 3y3z4

(2) ty ~ (4) X 4Y2


(1) lOx s (3) lOx s

(2) 12x 8 (4) 12x l5



(2) 12xy4 (4) 12x 2y 3


I Ii

(2) 5x o (4) 6X 2ll


(1)8x 1 y3 (3)8x 3 y4

(2) 8X 3y 3 (4) 8X 2y4


(1) 30x l y~ (3) 30x 5y5

(2) 30X 4 y 6 (4) 30X 5 y 6



(2) --1 x y 4 (4) ~x3y4 9 18



(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2


(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2


(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6


(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl


(l) I (3) 2 3

(2) 16 (4) 25


(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8


x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8


x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

I I








I 1--- r--- l----r-i-TshyI I

~ --f------shy

I

--f-- shy

-- shy

- shy

- shy

- shy - shy

-- shy

f--- shy -shy

f- shy -

r- shy --

LtJ

19




i I I


I Iii-- r-- j--i --- - 1- - -----_I__-----_~------





21






I C( (



(1) -15xy3-3x 3y 2 (3) -15x 2J)-3x 2y

(7) -15xy3 - 3x 3y (4) -15x v3 + xv


(1) 6- - 151 (3) 61 2 - 151 bull l )~

(2) 6r -5 (4) 62 -15


(l) c2 + 3c - 40 (J) c 1

+ 13c - 40

(2) c2 - 3c - 40 (4) c2

- 40


(1) X 2

- 36 (3) X 2 - 12x + 36

(2) x 2 + 36 (4) X2 -+ 12x + 36


(1) 0 4 +- b4 (3) a~ + 2a l b2 + b4

4 l b2 4 + b4(2) 0 + a + b4 (4) 0 + 4b 2


(1) -2x (3) x-+2 (2) 2x (4) x - 2


(1) 3x 2 + 2x (3) 4x 2 + 2x

(2) 3x 2 +2x+l (4) 4x 2 -+-2x+]


(l) 5x 2 - 6x + 1 (3) 5x 2

- 60x 2 + 1Ox ((--_li

(2) 5x 3 - 6x 2 + x (4) 5x 2

- 6x

1( -)( ~x



4x l) 4x(1) --- () ---- shy

3( x + 1)

4x 2

(2) --- (4) 4(x~22 l

J J


x + I 3y - 3 (1) x (3) x + 3

x(2) -- (4) ~+~ )

J J


x+3


4c +x x+4




x 2 +1x-15 2x- 6


x 2 + 2x (1)x (3) - shy

2(x + 5)

x(2)x+5 (4)-shy

x+5

6 2 2

f f 3x -27 d ) x -7x+12




(II)1I X + ] 3x - 15 2x - 8x-l0

8



x-4 --- ----- ------ -- shy

x- -)X _ - x - i 2 Xl - 3x -r 1G



(2) 7e3 (4) 7 ~


(2) 8-6-5 (4)19C


(1) 5-3-4 (3)12 C 3

(2) 5 + 3 +4 (4) 12 P3



(1)90 (3) uC

(2)72 (4) uP


I111 (1)9 (3)24

(2) 12 (4)29








(2) 25 (4) 75










16



(I) 6 (3) 50 (2) 12 (4) 53




(1) 27deg (3) 39

(2) 27~~ (4) 324


(1) 2 (3) 85

(2) i~ (4) 86


( 1) tV ~ (3) x 3y3z4

(2) ty ~ (4) X 4Y2


(1) lOx s (3) lOx s

(2) 12x 8 (4) 12x l5



(2) 12xy4 (4) 12x 2y 3


I Ii

(2) 5x o (4) 6X 2ll


(1)8x 1 y3 (3)8x 3 y4

(2) 8X 3y 3 (4) 8X 2y4


(1) 30x l y~ (3) 30x 5y5

(2) 30X 4 y 6 (4) 30X 5 y 6



(2) --1 x y 4 (4) ~x3y4 9 18



(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2


(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2


(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6


(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl


(l) I (3) 2 3

(2) 16 (4) 25


(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8


x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8


x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

I I

19




i I I


I Iii-- r-- j--i --- - 1- - -----_I__-----_~------





21






I C( (



(1) -15xy3-3x 3y 2 (3) -15x 2J)-3x 2y

(7) -15xy3 - 3x 3y (4) -15x v3 + xv


(1) 6- - 151 (3) 61 2 - 151 bull l )~

(2) 6r -5 (4) 62 -15


(l) c2 + 3c - 40 (J) c 1

+ 13c - 40

(2) c2 - 3c - 40 (4) c2

- 40


(1) X 2

- 36 (3) X 2 - 12x + 36

(2) x 2 + 36 (4) X2 -+ 12x + 36


(1) 0 4 +- b4 (3) a~ + 2a l b2 + b4

4 l b2 4 + b4(2) 0 + a + b4 (4) 0 + 4b 2


(1) -2x (3) x-+2 (2) 2x (4) x - 2


(1) 3x 2 + 2x (3) 4x 2 + 2x

(2) 3x 2 +2x+l (4) 4x 2 -+-2x+]


(l) 5x 2 - 6x + 1 (3) 5x 2

- 60x 2 + 1Ox ((--_li

(2) 5x 3 - 6x 2 + x (4) 5x 2

- 6x

1( -)( ~x



4x l) 4x(1) --- () ---- shy

3( x + 1)

4x 2

(2) --- (4) 4(x~22 l

J J


x + I 3y - 3 (1) x (3) x + 3

x(2) -- (4) ~+~ )

J J


x+3


4c +x x+4




x 2 +1x-15 2x- 6


x 2 + 2x (1)x (3) - shy

2(x + 5)

x(2)x+5 (4)-shy

x+5

6 2 2

f f 3x -27 d ) x -7x+12




(II)1I X + ] 3x - 15 2x - 8x-l0

8



x-4 --- ----- ------ -- shy

x- -)X _ - x - i 2 Xl - 3x -r 1G



(2) 7e3 (4) 7 ~


(2) 8-6-5 (4)19C


(1) 5-3-4 (3)12 C 3

(2) 5 + 3 +4 (4) 12 P3



(1)90 (3) uC

(2)72 (4) uP


I111 (1)9 (3)24

(2) 12 (4)29








(2) 25 (4) 75










16



(I) 6 (3) 50 (2) 12 (4) 53




(1) 27deg (3) 39

(2) 27~~ (4) 324


(1) 2 (3) 85

(2) i~ (4) 86


( 1) tV ~ (3) x 3y3z4

(2) ty ~ (4) X 4Y2


(1) lOx s (3) lOx s

(2) 12x 8 (4) 12x l5



(2) 12xy4 (4) 12x 2y 3


I Ii

(2) 5x o (4) 6X 2ll


(1)8x 1 y3 (3)8x 3 y4

(2) 8X 3y 3 (4) 8X 2y4


(1) 30x l y~ (3) 30x 5y5

(2) 30X 4 y 6 (4) 30X 5 y 6



(2) --1 x y 4 (4) ~x3y4 9 18



(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2


(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2


(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6


(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl


(l) I (3) 2 3

(2) 16 (4) 25


(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8


x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8


x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

I I





21






I C( (



(1) -15xy3-3x 3y 2 (3) -15x 2J)-3x 2y

(7) -15xy3 - 3x 3y (4) -15x v3 + xv


(1) 6- - 151 (3) 61 2 - 151 bull l )~

(2) 6r -5 (4) 62 -15


(l) c2 + 3c - 40 (J) c 1

+ 13c - 40

(2) c2 - 3c - 40 (4) c2

- 40


(1) X 2

- 36 (3) X 2 - 12x + 36

(2) x 2 + 36 (4) X2 -+ 12x + 36


(1) 0 4 +- b4 (3) a~ + 2a l b2 + b4

4 l b2 4 + b4(2) 0 + a + b4 (4) 0 + 4b 2


(1) -2x (3) x-+2 (2) 2x (4) x - 2


(1) 3x 2 + 2x (3) 4x 2 + 2x

(2) 3x 2 +2x+l (4) 4x 2 -+-2x+]


(l) 5x 2 - 6x + 1 (3) 5x 2

- 60x 2 + 1Ox ((--_li

(2) 5x 3 - 6x 2 + x (4) 5x 2

- 6x

1( -)( ~x



4x l) 4x(1) --- () ---- shy

3( x + 1)

4x 2

(2) --- (4) 4(x~22 l

J J


x + I 3y - 3 (1) x (3) x + 3

x(2) -- (4) ~+~ )

J J


x+3


4c +x x+4




x 2 +1x-15 2x- 6


x 2 + 2x (1)x (3) - shy

2(x + 5)

x(2)x+5 (4)-shy

x+5

6 2 2

f f 3x -27 d ) x -7x+12




(II)1I X + ] 3x - 15 2x - 8x-l0

8



x-4 --- ----- ------ -- shy

x- -)X _ - x - i 2 Xl - 3x -r 1G



(2) 7e3 (4) 7 ~


(2) 8-6-5 (4)19C


(1) 5-3-4 (3)12 C 3

(2) 5 + 3 +4 (4) 12 P3



(1)90 (3) uC

(2)72 (4) uP


I111 (1)9 (3)24

(2) 12 (4)29








(2) 25 (4) 75










16



(I) 6 (3) 50 (2) 12 (4) 53




(1) 27deg (3) 39

(2) 27~~ (4) 324


(1) 2 (3) 85

(2) i~ (4) 86


( 1) tV ~ (3) x 3y3z4

(2) ty ~ (4) X 4Y2


(1) lOx s (3) lOx s

(2) 12x 8 (4) 12x l5



(2) 12xy4 (4) 12x 2y 3


I Ii

(2) 5x o (4) 6X 2ll


(1)8x 1 y3 (3)8x 3 y4

(2) 8X 3y 3 (4) 8X 2y4


(1) 30x l y~ (3) 30x 5y5

(2) 30X 4 y 6 (4) 30X 5 y 6



(2) --1 x y 4 (4) ~x3y4 9 18



(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2


(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2


(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6


(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl


(l) I (3) 2 3

(2) 16 (4) 25


(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8


x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8


x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

I I



(1) -15xy3-3x 3y 2 (3) -15x 2J)-3x 2y

(7) -15xy3 - 3x 3y (4) -15x v3 + xv


(1) 6- - 151 (3) 61 2 - 151 bull l )~

(2) 6r -5 (4) 62 -15


(l) c2 + 3c - 40 (J) c 1

+ 13c - 40

(2) c2 - 3c - 40 (4) c2

- 40


(1) X 2

- 36 (3) X 2 - 12x + 36

(2) x 2 + 36 (4) X2 -+ 12x + 36


(1) 0 4 +- b4 (3) a~ + 2a l b2 + b4

4 l b2 4 + b4(2) 0 + a + b4 (4) 0 + 4b 2


(1) -2x (3) x-+2 (2) 2x (4) x - 2


(1) 3x 2 + 2x (3) 4x 2 + 2x

(2) 3x 2 +2x+l (4) 4x 2 -+-2x+]


(l) 5x 2 - 6x + 1 (3) 5x 2

- 60x 2 + 1Ox ((--_li

(2) 5x 3 - 6x 2 + x (4) 5x 2

- 6x

1( -)( ~x



4x l) 4x(1) --- () ---- shy

3( x + 1)

4x 2

(2) --- (4) 4(x~22 l

J J


x + I 3y - 3 (1) x (3) x + 3

x(2) -- (4) ~+~ )

J J


x+3


4c +x x+4




x 2 +1x-15 2x- 6


x 2 + 2x (1)x (3) - shy

2(x + 5)

x(2)x+5 (4)-shy

x+5

6 2 2

f f 3x -27 d ) x -7x+12




(II)1I X + ] 3x - 15 2x - 8x-l0

8



x-4 --- ----- ------ -- shy

x- -)X _ - x - i 2 Xl - 3x -r 1G



(2) 7e3 (4) 7 ~


(2) 8-6-5 (4)19C


(1) 5-3-4 (3)12 C 3

(2) 5 + 3 +4 (4) 12 P3



(1)90 (3) uC

(2)72 (4) uP


I111 (1)9 (3)24

(2) 12 (4)29








(2) 25 (4) 75










16



(I) 6 (3) 50 (2) 12 (4) 53




(1) 27deg (3) 39

(2) 27~~ (4) 324


(1) 2 (3) 85

(2) i~ (4) 86


( 1) tV ~ (3) x 3y3z4

(2) ty ~ (4) X 4Y2


(1) lOx s (3) lOx s

(2) 12x 8 (4) 12x l5



(2) 12xy4 (4) 12x 2y 3


I Ii

(2) 5x o (4) 6X 2ll


(1)8x 1 y3 (3)8x 3 y4

(2) 8X 3y 3 (4) 8X 2y4


(1) 30x l y~ (3) 30x 5y5

(2) 30X 4 y 6 (4) 30X 5 y 6



(2) --1 x y 4 (4) ~x3y4 9 18



(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2


(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2


(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6


(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl


(l) I (3) 2 3

(2) 16 (4) 25


(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8


x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8


x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

I I



4x l) 4x(1) --- () ---- shy

3( x + 1)

4x 2

(2) --- (4) 4(x~22 l

J J


x + I 3y - 3 (1) x (3) x + 3

x(2) -- (4) ~+~ )

J J


x+3


4c +x x+4




x 2 +1x-15 2x- 6


x 2 + 2x (1)x (3) - shy

2(x + 5)

x(2)x+5 (4)-shy

x+5

6 2 2

f f 3x -27 d ) x -7x+12




(II)1I X + ] 3x - 15 2x - 8x-l0

8



x-4 --- ----- ------ -- shy

x- -)X _ - x - i 2 Xl - 3x -r 1G



(2) 7e3 (4) 7 ~


(2) 8-6-5 (4)19C


(1) 5-3-4 (3)12 C 3

(2) 5 + 3 +4 (4) 12 P3



(1)90 (3) uC

(2)72 (4) uP


I111 (1)9 (3)24

(2) 12 (4)29








(2) 25 (4) 75










16



(I) 6 (3) 50 (2) 12 (4) 53




(1) 27deg (3) 39

(2) 27~~ (4) 324


(1) 2 (3) 85

(2) i~ (4) 86


( 1) tV ~ (3) x 3y3z4

(2) ty ~ (4) X 4Y2


(1) lOx s (3) lOx s

(2) 12x 8 (4) 12x l5



(2) 12xy4 (4) 12x 2y 3


I Ii

(2) 5x o (4) 6X 2ll


(1)8x 1 y3 (3)8x 3 y4

(2) 8X 3y 3 (4) 8X 2y4


(1) 30x l y~ (3) 30x 5y5

(2) 30X 4 y 6 (4) 30X 5 y 6



(2) --1 x y 4 (4) ~x3y4 9 18



(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2


(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2


(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6


(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl


(l) I (3) 2 3

(2) 16 (4) 25


(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8


x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8


x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

I I

8



x-4 --- ----- ------ -- shy

x- -)X _ - x - i 2 Xl - 3x -r 1G



(2) 7e3 (4) 7 ~


(2) 8-6-5 (4)19C


(1) 5-3-4 (3)12 C 3

(2) 5 + 3 +4 (4) 12 P3



(1)90 (3) uC

(2)72 (4) uP


I111 (1)9 (3)24

(2) 12 (4)29








(2) 25 (4) 75










16



(I) 6 (3) 50 (2) 12 (4) 53




(1) 27deg (3) 39

(2) 27~~ (4) 324


(1) 2 (3) 85

(2) i~ (4) 86


( 1) tV ~ (3) x 3y3z4

(2) ty ~ (4) X 4Y2


(1) lOx s (3) lOx s

(2) 12x 8 (4) 12x l5



(2) 12xy4 (4) 12x 2y 3


I Ii

(2) 5x o (4) 6X 2ll


(1)8x 1 y3 (3)8x 3 y4

(2) 8X 3y 3 (4) 8X 2y4


(1) 30x l y~ (3) 30x 5y5

(2) 30X 4 y 6 (4) 30X 5 y 6



(2) --1 x y 4 (4) ~x3y4 9 18



(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2


(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2


(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6


(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl


(l) I (3) 2 3

(2) 16 (4) 25


(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8


x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8


x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

I I



(2) 7e3 (4) 7 ~


(2) 8-6-5 (4)19C


(1) 5-3-4 (3)12 C 3

(2) 5 + 3 +4 (4) 12 P3



(1)90 (3) uC

(2)72 (4) uP


I111 (1)9 (3)24

(2) 12 (4)29








(2) 25 (4) 75










16



(I) 6 (3) 50 (2) 12 (4) 53




(1) 27deg (3) 39

(2) 27~~ (4) 324


(1) 2 (3) 85

(2) i~ (4) 86


( 1) tV ~ (3) x 3y3z4

(2) ty ~ (4) X 4Y2


(1) lOx s (3) lOx s

(2) 12x 8 (4) 12x l5



(2) 12xy4 (4) 12x 2y 3


I Ii

(2) 5x o (4) 6X 2ll


(1)8x 1 y3 (3)8x 3 y4

(2) 8X 3y 3 (4) 8X 2y4


(1) 30x l y~ (3) 30x 5y5

(2) 30X 4 y 6 (4) 30X 5 y 6



(2) --1 x y 4 (4) ~x3y4 9 18



(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2


(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2


(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6


(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl


(l) I (3) 2 3

(2) 16 (4) 25


(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8


x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8


x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

I I



(2) 25 (4) 75










16



(I) 6 (3) 50 (2) 12 (4) 53




(1) 27deg (3) 39

(2) 27~~ (4) 324


(1) 2 (3) 85

(2) i~ (4) 86


( 1) tV ~ (3) x 3y3z4

(2) ty ~ (4) X 4Y2


(1) lOx s (3) lOx s

(2) 12x 8 (4) 12x l5



(2) 12xy4 (4) 12x 2y 3


I Ii

(2) 5x o (4) 6X 2ll


(1)8x 1 y3 (3)8x 3 y4

(2) 8X 3y 3 (4) 8X 2y4


(1) 30x l y~ (3) 30x 5y5

(2) 30X 4 y 6 (4) 30X 5 y 6



(2) --1 x y 4 (4) ~x3y4 9 18



(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2


(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2


(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6


(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl


(l) I (3) 2 3

(2) 16 (4) 25


(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8


x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8


x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

I I

16



(I) 6 (3) 50 (2) 12 (4) 53




(1) 27deg (3) 39

(2) 27~~ (4) 324


(1) 2 (3) 85

(2) i~ (4) 86


( 1) tV ~ (3) x 3y3z4

(2) ty ~ (4) X 4Y2


(1) lOx s (3) lOx s

(2) 12x 8 (4) 12x l5



(2) 12xy4 (4) 12x 2y 3


I Ii

(2) 5x o (4) 6X 2ll


(1)8x 1 y3 (3)8x 3 y4

(2) 8X 3y 3 (4) 8X 2y4


(1) 30x l y~ (3) 30x 5y5

(2) 30X 4 y 6 (4) 30X 5 y 6



(2) --1 x y 4 (4) ~x3y4 9 18



(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2


(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2


(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6


(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl


(l) I (3) 2 3

(2) 16 (4) 25


(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8


x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8


x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

I I



(1) 27deg (3) 39

(2) 27~~ (4) 324


(1) 2 (3) 85

(2) i~ (4) 86


( 1) tV ~ (3) x 3y3z4

(2) ty ~ (4) X 4Y2


(1) lOx s (3) lOx s

(2) 12x 8 (4) 12x l5



(2) 12xy4 (4) 12x 2y 3


I Ii

(2) 5x o (4) 6X 2ll


(1)8x 1 y3 (3)8x 3 y4

(2) 8X 3y 3 (4) 8X 2y4


(1) 30x l y~ (3) 30x 5y5

(2) 30X 4 y 6 (4) 30X 5 y 6



(2) --1 x y 4 (4) ~x3y4 9 18



(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2


(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2


(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6


(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl


(l) I (3) 2 3

(2) 16 (4) 25


(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8


x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8


x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

I I



(1) 36x 6 y 12 (3) 12x 6 y 2

(2) 36x=y8 (4) 6X 6 y l2


(1) -16a 6Jl (3) 16a 5

(2) 160 6h2 (4) 80 6b2


(1) 9x 5 (3) 27x 5

(2) 9x 6 (4) 27x 6


(l) 24x 12 yl (3) 48x 12 y2

(2) 24x 7y 2 (4) 48x 7yl


(l) I (3) 2 3

(2) 16 (4) 25


(1) --3x 2 (3) - 27X 15

(2) 3x 2 (4) 27x8

16 ~ 15x 8


x =I- 0 IS

(1) _3x 4 (3) _3x 6

(2) -10x 4 (4) -IOx 6

17 -32x8


x (1) 8x 4 (3) -8x 4

(2) 8x 6 (4) --8x 6


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

I I


18 6


1-1 1(1) 5x 1 y (3) 5x yshy

(2) 5~ (4) 5y3 14x- X

19 4 y-

V


2x(1) -- (3) 2xy

v

2 v(1) -~ (4) ---2xy

x


4x ) ()(1) x- 3) 4xshy

(2) x9 (4) 4x 9


(1) x 3 (3) 3x (2) 3 -+- x (4) 1OOOx


(1) -30a 6b4 (3) -40[b4

i -~ ~ i ( 1 I

(2) -30a 7 b1 (4) -40a 7 b4


xshy1 )lt1

(1) 1000x (3) 1000 (2) 1000 -+- x (4) 0


(3) h-311

(4) b-111 1 +

I I

Regents Exam Questions by Topic Page 1 - Yorktown...

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Transcript of Regents Exam Questions by Topic Page 1 - Yorktown...