3 papers

Practice Test IA Time: 25 minutes

20 multiple-choice questions

Directions: Select the one correct answer of the five choices given and mark the corresponding circle on your answersheet. Your scratch work should be done on any available space in the section.

Notes

1. All numbers used are real numbers.

2. Calculators may be used.

3. Some problems may be accompanied by figures or diagrams. These figures are drawn as accurately as possibleEXCEPT when it is stated in a specific problem that a figure is not drawn to scale. The figures and diagrams aremeant to provide information useful in solving the problem or problems. Unless otherwise stated, all figures anddiagrams lie in a plane.

Data That Can Be Used for Reference

rectangleA = lw

Area

triangleA = 1⁄2 bh

circleA = πr 2

C = 2 πr

rectangular solidV = lwh

Volume

right circular cylinderV= πr 2h

Pythagorean Relationship

30° − 60° − 90°Special Triangles

45° − 45° − 90°

A circle is composed of 360°A straight angle measures 180°

The sum of the angles of a triangle is 180°

w

lh

b

rM

r

h

lh

w

a2 + b 2 = c 2

C B

A

c

a

b

30°

60°

2x

x

x√3

45°

45°

x

x x√2

200

Part III: Math Practice Tests

1. In the figure above, a circle of radius r is inside arectangle with dimensions as shown. In terms of l,w, and r, what is the area of the shaded region?

A. lw – 2πrB. 2l + 2w – πr2

C. 2l + 2w – πrD. lw – πr2

E. lw – r2

2. How many two-digit positive integers aremultiples of both 3 and 5?

A. 6B. 19C. 33D. 48E. 52

3. If 18% of n is 60, what is 6% of n?

A. 3.6B. 10.8C. 20D. 111.11E. 333.33

4. The linear function f is given by f(x) = mx + b,where m is a positive constant and b is a negativeconstant. Which of the following could be thegraph of f?

A.

B.

C.

D.

E.y

0x

y

0x

y

0x

y

0x

y

0x

l

wr

201

Practice Test IP

ractice Test I

GO ON TO THE NEXT PAGE

5. If 3x – 2 = 7, what is the value of 5x + 4?

A. 3B. 13

C. 337

D. 19E. 21

6. Shown above is the graph of f(x) for –5 ≤ x ≤ 6.For what values of x is f(x) positive?

A. 0 < x < 60B. –2 < x < 3 and 4 < x < 6C. –5 < x < 2 and 3 < x < 4D. 0 ≤ x ≤ 6E. –2 ≤ x ≤ 3 and 4 ≤ x ≤ 6

7. In a class of 35 students, 25 girls averaged 92% onthe last test, while the 10 boys averaged 85% onthe same test. What is the average for the entireclass on this test?

A. 87%B. 88.5%C. 89.5%D. 90%E. 92%

8. In the xy-plane, what is the x-coordinate of thepoint of intersection of the lines whose equations

are y x32 1= - and y x2

3 12=-

+ ?

A. 566-

B. 511

C. 6D. 12E. 18

9. If <x2 3 9- , which of the following is a possiblevalue of x?

A. –10B. –5C. 0D. 5E. 10

10. If x, y, and z are consecutive integers with x < y < z,which of the following could be equal to x + y + z?

A. 3z + 3B. 3z – 6C. 3y – 3D. 3x + 6E. 3y

11. If the perimeter of the triangle above is 18, what isthe value of y?

A. 6B. 30C. 45D. 60E. 90

12. A rectangle and a square have equal perimeters.If the rectangle has width 8 and length 12, what isthe area of the square?

A. 10B. 40C. 48D. 96E. 100

13. How many positive four-digit integers aremultiples of 5 and less than 4,000?

A. 270B. 300C. 540D. 600E. 800

xx

y°

6

x

yy = f(x)

−6 −5 −4 −3 −2 −1 1 2 3 4 5 6

202


203

Practice Test IP

ractice Test I

IF YOU FINISH BEFORE TIME IS CALLED, CHECK YOUR WORK ON THISSECTION ONLY. DO NOT WORK ON ANY OTHER SECTION IN THE TEST. STOP

14. Starting from point A, Milo rides his bicycle 5miles east, then 3 miles south, followed by a rideof 13 miles east, and finally 9 miles north, endingup at point B. After resting for a while, Milo ridesdirectly from point B back to point A. How fardoes he ride on his return trip?

A. 30B. 13C. 10D. 9E. 5

f xx

5 2 1 22 1 0 1- -

^ h15. The table above gives values of the quadratic

function f for some values of x. Which of thefollowing represents f?

A. f(x) = 3x2 – 7B. f(x) = 2x2 + 1C. f(x) = x2 – 1D. f(x) = x2 + x + 1E. f(x) = x2 + 1

16. If 5 less than some number is 3 more than twicethe number, what is the number?

A. –8

B. 32

C. 23

D. 38

E. 3

17. Using the data from the graph above, what was thepercent increase in profits from 1996 to 1997?

A. 20%B. 25%C. 40%D. 45%E. 80%

18. In parallelogram EFGH, points A and B trisectHG . What is the ratio of the area of ABFE to thearea of EFGH?

A. 61

B. 31

C. 21

D. 32

E. 65

19. At Smallville High School, the probability that itsboys’ basketball, wrestling, and soccer teams wintheir league titles this year are 80%, 75%, and60%, respectively. What is the probability that,for these three boys’ teams, basketball and soccerwill win league titles but wrestling will NOT?

A. 253

B. 203

C. 509

D. 259

E. 52

20. On a shopping trip, Amal spent 51 of his money

to buy a hat, and then used 21 of his remaining

money to purchase a coat. After spending $10.00on a belt, he then had $12.00 left. How muchmoney did Amal start out with before he wentshopping?

A. $110.00B. $100.00C. $60.00D. $55.00E. $50.00

F

GB

E

AH

1993

10

20

30

40

50

1994 1995 1996 1997

PRO

FIT

(thou

sand

s of

$)

Practice Test IB Time: 25 minutes

18 questions: (8 multiple choice and 10 grid-in)

Directions: This section is composed of two types of questions. Use the 25 minutes allotted to answer both questiontypes. For Questions 1–8, select the one correct answer of the five choices given and mark the corresponding circle onyour answer sheet. Your scratch work should be done on any available space in the section.

Notes





rectangleA = lw

Area


circleA = πr 2

C = 2 πr


Volume




45° − 45° − 90°



w

lh

b

rM

r

h

lh

w

a2 + b 2 = c 2

C B

A

c

a

b

30°

60°

2x

x

x√3

45°

45°

x

x x√2

204


1. If 4x + 3 > 27, which of the following CANNOTbe the value of x?

A. 3B. 7C. 11D. 12E. 17

2. On a map, the scale is 2 inches equals 120 miles.How many miles apart are two towns if the

distance between them on the map is 7 43 inches?

A. 420.75 milesB. 465 milesC. 930 milesD. 1,860 milesE. 4,650 miles

3. In the figure above, BC and DF are parallel. Ifm = 100 and x = 20, what is the value of x + z?

A. 20B. 80C. 100D. 120E. 160

4. If m + 3 = x(2 – x), then in terms of x, m – 2 =

A. –x2 + 2x + 5B. x2 – 2x – 5C. –x2 + 2x – 5D. –x2 + 2x + 1E. –x2 – 2x – 1

5. The midpoint of AB is point M. If point A hascoordinates (3, –2) and point M has coordinates(–1, 2), what are the coordinates of point B?

A. (1, 0)B. (–5, 6)C. (2, –2)D. (1, 2)E. (5, –6)

6. A taxicab charges $.90 for the first 51 mile

and $.60 for each additional 51 mile. If a

customer rides in this cab for m miles >m 51c m,

which of the following functions describes thecost, c(m), of this taxi ride in dollars?

A. c(m) = .90 + .60(m – 1)B. c(m) = .90 + .60m – 1C. c(m) = .90 + .60[5(m – 1)]D. c(m) = .90 + .60(5m – 1)

E. c(m) = .90 + .60(5m – 51 )

7. If xx x

m

57= and (xr)3 = x12, then the value of m – r =

A. 3B. 4C. 8D. 12E. 20

8. For circle C above, the area of the shaded sectorCAB is 6π. What is the length of arc AMB?

A. 2B. πC. 2πD. 12E. 12π

C

A

M

B60°

A

Bz°

x°

m°

D E F

C

205

Practice Test IP

ractice Test I


Directions for Student-Produced Response Questions (Grid-ins): Questions 9–18 require you to solve the prob-lem and enter your answer by carefully marking the circles on the special grid. Examples of the appropriate way to markthe grid follow.

Answer 3.7 Answer 21

Answer 2 21

Do not grid-in mixed numbers in the form of mixed numbers. Always change mixed numbers to improper fractions ordecimals.

1

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Decimal point

206


Answer 123

Space permitting, answers may start in any column. Each grid-in answer below is correct.

Note: Circles must be filled in correctly to receive credit. Mark only one circle in each column. No credit will be givenif more than one circle in a column is marked. Example:

Answer 258 (no credit)

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207

Practice Test IP

ractice Test I


Answer 8/9

Accuracy of decimals: Always enter the most accurate decimal value that the grid will accommodate. For example: Ananswer such as .8888. . . can be gridded as .888 or .889. Gridding this value as .8, .88, or .89 is considered inaccurateand therefore not acceptable. The acceptable grid-ins of 8/9 are:

Be sure to write your answers in the boxes at the top of the circles before doing your gridding. Although writing out theanswers above the columns is not required, it is very important to ensure accuracy. Even though some problems mayhave more than one correct answer, grid only one answer. Grid-in questions contain no negative answers.

1

8

9

6

7

4

5

2

3

/.

/.. .

1

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9

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0

208


9. The polygon above is a regular hexagon. What isthe value of x?

10. Five students are entered in a contest that willaward prizes of first, second, and third place. If agiven student can win only one prize, in how manydifferent ways can the three prizes be given awayin this contest?

11. According to the data in the graph above, what isthe average (arithmetic mean) of the number ofphone calls per day for the week Monday throughSunday?

3

2

1

6

5

4

Num

ber

of P

hone

Cal

ls Pe

r D

ay

MO

N

TU

ES

WE

D

TH

UR

FRI

SAT

SUN

x°

12. If m2 – n2 = 24 and m – n = 6, what is the value ofm + n?

13. If a b ab ba

5 = - , then what is the value of 12 35 ?

14. In a school having 300 students, 180 take Spanishand 150 take French. What percent of the studentsin this school took Spanish but not French? (Donot include the % symbol in your answer.)

15. The sum of four consecutive odd integers is 456.What is the sum of the smallest and largest ofthese integers?

16. A sack contains three red, four blue, and five greenmarbles. The marbles are all the same size and thesame weight. If a blindfolded person were to reachin the sack and draw one marble on each of threesuccessive tries (with no replacement), what is theprobability that he/she would draw a red, a blue,and then a red marble in exactly that order?

Note: Figure not drawn to scale.

17. In the figure above with AC and BD, what is thevalue of a + c + w + y?

18. If 2x + 3y is equal to 80% of 5y, what is the value

of yx ?

y°

c°

125°

D

BA C

a°w°

209

Practice Test IP

ractice Test I


Practice Test IC Time: 20 minutes



Notes





rectangleA = lw

Area


circleA = πr 2

C = 2 πr


Volume




45° − 45° − 90°



w

lh

b

rM

r

h

lh

w

a2 + b 2 = c 2

C B

A

c

a

b

30°

60°

2x

x

x√3

45°

45°

x

x x√2

210


1. If 3x + 15 = 36, then x + 5 =

A. 4B. 12C. 15D. 22E. 23

2. Xena bought a new refrigerator costing $625. Shepaid $100 as a down payment and will pay theremainder $75 per month. How many months willit take for Xena to pay off her new refrigerator?

A. 4B. 5C. 6D. 7E. 9

3. Points B, C, and D are equally spaced between A

and E on AE . If M is the midpoint of BC , what isthe value of x?

A. 2 161

B. 2 323

C. 2 163

D. 2 41

E. 2 83

4. The equation x2 3 5- = is true for which valueof x?

A. 0B. 4C. 9D. 16E. 25

5. The average (arithmetic mean) of the ages of 12girls is g and the average of the ages of 17 boys isb. What is the total of all the girls’ and boys’ agescombined?

A. g bg b12 17++

B.g b

29+

C.g b

2912 17+

D. 12g + 17b

E.g b

212 17+

6. If f(x) = x2 – 3x + 5, then f(2x) =

A. 4x2 – 6x + 5B. 2x2 – 6x + 10C. 2x2 – 6x + 5D. x2 – 6x + 5E. 4x2 – 6x + 5

7. The length of one side of triangle is 35. The lengthof another side of the same triangle is 10. Whichof the following could NOT be the value of thethird side of this triangle?

A. 24B. 27C. 31D. 39E. 43

8. If 2a + 6b = 16 and a + 3b + c = 12, what is thevalue of c?

A. –4B. 4C. 8D. 28E. It cannot be determined from the given

information.

E

2 2x

CB

M

A D

12

211

Practice Test IP

ractice Test I


10. What is the radius of a circle for which its areaand circumference are numerically equivalent?

A. 21

B. 1C. 2D. 3E. 4

11. If cx y

m2

5-

= , what is x in terms of y and m?

A.m y

25 3+ +

B. m y215

+

C. m y25 3+

+

D.m y2

12 +

E.m y2

15 +

12. In the xy-plane, the endpoints of a diameter of agiven circle are (–2, 3) and (4, 7). What is theradius of the circle?

A. 13

B. 15

C. 2 13

D. 2 26E. 13

13. If x is an odd integer and y is an even integer,which of the following must be an even integer?

I. xy

II. (x + 2)(y – 5)

III. yx

A. I onlyB. II onlyC. III onlyD. I and II onlyE. I and III only

212


9. The graphs of g and f are shown above. What is the value of f(g(3))?

A. 0B. 1C. 3D. 4E. 5

y = g(x)

y = f(x)

x4 4

5

−5

5

−5

−4 −4

y

x

y

14. If f(x) = 3x2 – 5, what is an integral value of r forwhich f(2r) = 7r?

A. –3B. –1C. 1D. 2E. 4

15. Maria hiked a distance of 15 miles at a rate of5 mph, and then returned the same distance at arate of 3 mph. What is her average rate for theentire hike?

A. 3.25B. 3.50C. 3.75D. 4.25E. 4.50

16. In the diagram above, PT is tangent to circle C atpoint T. If PT = 8 and PM = 4, what is the radiusof circle C?

A. 4B. 6C. 8D. 10E. 12

C

T

4P

8

rM

213

Practice Test IP

ractice Test I


Scoring Practice Test I

Answer Key for Practice Test I

Practice Test IA

214


1. D

2. A

3. C

4. D

5. D

6. B

7. D

8. C

9. D

10. E

11. D

12. E

13. D

14. C

15. E

16. B

17. E

18. D

19. A

20. D

Practice Test IB1. A

2. B

3. D

4. C

5. B

6. D

7. C

8. C

9. 60

10. 60

11. 4

12. 4

13. 32

14. 50

15. 228

16. 551 or .018

17. 125

18. 21 or .5

Practice Test IC1. B

2. D

3. C

4. D

5. D

6. A

7. A

8. B

9. E

10. C

11. E

12. A

13. E

14. C

15. C

16. B

Practice Test IIA Time: 25 minutes

18 questions (8 multiple-choice and 10 grid-in)


Notes





rectangleA = lw

Area


circleA = πr 2

C = 2πr


Volume




45° − 45° − 90°



w

lh

b

rM

r

h

lh

w

a2 + b 2 = c 2

C B

A

c

a

b

30°

60°

2x

x

x√3

45°

45°

x

x x√2

236


1. If 7x – 5 = 4x – 17, what is the value of x?

A. –6B. –4C. 1D. 4E. 5


2. In the figure above, if x = 50, what is the value ofm + n?

A. 50B. 65C. 75D. 110E. 130

3. In the xy-plane, the line with equation y = 3x – 12crosses the x-axis at one point. What is the x-coordinate of this point?

A. –12B. –4C. 0D. 3E. 4

4. The average (arithmetic mean) of 5x and 3y isequal to 4 less than the product of x and y. Whichof the following equations states the relationshipgiven in the previous sentence?

A.x y

xy25 3

4+

= -

B.x y xy

25 3

4+

=

C.x y

xy25 3

4-

= -

D.x y

xy25 3

4+

= -

E.x y

xy25 3

4-

= -

5. The number that results from 3n, where n is apositive integer, CANNOT end in which of thefollowing digits?

A. 1B. 3C. 5D. 7E. 9

6. A discount of 20%, followed by another discountof 25%, is equivalent to a single discount of whatpercent?

A. 33%B. 40%C. 45%D. 55%E. 60%

7. The equation x2 3 7- = is true for which value(s)of x?

A. 2 onlyB. 5 onlyC. 2 and 5D. –2 and 5E. 2 and –5


8. The figure above shows the graph of y = k – x2,where k is some positive constant. If V is themidpoint of side BC of rectangle ABCD, and if thearea of ABCD is 16, what is the value of k?

A. 2B. 2 2C. 4D. 4 2E. 8

x

y

OA D

VB C

y = k − x 2

m°

x°n°

237

Practice Test IIP

ractice Test II


Directions for Student-Produced Response Questions (Grid-ins): Questions 9–18 require you to solve the problemand enter your answer by carefully marking the circles on the special grid. Examples of the appropriate way to mark thegrid follow.

Answer 3.7 Answer 1/2

Answer 2 1/2


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Decimal point

238


Answer 123




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239

Practice Test IIP

ractice Test II


Answer 8/9

Accuracy of decimals: Always enter the most accurate decimal value that the grid will accommodate. For example: Ananswer such as .8888 . . . can be gridded as .888 or .889. Gridding this value as .8, .88, or .89 is considered inaccurateand therefore not acceptable. The acceptable grid-ins of 8/9 are:


1

8

9

6

7

4

5

2

3

/.

/.. .

1

8

9

6

7

4

5

2

3

0

1

8

9

6

7

4

5

2

3

0

1

8

9

6

7

4

5

2

3

0

1

8

9

6

7

4

5

2

3

/.

/.. .

1

8

9

6

7

4

5

2

3

0

1

8

9

6

7

4

5

2

3

0

1

8

9

6

7

4

5

2

3

0

1

8

9

6

7

4

5

2

3

/.

/.. .

1

8

9

6

7

4

5

2

3

0

1

8

9

6

7

4

5

2

3

0

1

8

9

6

7

4

5

2

3

0

240


9. Dividing a number by 52 and then multiplying the

result by 34 gives the same result as just dividing

the original number by what fraction?

10. If x y25

32

= , what is the value of yx ?

11. If m2 + n2 = 29 and if mn = 7, then the value of (m + n)2 =

12. If x 231

=-

and if y 221

= , what is the value of xy?

13. What is the largest of 5 consecutive even integerswhose sum is 170?

14. In the figure above, the circle with center C and

radius 5 is tangent to both the x and y axes. AB istangent to the circle at point B. What is the slope

of AB?

15. �ABC in the xy-plane has vertices at A (5, 2),B (11, 2), and C (11, 6). What is the area of�ABC?

16. If m2 + 2mn = 3n – 4w, what is the value of n whenm = 3 and w = –5?

17. The figure above consists of three circles havingthe same center. Their radii are 2, 3, and 4. Theshaded area is what fraction of the area of thelargest circle?

18. If 720 = ambncr, where a, b, and c are differentpositive prime integers, what is the value of m + n + r?

x

y

(9,−8)

AC

B

241

Practice Test IIP

ractice Test II


Practice Test IIBTime: 25 minutes



Notes





rectangleA = lw

Area


circleA = πr 2

C = 2πr


Volume




45° − 45° − 90°



w

lh

b

rM

r

h

lh

w

a2 + b 2 = c 2

C B

A

c

a

b

30°

60°

2x

x

x√3

45°

45°

x

x x√2

242


2, 3, 5, 8, 13, . . .

1. The first term in the sequence above is 2 and thesecond term is 3. For each term after the secondterm, its value represents the sum of the two termspreceding it. What is the tenth term of thissequence?

A. 34B. 55C. 89D. 144E. 233

2. In the xy-plane, the line l is perpendicular to thegraph of the equation 3x + 4y = 12. Which of thefollowing is the slope of line l?

A. –4B. –3

C. 43-

D. 34

E. 12

3. If 5(x + 3) = 17, what is the value of x?

A. 52

B. 25

C. 514

D. 522

E. 9

4. If 3(2x + 4)(5 – x) = 0, what are all the possiblevalues of x?

A. 0 onlyB. –2 and 5 onlyC. 2 and –5 onlyD. 0, –2, and 5E. 0, 2, and –5

5. For which of the following functions doesf f5 5!-^ ^h h?A. f x x=^ hB. f x 7=^ hC. f x x 53= +^ hD. f x x 32= -^ hE. f x x6 4= +^ h

6. When x = 2, what is the value of

x x x11 1

11

++ +

-?

A. 61

B. 1 52

C. 1 65

D. 5E. 11

7. Mark is taller than Rebecca, and Charles is shorterthan Rebecca but taller than Harriet. If m, r, c, andh represent the heights of Mark, Rebecca, Charles,and Harriet respectively, which of the followingcorrectly represent the order of their heights?

A. c < h < r < mB. r < c < h < mC. h < r < c < mD. c < h < r < mE. h < c < r < m

8. The radius of one circle is 31 the radius of a

second circle. What is the ratio of the area of thesmaller circle to the area of the larger circle?

A. 1:9B. 1:3C. 3:1D. 6:1E. 9:1

9. If 2 ≤ x ≤ 6 and 6 ≤ xy ≤ 30, which of the followinggives the range of all possible values of y?

A. y31

81# #

B. y31

51# #

C. 4 ≤ y ≤ 24D. 3 < y < 5E. 3 ≤ y ≤ 5

10. The quantity m varies inversely as the square ofthe quantity r. If m = 9 when r = 4, what is thevalue of m when r = 6?

A. 4B. 6C. 36D. 64E. 144

243

Practice Test IIP

ractice Test II


11. If x�y yx

= , with y ≠ 0, and if 4�m = 16�2,

what is the value of m?

A. 21

B. 1C. 2D. 8E. 16

12. What is the measure of the largest angle of atriangle, in which the degree measure of its angleshave a ratio of 5:6:7?

A. 10B. 35C. 50D. 70E. 75


13. For the parabola above, (5, –3) is its vertex. Whichof the following are the x-coordinates of twopoints on the graph of the parabola for which theiry-coordinates are equal?

A. 4 and 7B. 2 and 9C. 0 and 8D. –1 and 11E. 1 and 10

14. Mr. and Mrs. Franklin took their three children toa theatre to watch a movie. They select a row onthe side having only five seats. If each of theparents must sit at either end of the row, in howmany different ways can the Franklin family beseated in the five seats?

A. 3B. 6C. 12D. 24E. 120

15. How many inches are there in a distance of Y yards,F feet, and I inches?

A. 3Y + F + 12IB. 36Y + F + 12IC. 3Y + 12F + ID. 36Y + 12F + IE. 3Y + 12F + 12I

16. In the figure above, AB BC= and AC CD= . Ifthe length of AB 2= and the length of BC 2= ,what is the length of AD?

A. 2 2 (approximately 2.82)

B. 2 3 (approximately 3.46)C. 4D. 3 2 (approximately 4.24)

E. 2 5 (approximately 4.47)

17. The perimeter of an equilateral triangle is 18.What is the area of the triangle?

A. 29

B. 29 2

C. 9 2

D. 9 3E. 18

C

Dx°

B

A

x°

x

y

(5, −3)

O

244



18. In the figure above, BC AD. What is the ratio ofthe area of �ABF to the area of �CED?

A. :3 2

B. :2 1C. 3:2D. :3 1E. 2:1

19. If m and r are constants and if (x + m)(x + r) = x2 + cx + w, where c and w are constants, what is w

c in terms of m and r?

A. rm

B. mm r+

C. mrm r+

D. m rmr+

E. It cannot be determined from the giveninformation.

20. Let the function f be defined by f(x) = x2 – 2x. Forwhich values of m will f(2m) = 15?

A. –2 only

B. 23- and 2

5

C. 3 and –5D. –3 and 5E. 3 only

FA D

B

E

C

30° 45°

245

Practice Test IIP

ractice Test II


Practice Test IICTime: 20 minutes



Notes





rectangleA = lw

Area


circleA = πr 2

C = 2πr


Volume




45° − 45° − 90°



w

lh

b

rM

r

h

lh

w

a2 + b 2 = c 2

C B

A

c

a

b

30°

60°

2x

x

x√3

45°

45°

x

x x√2

246


1. Two positive integers are called “relatively prime”if their only common factor is 1. Which of thefollowing pair of numbers is “relatively prime?”

A. 6 and 9B. 10 and 5C. 8 and 15D. 12 and 4E. 9 and 12

2. If the volume of a cube is 8, what is its totalsurface area?

A. 6B. 8C. 16D. 18E. 24

3. The graph above shows the number of votesreceived by each of four candidates in an election.What fraction of the votes did candidate Y receive?

A. 61

B. 41

C. 31

D. 21

E. 52

4. If f x xx

73 2

=-

-^ h , then the value of f(–2) =

A. 512-

B. 34-

C. 76

D. 34

E. 512

5. At 5:00pm, what is the degree measure of theangle between the hour and minute hands onthe traditional clock above?

A. 75°B. 115°C. 120°D. 150°E. 165°

6. The denominator of a fraction is 3 more than its

numerator. If the fraction is equal to 3514 , what is

the numerator of the fraction?

A. 2B. 3C. 5D. 6E. 7

10

1112

6

1

7 5

9 3

2

8 4

CAND. X50

40

20

10CAND. Y CAND. A

CAND. B

247

Practice Test IIP

ractice Test II



7. In the figure above, what is the value of m?

A. 15B. 30C. 45D. 60E. 75

8. If 0 < x < 1, which of the following statementsmust be true?

I. >x x1

II. x2 < x

III. x3 – x2 > 0

A. I onlyB. II onlyC. III onlyD. I and II onlyE. II and III only

9. The average of two numbers is x. If one of thenumbers is 3m – 5, then the other number, in termsof x and m, is

A. x m2

3 5+ -

B. 6m – 10 – xC. 6m – 5 – x

D. xm6 10-

E. 6m – 10 + x

10. In the xy-plane, the graphs of y = 2x + 7 and y = –3x + r intersect at the point (–2, m). What isthe value of r?

A. –3B. –1C. 2D. 3E. 4

3x°

45°

m°

x°

248



11. The graph above is that of the equation y = f(x). Which of the following could be the graph of y f x= ^ h ?

x

y

64

(B)

x

y

64

(D)

x

y

64

(C)

x

y

64

(A)

−1 −1−3

−1−3 −1−3

−1−3

−3

x

y

64

(E)

x

y y = f (x)

64−1−3

249

Practice Test IIP

ractice Test II


12. The radius of a right circular cylinder is doubled,and its height is tripled. What is the ratio of thevolume of the original cylinder to the volume ofthe new larger cylinder?

A. 121

B. 61

C. 31

D. 21

E. 6

13. In the figure above, a circle is inscribed within asquare having a perimeter of 32. What is the areaof the shaded region?

A. 64 – 16πB. 32 – 8πC. 16 – 4πD. 8 – 2πE. 4 – π

14. In the xy-plane, how many different integer pairs

(x, y) are in the solution set of x y 2#+ ?

A. 4B. 5C. 8D. 12E. 13

15. The sum of three consecutive even integers is 72.If x represents the smallest, y the middle, and zthe greatest of these even integers, which of thefollowing equations could be used to represent thefirst sentence of this problem?

I. 3x + 6 = 72

II. 3y = 72

III. 3z – 6 = 72

A. I onlyB. II onlyC. I and II onlyD. I and III onlyE. I, II, and III

16. If x2

4+ is an integer, and if y

23-

is an integer,

then xy must be

A. an even integerB. a negative integerC. an odd integerD. a multiple of 12E. a positive integer

250



Scoring Practice Test II

Answer Key for Practice Test II

Practice Test IIA

251

Practice Test IIP

ractice Test II

1. B

2. E

3. E

4. D

5. C

6. B

7. D

8. C

9. 103

10. 1415 or 1.07

11. 43

12. 21 or .5

13. 38

14. 34 or 1.33

15. 12

16. 311 or 3.66 or 3.67

17. 165 or .312 or .313

18. 7

Practice Test IIB1. D

2. D

3. A

4. B

5. C

6. C

7. E

8. A

9. E

10. A

11. B

12. D

13. D

14. C

15. D

16. B

17. D

18. D

19. C

20. B

Practice Test IIC1. C

2. E

3. C

4. B

5. D

6. A

7. E

8. D

9. B

10. A

11. B

12. A

13. C

14. E

15. E

16. A

Practice Test IIIATime: 25 minutes



Notes





rectangleA = lw

Area


circleA = πr 2

C = 2πr


Volume




45° − 45° − 90°



w

lh

b

rM

r

h

lh

w

a2 + b 2 = c 2

C B

A

c

a

b

30°

60°

2x

x

x√3

45°

45°

x

x x√2

272


1. If 3x – 5 = 16, then x =

A. –7

B. 311

C. 4D. 7E. 18

2. If xx 4

79+

= , what is the value of x?

A. 3 21

B. 7C. 14D. 21E. 35


3. In the figure above, what is the value of x?

A. 20B. 50C. 60D. 80E. 140

4. At a flooring center, you can purchase carpet inone of five styles and in one of 10 colors. Howmany different style-color combinations arepossible at this flooring center?

A. 15 B. 36C. 40D. 45E. 50

5. In the xy-plane, a circle has its center at point C (0, 0) and contains the point P (–3, 4). Under thetranslation that moves point C to (–2, 3), wherewill point P be located after this translation?

A. (–1, 1)B. (1, –1)C. (–3, 2)D. (–4, 5)E. (–5, 7)

6. If f x xx2

53

2

=-

+^ ^h h, what is the value of f(5)?

A. 0

B. 1 51

C. 2 52

D. 3 53

E. 4

7. According to the data in the graph above, betweenwhich two consecutive days of the week was thepercent increase in temperature the greatest?

A. Sunday to MondayB. Monday to TuesdayC. Wednesday to ThursdayD. Thursday to FridayE. Friday to Saturday

30°

20°

10°

60°

70°

50°

40°

Tem

pera

ture

(°F)

MO

N

TU

ES

WE

D

TH

UR

FRI

SAT

SUN

100°

x°

20°

B

C

A

273

Practice Test IIIP

ractice Test III


8. An employee had to take a pay cut of 20%. Awhile later, she received a pay raise of 25%. Hernew salary after the pay raise was what percentof her salary before the pay cut?

A. 45%B. 55%C. 80%D. 95%E. 100%

9. If the average (arithmetic mean) of x, 6, 10, 12, 5x,and 10 is equal to 3x, what is the value of x?

A. 2B. 3C. 4D. 5E. 6

10. 3x – 2y = –12 and x + 3y = 7

For what values of x and y are the equations aboveboth true?

A. x = –6, y = –3B. x = 4, y = 1

C. x = –1, y 29

=

D. x = –2, y = 3E. x = 10, y = –1

11. It takes Lisa h hours to walk a distance of m miles.At this same rate, how many hours will it take herto walk a distance of d miles?

A. hdm

B. mdh

C. dmh

D. mhd

E. hdm

12. If the ratio of the number of boys to the number of

girls in a class is 43 , which of the following could

NOT be the number of students in this class?

A. 21B. 28C. 33D. 42E. 49

13. The ratio of the length of a rectangle to its widthis 5:3. If the length is 10, what is the area of therectangle?

A. 6B. 15C. 16D. 32E. 60

14. If x mb c

=- +

, what is c in terms of x, b, and m?

A. m2x2 – b2

B. (x – m + b)2

C. xm b+

D. (mx + b)2

E.b

x m2

2-^ h

15. The minimum speed on a given stretch of freewayis 45 mph, and the maximum speed is 65 mph.Which of the following inequalities could be usedto decided if a motorist driving at a rate of r mphis within legal limits?

A. r 45 10#-

B. r 55 10#-

C. r 65 10#-

D. <r 55 10-

E. r 10 55#-

274


16. Above is the graph of y = f(x). Which of the graphs below is that of y = f(x + 1) + 3?

x

y

0

A.

x0

yB.

x

y

0

C.

x

y

0

E.

x

y

0

D.

0 x

y = f (x)y

275

Practice Test IIIP

ractice Test III



17. In the figure above, AB BC= . What is the valueof y?

A. 23-

B. 32

C. 2D. 6E. 12

18. If 82x = 44x – 3, what is the value of x?

A. 41

B. 1C. 3D. 4E. 6


19. In the figure above, circles A and B are tangent atC, and line l is tangent to circles A and B at pointsP and Q respectively. If the radius of circle A is 2and the radius of circle B is 6, what is the lengthof PQ?

A. 6B. 4 3

C. 6 2D. 8E. 10

20. A small rocket is fired into the air from the top ofa tower. Its height h, in feet, after t seconds, isgiven by: h(t) = –16t2 + 64t + 32. The rocket is 80feet above the ground twice—once on the way upand then again on the way down. How manyseconds pass between these two times?

A. 1B. 2C. 3D. 4E. 5

BA C

P

l

Q

A (1, 5)

B (3, 2)

y

x

C (9, y)

276



Practice Test IIIBTime: 25 minutes

18 questions (8 multiple-choice and 10 grid-in)


Notes





rectangleA = lw

Area


circleA = πr 2

C = 2πr


Volume




45° − 45° − 90°



w

lh

b

rM

r

h

lh

w

a2 + b 2 = c 2

C B

A

c

a

b

30°

60°

2x

x

x√3

45°

45°

x

x x√2

277

Practice Test IIIP

ractice Test III


1. What is the average (arithmetic mean) of the

numbers 21 , 3

1 , and 61 ?

A. 221

B. 61

C. 31

D. 21

E. 125

2. 12 75+ =

A. 87

B. 7 6

C. 7 3

D. 10 3

E. 29 3

3. If n represents an even integer, which of thefollowing represents an odd integer?

A. 3n + 2B. n2 + 3C. (n + 4)2

D. 5n – 4E. 7n + n2


4. In the right triangle above, what is the value of x?

A. 2B. 2 5 (approximately 4.47)C. 5D. 5 2 (approximately 7.07)

E. 2 13 (approximately 7.21)

5. In the figure above, square ABCD is inscribedwithin circle P. If the area of the circle is 8π, whatis the area of the square?

A. 2 2B. 8C. 16D. 16 2E. 32


6. In �ABC above, AB BC= . What is the product ofthe slopes of the sides of �ABC?

A. –2B. –1

C. 21-

D. 1E. 2

7. If (x + m)(x + n) = x2 – 5x – 36, what is the value

of mnm n+ ?

A. 94-

B. 365

C. 49

D. 536

E. It cannot be determined from the giveninformation.

A (3, 4)

B (4, 7)

C (7, 6)

y

x

P

D C

A B

4

6x

278


8. In the figure above, a rectangle is inscribed withina square of side length 4. What is the area of theshaded region?

A. 16B. 10C. 6D. 3 2

E. 2

3

3

1

1

279

Practice Test IIIP

ractice Test III


Directions for Student-Produced Response Questions (Grid-ins): Questions 9–18 require you to solve the prob-lem and enter your answer by carefully marking the circles on the special grid. Examples of the appropriate way tomark the grid follow.

Answer: 3.7 Answer 1/2

1

8

9

6

7

4

5

2

3

/.

/.. .

1

8

9

6

7

4

5

2

3

0

1

8

9

6

7

4

5

2

3

0

1

8

9

6

7

4

5

2

3

0

Fraction bar

1

8

9

6

7

4

5

2

3

/.

/.. .

1

8

9

6

7

4

5

2

3

0

1

8

9

6

7

4

5

2

3

0

1

8

9

6

7

4

5

2

3

0

Decimal point

Answer 2 1/2


Answer 123


1

8

9

6

7

4

5

2

3

/.

/.. .

1

8

9

6

7

4

5

2

3

0

1

8

9

6

7

4

5

2

3

0

1

8

9

6

7

4

5

2

3

0

1

8

9

6

7

4

5

2

3

/.

/.. .

1

8

9

6

7

4

5

2

3

0

1

8

9

6

7

4

5

2

3

0

1

8

9

6

7

4

5

2

3

0

1

8

9

6

7

4

5

2

3

/..

/. .

1

8

9

7

4

5

2

3

01

8

9

6

7

4

5

2

01

8

9

6

7

4

5

2

3

0

6

3

0or 1

8

9

6

7

4

5

2

3

/..

/. .

1

8

9

7

4

5

2

3

01

8

9

6

7

4

5

2

01

8

9

6

7

4

5

2

3

0

6

3

0

280




Answer 8/9

Accuracy of decimals: Always enter the most accurate decimal value that the grid will accommodate. For example: Ananswer such as .8888 . . . can be gridded as .888 or .889. Gridding this value as .8, .88, or .89 is considered inaccurateand therefore not acceptable. The acceptable grid-ins of 8/9 are:


1

8

9

6

7

4

5

2

3

/.

/.. .

1

8

9

6

7

4

5

2

3

0

1

8

9

6

7

4

5

2

3

0

1

8

9

6

7

4

5

2

3

0

1

8

9

6

7

4

5

2

3

/.

/.. .

1

8

9

6

7

4

5

2

3

0

1

8

9

6

7

4

5

2

3

0

1

8

9

6

7

4

5

2

3

0

1

8

9

6

7

4

5

2

3

/.

/.. .

1

8

9

6

7

4

5

2

3

0

1

8

9

6

7

4

5

2

3

0

1

8

9

6

7

4

5

2

3

0

1

8

9

6

7

4

5

2

3

/.

/.. .

1

8

9

6

7

4

5

2

3

0

1

8

9

6

7

4

5

2

3

0

1

8

9

6

7

4

5

2

3

0

281

Practice Test IIIP

ractice Test III


9. The length of a rectangle is decreased by 25%while its width is decreased by 20%. The area ofthe new rectangle is what fraction of the area ofthe original rectangle?

10. If x = 4, what is the value of x y y

xy5

32 2 2

2

-?


11. In the figure above, point C is the center of thecircle. What is the value of x?

12. If x mx m10 15 12++

= , what is the value of xm ?

13. If 12(m + n)(c – r) = 72 and 3(m + n) = 9, what isthe value of c – r?

14. The population of bacteria in a culture doublesevery 10 minutes. If the current bacteriapopulation is 1,024, how many minutes ago wasthe bacteria population only 32?

15. If the median of a list of seven consecutive oddintegers is 23, what is the difference between thelargest and smallest of these integers?

16. The digits 2, 3, 4, 5, and 6 are used to create five-digit numbers that begin and end with an evendigit. If each digit can be used only once in eachof the numbers, how many of these five-digitnumbers can be created?


17. In the figure above, rectangle ABCD is inscribedin the circle with center at the origin in the xy-plane. Point C with coordinates (3, y) is located onthis circle. If the radius of the circle is 5, what isthe area of rectangle ABCD?

18. If the average (arithmetic mean) of five differenttwo-digit positive integers is 20, what is thegreatest possible difference between the largestand the smallest of these five integers?

C (3, y)D

x

y

BA

x°

25°C

282



Practice Test IIICTime: 20 minutes



Notes





rectangleA = lw

Area


circleA = πr 2

C = 2πr


Volume




45° − 45° − 90°



w

lh

b

rM

r

h

lh

w

a2 + b 2 = c 2

C B

A

c

a

b

30°

60°

2x

x

x√3

45°

45°

x

x x√2

283

Practice Test IIIP

ractice Test III


1. If m – n = 11, what is the value of 2m – 2n – 7?

A. 4

B. 7 21

C. 15D. 22E. 29

2. If rm

32

58

= , what is the value of mr ?

A. 125

B. 85

C. 512

D. 85

E. 23

Note: Figures not drawn to scale.

3. In the figures above, �ABC and square MNOPhave equal perimeters. What is the length of MP?

A. 2B. 4C. 5D. 8E. 16

4. The quantity 5x – 7 is how much larger than thequantity –10 + 5x?

A. –17B. –3C. 3D. 7E. 17

5. If 0 < x < y < 1, which of the following must bepositive?

A. x – yB. x2 – y2

C. x y1 1-

D. –(y – x)

E. xy

23-

6. When a given number is decreased by 5 and thisresult is tripled, the number obtained is 24. Whatis the given number?

A. 311

B. 329

C. 7D. 12E. 13


7. In �ABC above, AB BC= , x = 30, and the lengthof AC is 8 3. What is the area of �ABC?

A. 16B. 24 2

C. 24 3

D. 48 3E. 144

8. If the area of a circle is π4

9 , what is itscircumference?

A. π25681

B. π16

81

C. 23

D. π2

3

E. 3π

B

C

A

x°6 C M

N O

P

73

A

B

284


9. In the xy-plane, a given circle with center at theorigin contains the point (–3, 4). Which of thefollowing points is NOT on the given circle?

A. (3, –4)B. (0, –5)C. (3, 4)D. (0, 7)E. None of the above points are on the given

circle.

10. If 0 < x < 1, which of the following gives the

correct order of x3 , x , and x1 ?

A. < <x x x1 3

B. < <x x x13

C. < <x x x13

D. < <x x x13

E. < <x x x1 3

11. In the xy-plane, ,7 5` j is a point on the graph of

the equation y = x2 + k. For what positive value ofx will y = 7?

A. 2B. 3C. 4D. 5E. 6

12. If x y/ /3 4 3 8= , what is x in terms of y?

A. y1

B. y

C. y2

D. y3

E. y6

13. If xy 6= , which of the following could NOT bethe value of x + y?

A. 37B. 20C. 18D. 15E. 13

14. In the xy-plane, the set of points 5 units from thepoint A (6, 3) lie on a circle with center A andradius 5. What are all the possible points on thiscircle having an x-coordinate of 9?

A. (9, 8) onlyB. (9, 7) and (9, –1)C. (9, 8) and (9, –2)D. (9, –2) onlyE. (9, 7) only

15. Rachelle invested $1,000 in an IRA paying 6%per year. The accumulated value of her investmentt years later is given by the function A, where A(t) = 1,000(1.06)t. In how many years willRachelle’s investment be worth $1,191.02?

A. 1B. 2C. 3D. 4E. 5

16. The length of the longer leg of a right triangle isone less than twice the length of the shorter leg,and the length of the hypotenuse is one more thantwice the length of the shorter leg. If the lengthof the shorter leg is x, which of the followingequations could be used to find the value of x?

A. x + (2x – 1) = 2x + 1B. x2 + (2x – 1)2 = (2x – 1)2

C. x2 = (2x – 1)2 + (2x + 1)2

D. x2 + (2x – 1)2 = (2x + 1)2

E. x(2x – 1) = 2x + 1

285

Practice Test IIIP

ractice Test III


Scoring Practice Test III

Answer Key for Practice Test III

Practice Test IIIA

286


1. D

2. C

3. D

4. E

5. E

6. C

7. D

8. E

9. C

10. D

11. B

12. C

13. E

14. D

15. B

16. C

17. D

18. C

19. B

20. B

Practice Test IIIB1. C

2. C

3. B

4. B

5. C

6. C

7. B

8. B

9. 53

10. 1112 or 1.09

11. 65

12. 32 or .666 or .667

13. 2

14. 50

15. 12

16. 36

17. 48

18. 44

Practice Test IIIC1. C

2. A

3. B

4. C

5. C

6. E

7. C

8. E

9. D

10. C

11. B

12. B

13. C

14. B

15. C

16. D

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