SAT Practice Book 2009 2010

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TABLE of CONTENT

SAT Practice Book

2009-2010

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1. Properties of integers

2. Number Lines and Fractions

3. Elementary Number Theory(Divisibility)

4. Sequences

5. Sets

6. Ratio, Proposition, and Percents.

7. Exponents, Squares, and Square Roots

8. Word problems

9. Factoring

10. Mean, Median, and Mode

11. Solving Equations and Rational Equations

12. Direct Variation and Inverse Variation

13. Inequalities

14. System of Linear Equations

15. Solving Quadratic Equations

16. Functions

17. Made Up Operations

18. Coordinates Geometry

19. Parallel Lines and Angles

20. Triangles

21. Polygons

22. Circles

23. Solid Geometry

24. Statistics, Data and Graph

25. Probabilities

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PROPERTIES of INTEGERS

SAT Practice Book

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1. If x is an integer greater than 1 and if

x x y

1, which of the following must be

true?

I. y x II. y is an integer.III. xy > x 2

(A) I only(B) III only(C) I and II only(D) I and III only(E) I, II, and III

2. If x and y are positive consecutive oddintegers, where y > x , which of thefollowing is y2 – x 2?

(A) 2 x (B) 4 x

(C) 2 x + 2(D) 2 x + 4(E) 4 x + 4

3. If x, y, and z are positive integers suchthat the value of x + y is even and thevalue of ( x + y) 2 + x + z is odd, which of the following must be true?

(A) x is odd.(B) x is even.(C) If z is even, then x is odd.(D) If z is even, then xy is even.(E) xy is even.

4. If n is any negative number, which of the following must be positive?

(A)2n

(B) 2 n (C) n + 2(D) n – 2(E) 2 – n

5. If k is a positive even integer, then(k+1)(k+2) could equal which of thefollowing?

(A) 10

(B) 20(C) 30(D) 40(E) 50

6. Which of the following must be true forall integers a ,b , and c ?

I. a - 0 = aII. a -b=b-aIII. ( a -b)-c=a - (b-c)

(A) I only(B) II only(C) III only(D) I and II(E) II and III

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PROPERTIES of INTEGERS

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7. If a , b , and c are positive integers, and if (a −c)b=0, which of the following mustbe true?

(A) a <b(B) b<c(C) a =b(D) a =c(E) b=c

8. If a is an odd integer and b is an eveninteger, which of the following is an oddinteger?

(A) 3 b(B) a+ 3

(C) 2( a+b )(D) a +2 b(E) 2 a+ b

9. If ( p +1) ( t-3) =0 and p is positive, what isthe value of t?

(A) -3(B) -1(C) 0(D) 1(E) 3

10. If 2

3 xis an integer, then x must be

(A) a negative integer(B) a positive integer(C) a multiple of 3(D) an even integer(E) an odd integer

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NUMBER LINES & FRACTIONS

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1.

Which of the lettered points on thenumber line above could represent theresult when the coordinate of point P is multiplied by the coordinate of pointQ ?

(A) A (B) B (C) C (D) D

(E) E

2.

On the number line above, there are 9equal intervals between 0 and 1. What

is the value of x ?

3.

On the number line above, t , u, v, w, x, y, and z are coordinates of theindicated points. Which of thefollowing is closest in value to| u + v| ?

(A) t (B) w(C) x (D) y (E) z

4.

On the number line above, which of the following corresponds to wu ?

(A) t (B) v(C) x (D) y (E) z

2

17

2

3

5. What number, when used in place of above, makes the statement true?

(A) 4(B) 5(C) 9

(D) 12(E) 15

6. The numerator of a certain fraction is5 less than the denominator. If the

fraction is equal to4

3, what is the

denominator of this fraction?

(A) 8(B) 12(C) 16(D) 20(E) 24

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7.

In the figure above, AC = 24 and AB = BC . Point D (not shown) is on theline between A and B such that

AD = DB . What does DC equal?

(A) 6(B) 12(C) 16(D) 18(E) 20

8. If x =2

1, what is the value of

1

11

x x?

(A) – 4(B) 0(C) 1(D) 2(E) 3

9. Which of the following numbers is

between5

1and

4

1?

(A) 0.14(B) 0.15(C) 0.19(D) 0.21(E) 0.26

10.

If x, x 2, and x 3 lie on a number line inthe order shown above, which of thefollowing could be the value of x ?

(A) – 2

(B)2

1

(C)4

3

(D) 1

(E)2

3

11.

On the number line above, the tickmarks are equally spaced. What is thevalue of w – p ?

(A) 3/4(B) 2/3(C) 1/2(D) 1/3(E) 1/4

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12.

On the number line above, the tickmarks are equally spaced. Which of the lettered points represents y ?

(A) A(B) B(C) C (D) D(E) E

13.

Which of the following is the bestestimate of the length of segment AB onthe number line above?

(A) 4(B) 3.5(C) 3(D) 1.5

(E) 1

14.

In the figure above, if the coordinatesof points X and Y are added together,the result will be the coordinate of apoint between which two consecutiveintegers?

(A) − 3 and − 2(B) − 2 and − 1(C) − 1 and 0(D) 0 and 1(E) 2 and 3

15.

On the number line above, the tickmarks are equally spaced. What is thevalue of b − a ?

(A) 4/5(B) 3/4(C) 2/5(D) 1/4(E) 1/5

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16.

If the tick marks on the number lineabove are equally spaced, which of thelettered points A through E is between1/4 and 3/8?

(A) A(B) B(C) C

(D) D(E) E

17.

If x is the coordinate of the indicated pointon the number line above, which of thelettered points has coordinate 2x ?

(A) A(B) B(C) C (D) D(E) E

18. If 3 times a number is equal to 3/2,what is the number?

(A) 1/3(B) 1/2(C) 2/3(D) 2(E) 3

19.

On the number line above, the tickmarks are equally spaced and theircoordinates are shown. Of thesecoordinates, which has the smallestpositive value?

(A) a(B) b(C) c(D) d(E) e

7



DIVISIBILITY

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1. There are 8 sections of seats in anauditorium. Each section contains atleast 150 seats but not more than 200

seats. Which of the following could bethe number of seats in thisauditorium?

(A) 800(B) 1,000(C) 1,100(D) 1,300(E) 1,700

2. “All nu mbers that are divisible by both2 and 6 are also divisible by 4 .”

Which of the following numbers can beused to show that the statement aboveis FALSE?

(A) 4

(B) 8(C) 12(D) 18(E) 24

3. If m is the greatest prime factor of 38and n is the greatest prime factor of 100, what is the value of m + n ?

(A) 7(B) 12(C) 24(D) 29(E) 44

4. If p is an integer and 3 is theremainder when 2 p + 7 is divided by 5,then p could be

(A) 2(B) 3(C) 4(D) 5(E) 6

5. When 15 is divided by the positiveinteger k , the remainder is 3. For howmany different values of k is this true?

(A) One(B) Two(C) Three(D) Four

(E) Five

6. How many cubical blocks, each withedges of length 4 centimeters, areneeded to fill a rectangular box that

has inside dimensions 20 centimetersby 24 centimeters by 32 centimeters?

(A) 38(B) 96(C) 192(D) 240(E) 384

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DIVISIBILITY

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7. What is the greatest three – digitinteger that has a factor of 10?

8. If there is no waste, how many squareyards of carpeting is needed to cover arectangular floor that is 12 feet by 18feet?(1 yard = 3 feet)

(A) 8(B) 16(C) 24(D) 30(E) 216

9. If x is divisible by 3 and y is divisibleby 5, which of the following must bedivisible by 15?

I. xy

II. 3 x + 5 y

III. 5 x + 3 y


10. How many integers greater than 20and less than 30 are each the productof exactly two different numbers, both

of which are prime?

(A) Zero(B) One(C) Two(D) Three(E) Four

11. If the integer m is divided by 6, theremainder is 5. What is the remainderif 4 m is divided by 6 ?

(A) 0(B) 1(C) 2

(D) 4(E) 5

12. A large solid cube is assembled bygluing together identical unpaintedsmall cubic blocks. All six faces of thelarge cube are then painted red. If

exactly 27 of the small cubic blocksthat make up the large cube have nored paint on them, how many smallcubic blocks make up the large cube?

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DIVISIBILITY

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13. When the positive integer n is dividedby 6, the remainder is 2. What is theremainder when 24 n is divided by 36 ?

14. If k is a positive integer divisible by 7,and if k < 90, what is the greatestpossible value of k ?

(A) 83(B) 84(C) 87(D) 88(E) 89

15. There are 6 bookcases in a house.Each bookcase contains at least 125books but not more than 160 books.Which of the following could be thetotal number of books in all 6bookcases?

(A) 500(B) 625(C) 725(D) 925(E) 1,000

16. Which of the following is divisible by 3and by 5 but is not divisible by 10 ?

(A) 30(B) 35(C) 40(D) 45(E) 60

17. When the positive integer m isdivided by 5, the remainder is 3. Whatis the remainder when 20 m is dividedby 25?

18. For what positive number is thesquare root of the number the same asthe number divided by 40?

19. The result when a number is dividedby 2 is equal to the result when thatsame number is divided by 4. What isthat number?

(A) -4(B) -2(C) 0(D) 2(E) 4

20. What is the product of the smallestprime number that is greater than 50and the greatest prime number that isless than 50?

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SEQUENCES

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1. – 1, 0, 1, 2 A sequence is formed by repeating the4 numbers above in the same order

indefinitely. What is the sum of thefirst 28 terms of the sequence?

(A) 12(B) 13(C) 14(D) 15(E) 16

2. Rita’s dog weighed 5 pounds when shebought it. Over the next several years,the dog’s weight increased by 10percent per year. Which of thefollowing functions gives the weight,w, in pounds, of the dog after n yearsof weight gain at this rate?

(A) w(n) = 5 + 0.1n(B) w(n) = 5(0.1) n

(C) w(n) = 5(0.9)n

(D) w(n) = 5(1.1) n (E) w(n) = 5(n) 1.1

3. Each month, a telephone servicecharges a base rate of $10.00 and anadditional $0.08 per call for the first40 calls and $0.04 for every call afterthat. How much does the telephoneservice charge for a month in which 50calls are made?

(A) $12.20(B) $12.80(C) $13.60(D) $14.40(E) $17.60

y, 2 y + 7, y + 6 . . .4. In the increasing sequence above, the

first term is y and the difference

between any two consecutive terms is3. What is the value of the fourth termin the sequence?

(A) – 4(B) 2(C) 5(D) 13(E) 19

5. In a sequence of numbers, the firstnumber is 4 and each number after thefirst is 1 more than 5 times thepreceding number. What is the thirdnumber in the sequence?

(A) 16(B) 21

(C) 94(D) 96(E) 106

6. The first term of a sequence is 3, andeach term after the first is 2 more thanthe previous term. Which of thefollowing is an expression for the n th

term of the sequence for any positiveinteger n?

(A) 2 n (B) 1+2 n (C) 2+2 n (D) 3+2 n (E) 2+3 n

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SEQUENCES

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7. The n th term of a sequence is definedto be 4 n + 3. The 50th term is howmuch greater than the 45th term?

(A) 5(B) 16(C) 20(D) 23(E) 24

8. After the first term in a sequence of positive integers, the ratio of eachterm to the term immediatelypreceding it is 2 to 1. What is the ratioof the 8th term in this sequence to the5th term?

(A) 6 to 1(B) 8 to 5(C) 8 to 1

(D) 64 to 1(E) 256 to 1

4, 11, 18, . . .9. In the sequence above, the first term is

4 and each term after the first is 7more than the previous term. What is

the 12th term of the sequence?

(A) 77(B) 81(C) 84(D) 86(E) 92

10. 3, 5, – 5...

The first term in the sequence of

numbers shown above is 3. Each even –numbered term is 2 more than theprevious term and each odd – numberedterm, after the first, is – 1 times theprevious term. For example, thesecond term is 3 + 2, and the thirdterm is ( –1) × 5. What is th e 55th termof the sequence?

(A) – 5(B) – 3(C) – 1(D) 3(E) 5

11. The sum of 5 consecutive integers is1,000. What the value of the greatestof these integers?

12. 5.101001000100001 …

The decimal number above consists of only 1 ‘ s and 0’s to the right of thedecimal point. The first 1 is followedby one 0, the second 1 is followed bytwo 0’ s, the third 1 is followed bythree 0’ s, and so on. What is the total

number of 0’s between the 98th andthe 101st 1 in this decimal number?

(A) 288(B) 291(C) 294(D) 297(E) 300

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SEQUENCES

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13. a, 3a, ...

The first term in the sequence above is

a , and each term after the first is 3times the preceding term. If the sum of the first 5 terms is 605, what is thevalue of a ?

14. 7, 15, 31, 63, ...

The first term in the sequence above is7, and each term after the first isdetermined by multiplying thepreceding term by m and then adding

p . What is the value of m ?

(A) 1(B) 2(C) 3(D) 4(E) 9

15. Z W Y X

The sequence above may be changed ineither of two ways. Either twoadjacent letters may be interchangedor the entire sequence may bereversed. What is the least number of such changes needed to put the letters

into alphabetical order from left toright?

(A) 2(B) 3(C) 4(D) 5(E) 6

16. After the first term, each term in a

sequence is 3 greater than3

1of the

preceding term. If t is the first term of the sequence and t ≠ 0, what is theratio of the second term to the firstterm?

(A)3

9t

(B)3

3t

(C) t

t

3

9

(D)t

t

3

3

(E)3

29 t

17. 8, 17, 26, 35, 44, ...

The first 5 terms in a sequence areshown above. Each term after the firstis found by adding 9 to the termimmediately preceding it. Which termin this sequence is equal to8 + (26 – 1)9?

(A) The 8th

(B) The 9th(C) The 25th(D) The 26th(E) The 27th

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SEQUENCES

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18. What is the greatest of 5 consecutiveintegers if the sum of these integersequals 185?

19. 2, 6, 14, 30, ...

In the sequence above, the first termis 2. Each number after the first isobtained by adding 1 to thepreceding number and then doublingthe result. What is the sixth numberin the sequence?

(A) 122(B) 123(C) 124(D) 125(E) 126

20. “The sum of three consecutive oddintegers is 111 . “

If n represents the least of the threeintegers, which of the following

equations represents the statementabove?

(A) 3 n = 111(B) 3 n + 2 = 111(C) 3 n + 4 = 111(D) 3 n + 6 = 111(E) 3 n + 9 = 111

21. The first term of a sequence is 20 andthe second term is 8. The third termand each term thereafter is the

average (arithmetic mean) of the twoterms immediately preceding it. Whatis the value of the first term in thesequence that is not an integer?

22. The n th term of a sequence is given bythe formula .22

nn How much largeris the 10th term of the sequence thanthe 9th term?

23. 150, 30, 6,…

In the sequence above, each term after

the 1st term is5

1of the term preceding

it. What is the 5th term of thissequence?

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SETS

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1. How many positive four-digit integershave 1 as their first digit and 2 or 5 astheir last digit?

(A) 144(B) 180(C) 200(D) 300(E) 720

2. In the figure above, circular region P represents shirts with pockets,circular region Q represents shirtswith buttons, and circular region Rrepresents shirts with collars. What isrepresented by the shaded region?

(A)Shirts with pockets, buttons, andcollars(B) Shirts with pockets and buttons,but without collars(C) Shirts with pockets and buttons(some possibly with collars ) (D) Shirts with pockets and collars(some possibly with buttons)(E) Shirts with buttons and collars(some possibly with pockets)

3. P = 6,5,3,1 Q = 9,7,6,4,2 Sets P and Q are shown above. If x is amember of set P and y is a member of set Q , which of the following CANNOTbe equal to the product xy ?

(A) 16(B) 18(C) 20(D) 21(E) 24

4. How many positive integers less than1,000 are multiples of 5 and are equalto 3 times an even integer?

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SETS

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5. The Lyndhurst High School twelfthgraders are represented in the circlegraph in Figure 1. Figure 2 is anotherway to illustrate the use of computersby these twelfth graders. If the same200 twelfth graders are represented inboth figures, what is the total numberof twelfth graders represented by theshaded circle in Figure 2 ?

6. A set has property X if t t 2 is in theset whenever t is in the set. Which of the following sets has property X ?

(A) 0,1,2 (B) 0,1 (C) 1,0,1 (D) 1,0 (E) 2,1

7. Which of the following is an element of both the set of positive odd integersand the set of prime numbers?(A) 2(B) 5(C) 9(D) 12(E) 21

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SETS

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8. Students at Northern High School arerepresented in Figure 1 above. Figure2 above is another way to show whichpets these students have. If the same500 students are represented in bothfigures, what is the total number of students represented by the shadedcircle in Figure 2 ?

9. Some integers in set X are even.If the statement above is true, whichof the following must also be true?

(A) If an integer is even, it is in set X .(B) If an integer is odd, it is in set X .(C) All integers in set X are even .(D) All integers in set X are odd .(E) Not all integers in set X are odd.

7,2

11,4,

2

5,1,

7

4 A , 7,4,

4

7,

7

4 B

10. If n is a member of both set A and set

B above, which of the following mustbe true?

I. n is an integer.II. 4n is an integer.III. n = 4

(A) None(B) II only(C) I and II only(D) I and III only(E) I, II, and III

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SETS

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11. If A is the set of prime numbers and Bis the set of two-digit positive integerswhose units digit is 5, how many

numbers are common to both sets?

(A) None(B) One(C) Two(D) Five(E) Nine

12. There are 25 trays on a table in thecafeteria. Each tray contains a cuponly, a plate only, or both a cup and aplate. If 15 of the trays contain cupsand 21 of the trays contain plates, howmany contain both a cup and a plate?

13. The least integer of a set of consecutive integers is – 25. If the sumof these integers is 26, how many

integers are in this set?

(A) 25(B) 26(C) 50(D) 51(E) 52

14. Set X has x members and set Y has y members. Set Z consists of allmembers that are in either set X or set

Y with the exception of the k commonmembers ( k > 0). Which of thefollowing represents the number of members in set Z?

(A) x + y + k(B) x + y – k (C) x + y + 2k (D) x + y – 2k (E) 2 x + 2 y – 2k

15. If E is the set of even integers, P is theset of positive integers, and F is the setof integers less than 5, which of thefollowing integers will be in all threesets?

(A) 6(B) 4

(C) 1(D) 0(E) – 2

16. If 80 x and 31 y , which of the following gives the set of allpossible values of xy?

(A) xy = 4(B) 240 xy (C) 111 xy (D) 241 xy (E) 248 xy

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SETS

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17. How many integers in the set of allintegers from 1 to 100, inclusive, arenot the square of an integer?

(A) 19(B) 50(C) 81(D) 89(E) 90

18. In a set of eleven different numbers,which of the following CANNOT affect

the value of the median?

(A) Doubling each number(B) Increasing each number by 10(C) Increasing the smallest numberonly(D) Decreasing the largest numberonly(E) Increasing the largest number only

.

19. Set X = {30, 31, 32, 33}Set Y = {32, 33, 34, 35, 36}

Sets X and Y are shown above. Howmany numbers in set X are also inset Y ?

(A) Two(B) Three(C) Four(D) Seven(E) Nine

20. If k is a positive integer, let bedefined as the set of all multiples of k.

All of the numbers in which of thefollowing sets are also in all three of the sets , and ?

(A)(B)

(C)(D)(E)

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RATIO, PROPORTION & PERCENT

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1. Which of the following tables shows arelationship in which w is directlyproportional to x ?

(A) (B)

(C) (D)

(E)

2. Dwayne has a newspaper route forwhich he collects k dollars each day.

From this amount he pays out 3

k

dollars per day for the cost of thepapers, and he saves the rest of themoney. In terms of k , how many dayswill it take Dwayne to save $1,000?

(A)5001

,

k (B)

0001,

k

(C)k

0001 ,(D)

k

5001 ,

(E) 1,500 k

3. If 3

2

y x , what is the value of

y x

2

3?

(A)31

(B)3

2

(C) 1

(D)2

3

(E)4

9

4. If 30 percent of 40 percent of a positivenumber is equal to 20 percent of w percent of the same number, what isthe value of w?

(A) 80(B) 60(C) 50(D) 15(E) 10

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RATIO, PROPORTION & PERCEN

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5. There are 75 more women than menenrolled in Linden College. If there aren men enrolled, then, in terms of n,

what percent of those enrolled aremen?

(A)75n

n %

(B)752 n

n %

(C))( 752100 n

n %

(D)75

100

n

n %

(E)752

100

nn %

6. The eggs in a certain basket are eitherwhite or brown. If the ratio of thenumber of white eggs to the number of

brown eggs is 3

2

, each of the followingcould be the number of eggs in thebasket EXCEPT

(A) 10(B) 12(C) 15(D) 30(E) 60

7. The price of a telephone was firstincreased by 10 percent and then thenew price was decreased by 25

percent. The final price was whatpercent of the initial price?

(A) 78%(B) 80%(C) 82.5%(D) 85%(E) 87.5%

8. The force required to stretch a springbeyond its natural length isproportional to how far the spring is

being stretched. If a force of 15 poundsstretches a spring 8 centimetersbeyond its natural length, what force,in pounds, is needed to stretch thisspring 20 centimeters beyond itsnatural length?

(A) 23(B) 27(C) 30.5(D) 35

(E) 37.5

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9. A measuring cup contains5

1of a cup of

orange juice. It is then filled to the 1

cup mark with a mixture that containsequal amounts of orange, grapefruit,and pineapple juices. What fraction of the final mixture is orange juice?

10. If a + 2b is equal to 125 percent of 4 b,

what is the value of ba ?

11. In a poll, 35 people were in favor of building a new library, 14 people wereagainst it, and 1 person had noopinion. What fraction of those polledwere in favor of building a newlibrary?

(A)10

7

(B)3

2

(C)7

3

(D)3

1

(E)10

3

12. If 20 percent of x equals 80 percent of y, which of the following expresses y interms of x ?

(A) y = 16% of x (B) y = 25% of x (C) y = 60% of x (D) y = l00% of x (E) y = 400% of x

13. If a, b, c and f are four nonzeronumbers, then all of the followingproportions are equivalent EXCEPT

(A)cb

f a

(B)ab

c f

(C)b

f

a

c

(D) f b

ca

(E)1

1

bcaf

14. When the positive even integer n isincreased by 50 percent of itself, theresult is between 10 and 20. What isone possible value of n ?

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15. If a x x 2

4and x ≠ 0, what is the value

of a ?

(A) 8(B) 4(C) 2

(D)2

1

(E)4

1

16. One circle has a radius of 2

1and

another circle has a radius of 1. Whatis the ratio of the area of the largercircle to the area of the smaller circle?

(A) 2 : 1(B) 3 : 1(C) 3 : 2(D) 4 : 1(E) 5 : 2

17. The ratio 1.2 to 1 is equal to which of the following ratios?

(A) 1 to 2(B) l2 to l(C) 5 to 6(D) 6 to 5(E) 6 to 50

18. If 30 percent of m is 40, what is 15percent of m ?

(A) 15(B) 20(C) 25(D) 30(E) 35

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SAT Practice Book

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11

1. If 12

10 ba

, what is the value of ab ?

2. The price of ground coffee beans is d dollars for 8 ounces and each ouncemakes c cups of brewed coffee. Interms of c and d , what is the dollarcost of the ground coffee beansrequired to make 1 cup of brewedcoffee?

(A) cd

8 (B) 8

cd

(C)d c8

(D)cd 8

(E) 8 cd

3.

The circle graph above represents allthe jeans that were sold by a retailstore in 2001, according to

their brands. If the store sold 900pairs of jeans other than brands J, K,L, M, and N, how many pairs of jeansdid it sell altogether?

(A) 1,500 (B) 2,250(C) 3,000 (D) 3,600(E) 4,500

4. The Smith Metal Company’s oldmachine makes 300 bolts per hour. Itsnew machine makes 450 bolts per

hour. If both machines begin runningat the same time, how many minuteswill it take the two machines to makea total of 900 bolts?

(A) 36(B) 72(C) 120(D) 144(E) 180

5. If y = z x35

, what happens to the value

of y when both x and z are doubled?

(A) y is not changed.

(B) y is halved.(C) y is doubled.(D) y is tripled.(E) y is multiplied by 4.

6. If n is a positive integer and 2

1

2

1n

n,

then n =?

(A) 1(B) 2(C) 3(D) 4(E) 5

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SAT Practice Book

2009-

2010

2

2009-2010

2

7. If y is directly proportional to x 2 and

8

1 y when

2

1 x what is the positive

value of x when29 y ?

(A)4

3

(B)2

3

(C)4

9

(D) 3

(E) 9

8.

If the five line segments in the figureabove are all congruent, what is theratio of the length of AC (not shown) tothe length of BD ?

(A) 2 to 1(B) 3 to1(C) 2 to 2(D) 3 to 2(E) 3 to 2

9.

The chart above shows the resultswhen 1,000 people were asked, “Howold are you?” The age they gave isrepresented by x . How many peoplesaid that their age was less than 40?

(A) 200(B) 300(C) 450(D) 500(E) 550

10. 37

39

2 x x , then x = ?

(A) 37(B) 39(C) 41

(D) 74(E) 78

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2009-2010

3

11. From 1979 to 1989, the total elephantpopulation in the four regions of Africadecreased by approximately what

percent?

(A) 10%(B) 30%(C) 50%(D) 70%(E) 90%

12. If n1

=5

2, what is the value of n ?

13.

In a survey, 3,400 people responded to thefollowing question: “How many weeks of vacation did you take last year?” Theirresponses to the question are summarized inthe chart above, where n equals the numberof vacation weeks indicated. How manyrespondents took more than 2 weeks of vacation last year?

14. A box contains 2,900 solid-coloredmarbles that are either orange, blue,or green. If 29 percent of the marbles

are orange and 29 percent of themarbles are blue, what percent aregreen?

(A) 29%(B) 42%(C) 52%(D) 58%(E) 71%

15. What is the ratio of the radius r of acircle to the circumference of thecircle?

(A) 1: 2(B) 1:(C) 1: r(D) :1(E) 2 :1

16. Fifty percent of the songs played on acertain radio station are 3 minuteslong, 30 percent are 5 minutes long,and 20 percent are 2 minutes long.

What is the average (arithmetic mean)number of minutes per song played onthis radio station

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SAT Practice Book

2009-

2010

4

2009-2010

4

17. If t r t r =

2

5what is the value of

t r ?

(A) -3

7

(B) - 1

(C)7

3

(D) 1

(E)3

7

18. If q and r are positive numbers, whatpercent of ( q + 1) is r ?

(A))1(100

1

qr %

(B)r

q100

1%

(C)r q )1(100

%

(D) (q

r 100+ 1 ) %

(E) 1

100

qr

%

27




SAT Practice Book

2009-2010

11

1. If 4

3)25( m= 6 what is the value of

m ?

2. If r is directly proportional to s and if

S = 3

2when r =

5

4, what is the value

of r when s = 9

4

?

3. If 7.5 is x percent of 75, what is x percent of 10 ?

(A) 10(B) 1(C) 0.75(D) 0.1(E) 0.075

4. If 1

1

x = 2

1

what is the value of x ?

(A) 2(B) 1(C) 0(D) - 1(E) - 2

5. A box of staples contains 4,600staples that are either silver, black, orred. If 46 percent of the staples are

silver and 46 percent are black, whatpercent are red?

(A) 8%(B) 18%(C) 46%(D) 54%(E) 92%

6. The original price of a book was bdollars. This price was discounted x percent during a sale. James used a

coupon to buy the book for t percent off the sale price. Which of the followingrepresents the price, in dollars,that James paid for the book?

(A) b100

1x

1001

t

(B) b100

)1)(1( t x

(C) b100

1t x

(D) b100

1xt

(E) b100

x100

t

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SAT Practice Book

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2009-2010

2

7.

Students at Northern High School arerepresented in Figure 1 above. Figure 2above is another way to show which petsthese students have. If the same 500students are represented in both figures,what is the total number of studentsrepresented by the shaded circle inFigure 2 ?

8. If the value of -t1

is twice the value

of t

1, what is the value of t ?

9. What is the ratio of the diameter d of a circle to half the circumference of thecircle?

(A) 1 : 2(B) 1 :(C) 2 :(D) : 1(E) 2 : 1

10. If y is directly proportional to x and if y = 20 when x = 6, what is the value of y when x = 9 ?

(A)3

10

(B) 3

40

(C) 23(D) 27(E) 30

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SAT Practice Book

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2010

3

2009-2010

3

11. Flour, water, and salt are mixed byweight in the ratio of 5:4:1,respectively, to produce a certain type

of dough. In order to make 5 pounds of this dough, what weight of salt, inpounds, is required?

(A)4

1(B)

2

1

(C)4

3(D) 1

(E) 2

12. If 0.03 percent of n is 3, what is 3percent of n ?

(A) 900(B) 600

(C) 300(D) 0.006(E) 0.003

13. If Marisa drove n miles in t hours,which of the following represents heraverage speed, in miles per hour?

(A)t n (B)

nt

(C)nt

1(D) nt

(E) n 2 t

14. If 75 percent of m is equal to kpercent of 25, where k > 0, what is the

value of k

m?

(A)16

3

(B)3

1

(C)4

3

(D) 3

(E)3

16

15. If ba y x

=3

2, then

ba y x

101099

= ?

(A)10

9

(B)23

20

(C)27

20

(D) 3

2

(E)5

3

16. 30




SAT Practice Book

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2010

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2009-2010

4

The circle graph above shows howDavid’s monthly expenses are divided.

If David spends $450 per month forfood, how much does he spend permonth on hiscar?

(A) $200(B) $320(C) $360(D) $400(E) $450

17. In a certain store, the regular price of a refrigerator is $600. How muchmoney is saved by buying thisrefrigerator at 20 percent off theregular price rather than buying it onsale at 10 percent off the regular pricewith an additional discount of 10percent off the sale price?

(A) $6(B) $12(C) $24(D) $54(E) $60

18.

According to the graph above, if there are6,000 registered voters aged 60 and overin Washington County, how manyregistered voters are under the age of 30 ?

(A) 1,000(B) 2,000(C) 3,000(D) 4,000(E) 5,000

31



EXPONENTS, SQUARES & SQUARE R

SAT Practice Book

2009-2010

11

1. 22x = 8 x – 1, what is the value of x ?

(A) 2

(B) 3(C) 4(D) 5(E) 6

2. If 2 4x = 16, then x =?

(A) 1(B) 2(C) 4(D) 8(E) 12

3. If 3513t , what is the value of 34 t ?

4. If t r 1818 , where r and t arepositive integers and r > t , which of thefollowing could be the value of rt ?

(A) 18(B) 36(C) 108(D) 162(B) 324

5. Positive integers x, y , and z satisfy the

equations3

12

1

x and 16 z y . If z > y

what is the value of x + z ?

(A) 5(B) 7(C) 11(D) 13(E) 15

6. 22 33 )( x x

For what value of x is the statementabove FALSE?

(A) – 3(B) 0

(C)3

1

(D) 1(E) For no value of x

7. If x and y are positive consecutive oddintegers, where y > x , which of the

following is y2

– x 2?

(A) 2 x (B) 4 x (C) 2 x + 2(D) 2 x + 4(E) 4 x + 4

32




SAT Practice Book

2009-

2010

2

2009-2010

2

8. If m and k are positive andmk m 10010 12 , what is 1m in terms of

k?

(A)10

k

(B)90

k

(C)10

k

(D)k 10

1

(E)k 90

1

9. If 8 + k = 15, then k = ?

(A) 7(B) 49(C) 529(D) 7

(E) 23

10. If a, b, and c are different positiveintegers and 64222 cba , then

?cba 222

(A) 14(B) 17(C) 21(D) 28(E) 34

11. If a and b are positive integers and

432

6

3

1

2

1

ba , what is the value of ab ?

(A) 6(B) 12(C) 18(D) 24(E) 36

12. If xy = 10, what is the value of 22 y y x ?

(A) 5(B) 8(C) 10

(D) 12(E) 20

13. If 93 y x what is x in terms of y?

(A) y

(B) y2

(C) y3 (D) y6

(E) y12

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SAT Practice Book

2009-

2010

3

2009-2010

3

14. 39 x x

For all values of x greater than 3, the

equation above is equivalent to whichof the following?

(A) x = x 2 (B) x = x 2 + 18(C) x = x 2 – 6x (D) x = x 2 – 6x + 9(E) x = x 2 – 6x + 18

15. If k, n, x, and y are positive numbers

satisfying 23

4

k x and 23

4

n y ,

what is 3

2

)( xy in terms of n and k?

(A)nk

1

(B)k

n

(C)nk

(D) nk(E) 1

16. If 287 mmm x and 155 mm y)( , what isthe value of x + y ?

(A) 7(B) 12(C) 14(D) 24(E) 31

17. If 722222 x x x x , what is the valueof x ?

18. If k is a positive integer, what is the

least value of k for which3

5 k is an

integer?

(A) 3(B) 5(C) 15(D) 25(E) 60

19. If n is a positive integer, then)()( nn 101106 must equal

(A) 10

7

(B)n10

7

(C)n210

7

(D)n10

6

(E)n210

6

34




SAT Practice Book

2009-

2010

4

2009-2010

4

20. If x and y are positive integers and y x 224 , what is x in terms of y?

(A) y – 2(B) y – 1(C) y (D) y + 1(E) y + 2

21. If 16 = 2 k what is the value of k?

(A) 1(B) 2(C) 3(D) 4(E) 8

35




SAT Practice Book

2009-2010

11

1. If x = 5 y and y = z + 1, what is5

x in

terms of z ?

(A) z(B) z + 1(C) 5 z (D) 5 z +1(E) 5 1 z

2. If k is a positive integer, which of thefollowing is equivalent to 3 k + 3 k ?

(A) 2 3 k (B) 3 k 2 (C) 6 k (D) 6 k 2 (E) 9 k 2

3. If 7 10 = 7 7 n what is the value of n?

(A) 10

(B) 9(C) 7(D) 5(E) 3

4. If 2 y = 8 and y =2

xwhat is the value

of x ?

(A) 6(B) 5(C) 4(D) 3(E) 2

5. If x 2 − 64 = 0, which of the followingcould be a value of x?

(A) −8(B) −4(C) 0(D) 16(E) 32

6. If a and b are positive integers and9(3 a ) = 3 b what is a in terms of b ?

(A) b − 2(B) b − 1(C) b(D) b + 1(E) b + 2

36




SAT Practice Book

2009-

2010

2

2009-2010

2

7. If y is a positive integer, and3 y − 7 = 8, what is the value of y ?

8. If a

2

= 4, which of the following couldbe the value of a ?

(A) −2

(B) −4

1

(C) 0

(D)4

1

(E)2

1

9. If x 2 - 36 = 0, which of the followingcould be a value of x ?

(A) -6(B) -4(C) 0(D) 3(E) 12

10. If x and y are integers such that x 2 =64 and y 3 = 64 , which of the followingcould be true?

I. x = 8II. y = -4III. x + y = -4

(A) I only(B) II only(C) I and III only(D) II and III only(E) I, II, and III

11. If x 1 h = 1, what does h equal in termsof x ?

(A) - x

(B) x

1

(C) 2

1

x

(D) x (E) x 2

12. If 7 n 7 3 7 12 , what is the value of n ?

(A) 2(B) 4(C) 9(D) 15(E) 36

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SAT Practice Book

2009-

2010

3

2009-2010

3

13. If x is a positive integer satisfyingx 7 = k and x 9 = m, which of the followingmust be equal to x 11 ?

(A)k

m 2

(B) m 2 - k-(C) m 2 - 7

(D) 2k -3

m

(E) k + 4

14. If n and k are positive integers and 8 n

= 2k

, what is the value of k

n ?

(A)4

1

(B)3

1

(C)2

1

(D) 3(E) 4

15. If t is a number greater than 1, then t 2 is how much greater than t ?

(A) 1(B) 2(C) t(D) t (t − 1)(E) ( t − 1)( t + 1)

16. If ( x – 2) 2 = 49, then x could be

(A) -9(B) -7(C) 2(D) 5(E) 9

38



WORD PROBLEMS

SAT Practice Book

2009-2010

11

1. There are 8 sections of seats in anauditorium. Each section contains atleast 150 seats but not more than 200

seats. Which of the following could bethe number of seats in thisauditorium?

(A) 800(B) 1,000(C) 1,100(D) 1,300(E) 1,700

2. If 4 less than 3 times a certain numberis 2 more than the number, what is thenumber?

(A) – 1(B) – 3(C) 1(D) 2

(E) 3

3. During a game, the blue team scoredone – sixth of its points in the firstquarter, one – fourth in the secondquarter, one – third in the thirdquarter, and the remaining points inthe fourth quarter. If its total scorewas 36, how many points did the blue

team score in the fourth quarter?

(A) 6(B) 8(C) 9(D) 12(E) 25

4. At a bottling company, machine A fillsa bottle with spring water andmachine B accepts the bottle only if

the number of fluid ounces is between

8

711 and

8

112 . If machine B accepts a

bottle containing n fluid ounces, whichof the following describes all possiblevalues of n ?

(A)8

112n

(B)8

112n

(C)8

112n

(D)8

112n

(E)8

112n

5. Esther drove to work in the morningat an average speed of 45 miles perhour. She returned home in theevening along the same route andaveraged 30 miles per hour. If Estherspent a total of one hour commuting toand from work, how many miles did

Esther drive to work in the morning?

39



WORD PROBLEMS

SAT Practice Book

2009-

2010

2

2009-2010

2

6. Schedule

I

n the sc

hedule above, each session is to be2

11

hours long, each break is to be 4

1

hourlong, and lunch is to be 1 hour long. If session IV is to end at 4:30 P.M. , atwhat time should session I begin?

(A) 8:15 A.M .(B) 8:30 A.M. (C) 8:45 AM.(D) 9:00 A.M.(E) 9:15 A.M.

7. Carlos delivered n packages onMonday, 4 times as many packages onTuesday as on Monday, and 3 morepackages on Wednesday than onMonday. What is the average(arithmetic mean) number of packageshe delivered per day over the threedays?

(A) 2 n – 3(B) 2 n – 1(C) 2 n + 1(D) 2 n + 3(E) 6 n + 1

8. 5.101001000100001 …

The decimal number above consists of

only 1 ‘ s and 0’s to the right of thedecimal point. The first 1 is followedby one 0, the second 1 is followed bytwo 0’ s, the third 1 is followed bythree 0’ s, and so on. What is the totalnumber of 0’s between the 98th andthe 101st 1 in this decimal number?

(A) 288(B) 291(C) 294(D) 297(E) 300

9. There is the same number of boys andgirls on a school bus when it departsfrom school. At the first stop, 4 boysget off the bus and nobody gets on.

After the first stop, there are twice asmany girls as boys on the bus. How

many girls are on the bus?

(A) 4(B) 6(C) 8(D) 12(E) 16

10. Stacy noted that she is boththe12 th tallest and the 12 th shortest

students in her class. If everyone inthe class is of the different height, howmany students are in the class?

(A) 22(B) 23(C) 24(D) 25(E) 34

Event BeginningTime

EndingTime

Session I ?BreakSession IILunchSession IIIBreakSession IV 4:30 P.M.

40



WORD PROBLEMS

SAT Practice Book

2009-

2010

3

2009-2010

3

11. A total of k passengers went on abus trip. Each of the n buses that wereused to transport the passengers could

seat a maximum of x passengers. If one bus had 3 empty seats and theremaining buses were filled, which of the following expresses therelationship among n, x, and k?

(A) nx – 3 = k (B) nx + 3 = k(C) n + x + 3 = k(D) nk = x + 3(E) nk = x – 3

12. The numerator of a certainfraction is 5 less than thedenominator. If the fraction is equal to

4

3, what is the

denominator of this fraction?

(A) 8(B) 12(C) 16(D) 20(E) 24

13. A family of 5 is planning a 4 – daycamping trip. Each person will need tobring 1 bottle of water for each day of the trip. If the water is sold only in 3 – bottle packages, how many packagesmust the family buy for the trip?

14. A measuring cup contains5

1of a cup of

orange juice. It is then filled to the 1 cup

mark with a mixture that contains equalamounts of orange, grapefruit, and pineapple

juices. What fraction of the final mixture isorange juice?

15. When Ms. Yun arrived at the grocerystore, there were 5 packages of hot dog rollsleft on the shelf. One package contained 12rolls, and each of the otherscontained 8 rolls. If Ms. Yun bought all 5packages, how many hot dog rolls did shepurchase at the store?

(A) 32(B) 36(C) 44

(D) 48(E) 52

16. How old was a person exactly 1 year agoif exactly x years ago the person was y yearsold?

(A) y – 1(B) y – x – 1(C) x – y – 1(D) y + x + 1(E) y + x – 1

41



WORD PROBLEMS

SAT Practice Book

2009-

2010

4

2009-2010

4

17. When it is noon eastern standardtime (EST) in New York City, it is 9:00

AM. Pacific standard time (PST) in San

Francisco. A plane took off from New York City at noon EST and arrived inSan Francisco at 4:00 P.M. PST on thesame day. If a second plane left SanFrancisco at noon PST and took exactlythe same amount of time for the trip,what was the plan e’s arrival time (EST)in New York City?

(A) 10:00 P.M .EST(B) 9:00 P.M. EST(C) 7:00 P.M . EST(D) 6:00 P.M. EST(E) 4:00 P.M. EST

18. Todd is older than Marta butyounger than Susan. If t, m, and s represent the ages, in years, of Todd,

Marta, and Susan, respectively, whichof the following is true?

(A) m < t < s(B) s < m < t(C) s < t < m(D) t < m < s (E) t < s < m

19. A school ordered $600 worth of lightbulbs. Some of the light bulbs cost $1each and the others cost $2 each. If twice as many $1 bulbs as $2 bulbswere ordered, how many light bulbswere ordered altogether?

20. When twice a number is decreasedby 3, the result is253. What is the number?

21. h(t) = c – (d – 4t) 2

At time t = 0, a ball was thrown upwardfrom an initial height of 6 feet. Until theball hit the ground, its height, in feet,after t seconds was given by thefunction h above, in which c and d arepositive constants. If the ball reachedits maximum height of 106 feet at time t= 2.5, what was the height, in feet, of the ball at time t = 1?

22. Bobby receives $2 for each chore hedoes during the week, plus a weeklyallowance of $10. If Bobby receives noother money, which of the followingexpressions represents the total dollaramount Bobby receives for a week inwhich he has done n chores?

(A) 10 + n

(B) (10 + 2) n (C) 10 n + 2(D) 10 + 2 n (E) (10 + n )2

42



WORD PROBLEMS

SAT Practice Book

2009-

2010

5

2009-2010

5

23. A computer program randomlyselects a positive two – digit integer. If the integer selected is odd, twice that

integer is printed. If the integer selectedis even, the integer itself is printed. If the integer printed is 26, which of thefollowing could have been the integerselected?

I. 13II. 26III. 52

(A) I only(B) II only(C) I and II only(D) I and III only(E) I, II and III

24. How many seconds are there in m

minutes and s seconds?

(A) 60 m + s(B) m + 60 s(C) 60( m + s )

(D)60

sm

(E) sm

60

25. Kyle’s lock combination consists of 3two – digit numbers. The combinationsatisfies the three conditions below.

One number is odd.One number is a multiple of 5.One number is the day of themonth of Kyle’s birthday.

If each number satisfies exactly oneof the conditions, which of thefollowing could be the combination tothe lock?

(A) 14 – 20 – 13(B) 14 – 25 – 13(C) 15 – 18 – 16(D) 20 – 15 – 20(E) 34 – 30 – 21

26. Phillip used four pieces of masking

tape, each 6 inches long, to put up each of his posters. Phillip had a 300 – foot roll of masking tape when he started. If no tapewas wasted, which of the followingrepresents the number feet of maskingtape that was left on the roll after heput up n posters? (12 inches = 1 foot)

(A) 300 – 6n (B) 300 – 2n (C) 300 – n

(D) 300 – n

21

(E) 300 – n

4

1

43



WORD PROBLEMS

SAT Practice Book

2009-2010

11

1. A number n is increased by 5 and theresult is multiplied by 5. This result isdecreased by 5. Finally, that result is

divided by 5. In terms of n , what is thefinal result?

2 . In a certain game, points are assigned toevery word. Each q, x , and z in a word isworth 5 points, and all other letters areworth 1 point each. What is the sum of thepoints assigned to the word “exquisite”?

(A) 21(B) 17(C) 16(D) 13(E) 9

3. A certain scale only registers weightsthat are greater than 6 pounds. A personwho wanted to know the weights of apuppy, a kitten, and a bunny weighedthem in pairs and got the followingresults.

The kitten and the bunny weighed 7 pounds.The kitten and the puppy weighed 8 pounds.

The bunny and the puppy weighed 9 pounds.

What is the weight of the puppy?

(A) 2 pounds(B) 3 pounds(C) 4 pounds(D) 5 pounds(E) 6 pounds

4. The scenic route from Mia’s home to heroffice is 5 kilometers longer than the directroute. When she goes by the scenic route and

returns by the direct route, the round trip is35 kilometers. How many kilometers is thedirect route?

(A) 5

(B)2

112

(C) 15(D) 20

(E)2

122

5. For a certain hot – water heater, theincrease in heating expenses is directlyproportional to the increase in water – temperature setting. If heating expensesincrease by $24 when the water – temperature setting is increased by 20degrees Fahrenheit, by how much willheating expenses increase when the

water – temperature setting is increasedby 15 degrees Fahrenheit?

(A) $16(B) $18(C) $19(D) $20(E) $21

6. If Peg traveled 10 miles in 2 hours andLinda traveled twice as far in half thetime, what was Linda ’ s average speed,in miles per hour?

(A) 5(B) 10(C) 20(D) 30(E) 40

44



WORD PROBLEMS

SAT Practice Book

2009-

2010

2

2009-2010

2

7. If the product of 0.3 and a number isequal to 1, what is the number?

8. A company sells boxes of balloons inwhich the balloons are red, green, orblue. Luann purchased a box of balloons

in which3

1of them were red. If there

were half as many green balloons in thebox as red ones and 18 balloons wereblue, how many balloons were in the box?

9. Alice and Corinne stand back-to-back.They each take 10 steps in oppositedirections away from each other andstop. Alice then turns around, walkstoward Corinne, and reaches her in 17steps. The length of one of Alice’s steps is

how many times the length of one of Corinne’s steps? (All of Alice’s steps arethe same len gth and all of Corinne’ssteps are the same length.)

10. If 3 more than n is a negative numberand if 5 more than n is a positivenumber, which of the following could bethe value of n ?

(A) – 5(B) – 4(C) – 3(D) 0(E) 4

11. If all men in the Williams family are oversix feet tall, which of the followingstatements must be true?

(A) No man under six feet tall is amember of the Williams family.(B) All men over six feet tall aremembers of the Williams family.(C) All men who are not members of theWilliams, family are under six feet tall.(D) Every member of the Williams familyover six feet tall is a man.(E) There is one man in the Williamsfamily under six feet tall.

12. The total cost of 3 equally pricedmechanical pencils is $4.50. If the costper pencil is increased by $0.50, howmuch will 5 of these pencils cost at thenew rate?

(A) $7.50(B) $8.00(C) $9.00(D) $9.50(E) $10.00

13. Car A traveled 60 miles and averaged 20miles per gallon of gasoline. If car B traveled 15 miles

for each gallon of gasoline it used, howmany miles had car B traveled

when it had used the same amount of gasoline that car A used to travel 60miles?

45



WORD PROBLEMS

SAT Practice Book

2009-

2010

3

2009-2010

3

14. At Maple Creek High School, somemembers of the chess club are on theswim team and no members of the swim

team are tenth graders. Which of thefollowing must also be true?

(A) No members of the chess club aretenth graders.(B) Some members of the chess clubare tenth graders.(C) Some members of the chess clubare not tenth graders.(D) More tenth graders are on theswim team than are in the chessclub.(E) More tenth graders are in thechess club than are on the swimteam.

15. To celebrate a colleague’ s graduation, them coworkers in an office agreed to

contribute equally to a catered lunch thatcosts a total of y dollars. If p of thecoworkers fail to contribute, which of thefollowing represents the additionalamount, in dollars, that each of theremaining coworkers must contribute topay for the lunch?

(A)m

y

(B) pm

y

(C) pm

py

(D)m

pm y )(

(E))( pmm

py

16. While driving on a 500-mile trip, Mr.Smith averages 60 miles per hour for thefirst t hours. In terms of t , where

t < 8, how many miles remain to betraveled?

(A) 60 t − 500(B) 500 − 60 t(C) 30,000 − t

(D) 500 − t

60

(E)t 60

500

17. By 7:00 P.M.,3

1of the junior class had

arrived at a school dance. By 8:00 P.M.,30 more juniors had arrived, raising

attendance to2

1of the junior class. How

many people are in the junior class?

(A) 30(B) 90(C) 120(D) 180(E) 240

46



WORD PROBLEMS

SAT Practice Book

2009-

2010

4

2009-2010

4

18. The total cost of a taxicab ride is the sumof (1) a basic fixed charge for using the

taxicab, and(2) an additional charge for each

4

1of a

mile that is traveled.

If the total cost to ride4

3mile is $4.00

and the total cost to ride 12

1miles is

$5.50, what is the total cost, in dollars, of a 3-mile ride?

(Disregard the $ sign when gridding youranswer. If, for example, your answer is$1.37, grid 1.37)

19. Classified ads cost $2.50 per 30 words atCityNewspaper . What is the leastnumber of words that must be deletedfrom the text of a 75-word classified ad toreduce the cost to $5.00 or less?

(A) 5(B) 15(C) 20(D) 30(E) 60

20. Which of the following represents the totalcost, in dollars, of k compact discs at $15each and p compact disc cases at $25 each?(Disregard sales tax.)

(A) 15 k + 25 p(B) 25 k + 15 p(C) 40( k + p )(D) 0.40( k + p )(E) (15 + k)(25 + p )

21. If x and y are two different integers andthe product 35 xy is the square of aninteger, which of the following could be

equal to xy?

(A) 5(B) 70(C) 105(D) 140(E) 350

22. An amusement park charges $7 more foran adult’s admission than for a child’s

admission. If a group of 4 adults and 3children spent $119 on admission, whatis the price of admission for one child?

(A) $11(B) $13(C) $16(D) $17(E) $18

47



WORD PROBLEMS

SAT Practice Book

2009-

2010

5

2009-2010

5

23. The figure above shows four apartmentsin a building. In this building, eachapartment is occupied by only oneperson. Alice lives next to Sam, and Paullives next to Alice and Dara. In whichapartment could Alice live?

(A) 1 only

(B) 2 only(C) 3 only(D) 2 or 3(E) 1 or 4

24. A community college charges an activityfee of $4.00 per student and has astudent body of 8,200 students. If everystudent pays the fee, what is the totalamount in activity fees collected from thestudents?

(A) $32.80(B) $328.00

(C) $3,280.00(D) $32,800.00(E) $328,000.00

48



WORD PROBLEMS

SAT Practice Book

2009-2010

11

1. Each month, a telephone service chargesa base rate of $10.00 and an additional$0.08 per call for the first 40 calls and

$0.04 for every call after that. How muchdoes the telephone service charge for amonth in which 50 calls are made?

(A) $12.20(B) $12.80(C) $13.60(D) $14.40(E) $17.60

2. How many4

1-pound sticks of butter

together weigh as much as 25 pounds of butter?

3. The total cost of 5 equally pricednotebooks is $12.50. If the cost pernotebook is reduced by $1, how much will3 of these notebooks cost at the new rate?

(A) $4.50(B) $5.00(C) $6.50(D) $7.50(E) $9.50

4. When the number k is multiplied by 5,the result is the same as when 5 is addedto k . What is the value of 4 k?

(A)5

4

(B) 1

(C)4

5

(D) 4(E) 5

5. The bus fare from city A to city B is $5more for adults than for children. If agroup of 5 adults and 6 children pay atotal of $124 to travel by bus from city Ato city B , what is the cost of the ticket forone adult?

(A) $11

(B) $12(C) $14(D) $16(E) $17

6. Which of the following represents thetotal cost, in dollars, of x rolls of wrapping paper that cost $6 each and ygreeting cards that cost $2 each?

(A) 2 x + 6 y(B) 6 x + 2 y(C) 8( x + y)(D) 0.8( x + y)(E) (2 + x ) (6 + y )

49



WORD PROBLEMS

SAT Practice Book

2009-

2010

2

2009-2010

2

7. Jamal has some coins in his pocket.Some of these coins are quarters, and

none of the quarters in his pocket aredated earlier than 2000. Which of thefollowing must be true?

(A) None of the coins in Jamal’s pocketare dated earlier than 2000.(B) Some of the coins in Jamal’s pocket are dated earlier than 2000.(C) Some of the coins in Jamal’s pocketare dated 2000 or later.(D) Most of the coins in Jamal’s pocketare either quarters or dated earlier than2000.(E) Most of the coins in Jamal’s pocketare not quarters.

8. There are 6 bookcases in a house. Eachbookcase contains at least 125 books butnot more than 160 books. Which of thefollowing could be the total number of books in all 6 bookcases?

(A) 500(B) 625(C) 725

(D) 925(E) 1,000

9. The city library donated some children’sbooks to Mr. Clark’s first -grade class. If each student takes 4 books, there will be

20 books left. If 3 students do not take abook and the rest of the students take 5books each, there will be no books left.How many books were donated to theclass?

(A) 120(B) 140(C) 160(D) 175(E) 185

10. Bernardo drives to work at an averagespeed of 50 miles per hour and returnsalong the same route atan average speed of 25 miles per hour. If

his total travel time is 3 hours, what isthe total number of miles in the round-trip?

(A) 225(B) 112.5(C) 100(D) 62.5(E) 50

11. When a certain number is multiplied by

4

1and the product is then multiplied by

32, the result is 60. What is the number?

50



WORD PROBLEMS

SAT Practice Book

2009-

2010

4

2009-2010

4

18. The result when a number is divided by 2is equal to the result when that samenumber is divided by 4. What is that

number?

(A) -4(B) -2(C) 0(D) 2(E) 4

19. All of Kay’s brothers can swim.

If the statement above is true, which of thefollowing must also be true?

(A) If Fred cannot swim, then he is notKay’s brother.

(B) If Dave can swim, then he is not Kay’sbrother.

(C) If Walt can swim, then he is Kay’sbrother.

(D) If Pete is Kay’s brother, then he cannot

swim.(E) If Mark is not Kay’s brother, then hecannot swim.

20. When her son’s class held its magazinedrive, Dr. Nelson bought 7 one-yearmagazine subscriptions for the waiting roomin her office. She bought

4 subscriptions that have 12 issues per year,2 subscriptions that have 4 issues per year,and 1 subscription that has 52 issues peryear. Altogether, how many magazines willher office receive from these subscriptions?

52



FACTORING

SAT Practice Book

2009-2010

11

1. If a + 2( x + 1) = s, what is x + 1, interms of s and a ?

(A)a

s

2

(B)2

as

(C)2

as

(D) as

2

(E) as

2

2. If x 2+ y2 = 73 and xy = 24, what is thevalue of ( x + y )2?

(A) 73(B) 97(C) 100(D) 121(E) 144

3. If 2

1

2

1

)()( baba , which of thefollowing must be true?

(A) b = 0(B) a + b = 1(C) a – b = 1(D) a 2 + b 2 = 1(E) a 2 – b 2 = 1

4. If x 2 – y2 = 77 and x + y = 11, what isthe value of x ?

(A) 10(B) 9 (C) 8 (D) 7 (E) 6

5. If a, b, and c are different positiveintegers and 64222 cba , then

?cba 222

(A) 14(B) 17(C) 21

(D) 28(E) 34

6. If (2 x – 2)(2 – x ) = 0, what are all thepossible values of x ?

(A) 0 only(B) 1 only(C) 2 only(D) 1 and 2 only(E) 0, 1, and 2

53



FACTORING

SAT Practice Book

2009-

2010

2

2009-2010

2

7. If a and b are positive integers anda 2 – b 2 = 7, what is the value of a ?

(A) 3(B) 4(C) 5(D) 6(E) 7

8. If x 2 – y2 = 10 and x + y = 5, what is thevalue of x – y?

9. If xy = 7 and x – y = 5, thenx 2 y – xy2 =?

(A) 2

(B) 12(C) 24(D) 35(E) 70

10. If 2 x + z = 2y and 2 x + 2 y + z = 20,what is the value of y?

(A) 5(B) 8(C) 10(D) 15(E) It cannot be determined from theinformation given.

11. if

d cxbxax x x x 2323

90

1

30

1

10

1

for all values of x, where a,b,c, and d areconstants, what is the value of a+b+c+d ?

12. 3(x -7)( x -2)= kIn the equation above, k is a constant. If theroots of the equation are 7 and 2, what is thevalue of k?

(A) 0(B) 2(C) 3(D) 7(E) 14

54



FACTORING

SAT Practice Book

2009-

2010

3

2009-2010

3

13 . If 2 x − 64 = 0, which of the following could

be a value of x?

(A)−

8(B) − 4(C) 0(D) 16(E) 32

14. If n is a positive odd integer, then(n +1)( n +2) could equal which of thefollowing?

(A) 10(B) 15(C) 20(D) 25(E) 30

15. If x and y are numbers such that(x +9)( y − 9)=0, what is the smallest possiblevalue of 22 y x ?

(A) 0(B) 9(C) 18(D) 81(E) 162

16. If ( x +5) y= 2 x − x +13, what is the value of y

When x = 2?

17. If ( w − 2) 2 =0, what is the value of (w+3)( w+4)=?

(A) 30(B) 12(C) 7(D) − 1(E) It cannot be determined from theinformation given.

18. If x 2 +x =30, which of the following is apossible value of x 2 x?

(A) -30(B) 10(C) 20(D) 30(E) 870

55



MEAN, MEDIAN & MOD

SAT Practice Book

2009-2010

11

1. Carlos delivered n packages onMonday, 4 times as many packages onTuesday as on Monday, and 3 more

packages on Wednesday than onMonday. What is the average(arithmetic mean) number of packageshe delivered per day over the threedays?

(A) 2 n – 3(B) 2 n – 1(C) 2 n + 1(D) 2 n + 3(E) 6 n + 1

2. If the average (arithmetic mean) of x and y is k , which of the following is theaverage of x, y, and z?

(A)3

2 zk

(B)2

2 zk

(C)3

zk

(D)2

zk

(E)3

2 )( zk

3. The median of a set of 9 consecutiveintegers is 42. What is the greatest of these 9 integers?

4.

What was the average (arithmetic mean)of the scores of the 5 students on test II?

(A) 60(B) 65(C) 68(D) 70(E) 72

5. If the areas of two regions are equaland the sum of the areas of the regionsis 5, what is the average (arithmeticmean) of the areas of the two regions?

(A) 0

(B)2

5

(C)4

5

(D) 5(E) 10

56



MEAN, MEDIAN & MO

SAT Practice Book

2009-

2010

2

2009-2010

2

6. When the sum of a list of prices isdivided by the average (arithmeticmean) of the prices, the result is k .

What does k represent?

(A) The sum of the prices(B) Half of the sum of the prices(C) The average of the prices(D) The number of prices(E) Half of the number of prices

7. Number of Siblings per

Student in a Preschool ClassNumber

of SiblingsNumber

of Students0 3I 62 2

3 1

The table above shows how manystudents in a class of 12 preschoolershad 0, 1, 2, or 3 siblings. Later, a newstudent joined the class, and theaverage (arithmetic mean) number of siblings per student became equal tothe median number of siblings perstudent. How many siblings did thenew student have?

(A) 0(B) 1(C) 2(D) 3(E) 4

8. Each of 5 people had a blank card onwhich they wrote a positive integer. If the average (arithmetic mean) of these

integers is 15, what is the greatestpossible integer that could be on one of the cards?

9. The first term of a sequence is 20 andthe second term is 8. The third termand each term thereafter is theaverage (arithmetic mean) of the twoterms immediately preceding it. Whatis the value of the first term in thesequence that is not an integer?

10. If the average (arithmetic mean) of x and 3 x is 12, what is the value of x ?

(A) 2(B) 4(C) 6(D) 12(E) 24

57



MEAN, MEDIAN & MO

SAT Practice Book

2009-

2010

3

2009-2010

3

11. The average (arithmetic mean) of a , b ,and c is equal to the median of a , b ,and c. If 0 < a < b < c , which of the

following must be equal to b ?

(A)2

ca

(B)3

ca

(C)2

a-c

(D)3

a-c

(E) ac

12. Fifty percent of the songs played on acertain radio station are 3 minuteslong, 30 percent are 5 minutes long,and 20 percent are 2 minutes long.What is the average (arithmetic mean)number of minutes per song played onthis radio station?

13. If the average (arithmetic mean) of 5and r is 7 and the average of 3 and s is3, what is the average of r and s ?

(A) 3(B) 5(C) 6(D) 9(E) 12

14. a , 2 a , b

If the average (arithmetic mean) of the

3 numbers above is 2 a , what is b interms of a ?

(A) a

(B)2

3a

(C) 2 a

(D)2

5a

(E) 3 a

15. For which of the following lists of 7numbers is the average (arithmeticmean) less than the median?

(A) 1, 2, 3, 8, 9, 10, 11

(B) 3, 4, 5, 8, 11, 12, 13(C) 5, 5, 5, 8, 11, 11, 11(D) 5, 6, 7, 8, 9, 10, 11(E) 5, 6, 7, 8, 9, 10, 20

58



MEAN, MEDIAN & MO

SAT Practice Book

2009-

2010

4

2009-2010

4

16. For 12 bottles of shampoo of variousbrands, the cost and volume of eachare displayed in the scatterplot above,and the line of best fit for the data isshown. Of the following, which isclosest to the average (arithmeticmean) cost per ounce for the 12bottles?

(A) $0.06(B) $0.09(C) $0.12(D) $0.15(E) $0.18

17.

The table above shows the number of items100customers purchased from a hardware storeover a 4 -hour period. Which of the followingcan be determined from the information inthe table?

I. The average (arithmetic mean) number of items purchased per customer

II. The median number of items purchasedpercustomerIII. The mode of the number of itemspurchased per customer

(A) None(B) I and II only(C) I and III only(D) II and III only(E) I, II, and III

59



MEAN, MEDIAN & MO

SAT Practice Book

2009-

2010

5

2009-2010

5

18. The median of a list of 99 consecutiveintegers is 60. What is the greatestinteger in the list?

19. The average (arithmetic mean) of 6,19, and x is 19. What is the value of x ?

(A) 19(B) 25(C) 31(D) 32(E) 57

20. If the average (arithmetic mean) of tand t 2 is x and if the average of tand t 2 is y , what is the average of x and y ?

(A) 1

(B)2

t

(C) t

(D) t 2

1

(E) 2 t

21.

The bar graph above shows the number of tons of beans produced on a large farm forthe years 1985 through 1991. For which of the following two-year periods was theaverage (arithmetic mean) bean productionclosest to the bean production in 1985?

(A) 1986-1987(B) 1987-1988(C) 1988-1989(D) 1989-1990(E) 1990-1991

22. The average (arithmetic mean) of tand y is 15, and the average of w and xis 15. What is the average of t , w , x ,and y ?

(A) 7.5(B) 15

(C) 22.5(D) 30(E) 60

60



MEAN, MEDIAN & MO

SAT Practice Book

2009-

2010

6

2009-2010

6

23. 10, 18, 4, 15, 3, 21, x

If x is the median of the 7 numberslisted above, which of the followingcould be the value of x ?

(A) 5(B) 8(C) 9(D) 14(E) 16

24. If 2 x – 5, x + 1, and 3 x – 8 are allintegers and x + 1 is the median of

these integers, which of the followingcould be a value for x ?

(A) 5(B) 7(C) 9(D) 10(E) 11

61



EQUATIONS

SAT Practice Book

2009-2010

11

1. If 2 x + 3 = 9, what is the value of 4x – 3?

(A) 5(B) 9(C) 15(D) 18(E) 21

2. If 3

2

y

x , what is the value of y

x

2

3?

(A)3

1

(B)3

2

(C) 1

(D)2

3

(E)4

9

3. If 5 t = 45 and tk = 1, what is the valueof k?

(A)45

1

(B)9

1

(C)5

1

(D) 5(E) 9

4. If 3

2

y

x , what is the value of y

x

2

3?

(A)31

(B)3

2

(C) 1

(D)2

3

(E)4

9

5. If 3 x + 9 = 5 x + 1, what is the value of x ?

(A) 1(B) 2(C) 3(D) 4(E) 8

6. If 2( x – 3) = 8, what does3

3

x x equal?

62



EQUATIONS

SAT Practice Book

2009-

2010

2

2009-2010

2

7. If 6,565 = 65( x + 1), then x = ?

(A) 10

(B) 11(C) 100(D) 101(E) 1001

8. If 2 x – 10 = 20, then x – 5 = ?

(A) 5(B) 10(C) 15(D) 20(E) 30

9. If x = k (k

– 2), then x + 1 = ?

(A) k 2 – k (B) k 2 – 3k (C) k 2 – 2k + 1(D) k2 + 2 k + 1(E) k 2 – 1

10. 3739

2 x x , then x =

(A) 37(B) 39(C) 41(D) 74(E) 78

11. If 40,404 + x=44,444, then 40,404 -10 x = ?

(A) - 4.04

(B) 0.004(C) 4(D) 4.04(E) 40.4

12. If 0.0002 x 0.0002, then x

(A) 0.0001(B) 0.1

(C)2

1

(D) 1(E) 1,000

13. If n is 3 less than w and w is 1 more thanz, what is the value of n when z =1 ?

(A) 1(B) 0(C) 1(D) 2(E) 3

14. If 3 x x 2 x x 20, then x

(A) 20(B) 10(C) 5(D) 10(E) 20

63



EQUATIONS

SAT Practice Book

2009-

2010

3

2009-2010

3

15. Which of the following represents thetotal cost, in dollars, of k compact discs at$15 each and p compact disc cases at $25

each? (Disregard sales tax.)

(A) 15 k 25 p(B) 25 k 15 p(C) 40 (k p)(D) 0.40( k p)(E) (15 k )(25 p)

16. If tx 5 t 1 x, which of the following must betrue?

(A) x 4(B) x 5(C) t 4(D) t 5(E) t 5 x

17. If x = 5 y and y= z+1, what is5

x in terms of z ?

(A) z(B) z + 1(C) 5 z (D) 5 z +1(E) 5 1 z

18. If x 3 y and y 4 z, what is x in terms of z ?

(A) z4

3

(B) z

(C) z3

4

(D) 7 z(E) 12 z

19. 64

3)25( mif What is the value of m?

20. if then x x x ,24642 x=?

A) -288B) -2

C) -2

1

D)2

1

E) 2

21.if 2

1

1

1

x , What is the value of x?

A) 2B) 1C) 0D) -1E) -2

22. if 13)5( 2 x x y x what is the

value of y when x=2?

64



EQUATIONS

SAT Practice Book

2009-

2010

4

2009-2010

4

23. if ?1010

99,

3

2

ba y x

thenba y x

A)109

B)23

20

C)27

20

D)3

2

E)5

3

24 . If 10 + x is 5 more than 10, what is thevalue of 2 x ?

(A) -5(B) 5(C) 10(D) 25(E) 50

25 . The result when a number is divided by 2is equal to the result when that samenumber is divided by 4. What is thatnumber?

(A) -4(B) -2(C) 0(D) 2(E) 4

26. If a positive integer n is picked atrandom from the positive integers less thanor equal to 10, what is the probability that

5n +3 ≤ 14 ?

A) 0

B)10

1

C)5

1

D)10

3

E)5

2

27. If ( x -2) 2 =49, then x could be?

(A) -9(B) -7(C) 2(D) 5(E) 9

28. If (2 m)k =6, then mk =?

(A) 3(B) 4(C) 5(D) 6(E) 12

65



VARIATIONS

SAT Practice Book

2009-2010

11

1. Which of the following tables shows arelationship in which w is directlyproportional to x ?

(A)

(B)

(C)

(D)

(E)

2. If 5 t = 45 and tk = 1, what is the valueof k?

(A)45

1

(B)9

1

(C)5

1

(D) 5(E) 9

3 . If xr = v, v = kr, and rv 0, which of thefollowing is equal to k?

(A) 1(B)

x

1

(C) x – 1(D) x (E) x + 1

4. If y is directly proportional to x 2 and8

1 y

when2

1 x what is the positive value of x

when2

9 y ?

(A)4

3

(B)2

3

(C)4

9

(D) 3(E) 9

66



VARIATIONS

SAT Practice Book

2009-

2010

2

2009-2010

2

5. If y is inversely proportional to x and y = 15 when x = 5, what is the value of y when x = 25?

(A)5

1

(B)3

1

(C) 3(D) 5(E) 75

6. If r is directly proportional to s and if s =

when r = what is the value of r when

s =9

4?

7. If y is directly proportional to x and if y = 20 when x = 6, what is the value of ywhen x = 9?

(A)3

10

(B)3

40

(C) 23(D) 27(E) 30

67



INEQUALITIES & ABSOLUTE VA

SAT Practice Book

2009-2010

11

1. If rstv = 1 and stuv = 0, which of thefollowing must be true?

(A) r < 1(B) s < 1

(C) t >2

1

(D) u = 0(E) v = 0

2. If 2 x < y < 0, which of the following isgreatest?

(A) – 2x (B) – (2x + y )(C) 2 x (D) 0

(E) – y

3. If 3 b + 1 < 10, which of the followingCANNOT be the value of b?

(A) – 1(B) 0(C) 1(D) 2(E) 3

4. If x is an integer greater than 1 and if

x x y

1, which of the following must

be true?

I. y x II. y is an integer.III. xy > x 2


5. At a bottling company, machine A fillsa bottle with spring water andmachine B accepts the bottle only if the number of fluid ounces is between

8

711 and

8

112 If machine B accepts a

bottle containing n fluid ounces, whichof the following describes all possiblevalues of n ?

(A)8

112n

(B)8

112n

(C)8

112n

(D)8

112n

(E)8

112n

68




SAT Practice Book

2009-

2010

2

2009-2010

2

6. 22 33 )( x x

For what value of x is the statement

above FALSE?

(A) – 3(B) 0

(C)3

1

(D) 1(E) For no value of x

7. For how many ordered pairs of positiveintegers ( x, y ) is 2 x + 3 y < 6?

(A) One(B) Two(C) Three(D) Five

(E) Seven

8. If x and y are positive consecutive oddintegers, where y > x , which of thefollowing is y2 – x 2?

(A) 2 x (B) 4 x (C) 2 x + 2(D) 2 x + 4(E) 4 x + 4

9. 85

310

k

k

What is the value of k that satisfiesboth equations above?

10. A regulation for riding a certainamusement park ride requires that achild be between 30 inches and 50inches tall. Which of the followinginequalities can be used to determinewhether or not a child’s height h satisfies the regulation for this ride?

(A) 5010h

(B) 4020h

(C) 2030h

(D) 1040h

(E) 545h

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11. If 0 < x < 1, which of the followingstatements must be true?

I. x 2

> x 3

II. x >2

x

III. x> x 3

(A) I only(B) II only(C) I and II only(D) I and III only(E) I, II, and III

12.

On the number line above, t , u, v, w, x, y, and z are coordinates of theindicated points. Which of thefollowing is closest in value to | u + v| ?

(A) t (B) w(C) x (D) y (E) z

13. If 0 < n < 1, which of the followinggives the correct ordering of n , n ,and n 2 ?

(A) n < n < n 2

(B) n < n 2 < n (C) n < n < n 2

(D) n < n 2 < n (E) n 2 < n < n

14. If 80 x and 31 y , which of the following gives the set of allpossible values of xy?

(A) xy = 4(B) 240 xy (C) 111 xy (D) 241 xy (E) 248 xy

15. If x + y = 30 and x > 8, then which of the following must be true?

(A) y > 0(B) y < 22(C) y = 22(D) y > 22(E) x < 30

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16.

On the number line above, which of the following corresponds to wu ?

(A) t (B) v(C) x (D) y (E) z

17. 157

53

k

m

In the equations above, m < 0 and k< 0. What is the value of m – k?

(A) – 24(B) – 14(C) 8(D) 16(E) 20

18. If k(2x + 3)( x – 1) = 0 and x > 1,what is the value of k?

(A)2

3

(B) 0

(C)3

2

(D) 1(E) 2

19. If 4 x = 6 u = 5 v = 7 w > 0, which of the following is true?

(A) x < v < u < w (B) x < u < v < w (C) x < v < w < u (D) w < u < v < x (E) u < v < w < x

20. If x = – 1 and k > 0, which of thefollowing has the greatest value?

(A) 2 kx (B) 4 kx 2(C) 6 kx 3 (D) 8 kx 4 (E) l0 kx 5

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1. If 32 x , which of the following is a

possible value of x ?

(A) 4(B) 5{C) 6(D) 7(E) 8

2. If a >b>0, which of the following is greater

than b

a?

(A) 1

(B)a

b

(C)

b

a

1

(D)b

a

2

(E)b

a2

3. If -9 < x <9, which of the following must betrue?

(A) 2 x < 9(B) 3 x > 9(C) x < 9

(D) 2 x >7

(E) 9 x <9

4. If 8

1

7

11

8

1

7

1

6

1

xthen x could be

which of the following?

(A) 3(B) 4{C) 5(D) 6(E) 7

5. If m>0, thenm

m

m

mm

2

(A) 0(B) 1{C) m(D) 12m (E) 2m

6. . If y

1

6

1

5

1

7

1

6

1

5

1then y could be

which of the following?

(A) 6(B) 7{C) 8(D) 9(E) 10

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7. If a +b= 40 and a < 15, which of thefollowing must be true?

(A) a > 0(B) b < 25(C) b = 25(D) b > 25(E) b < 40

8. if x>0, then 2

22

x

x

x

x x

(A) 0(B) 1{C) x(D) 2 x (E) 1 x

9. If k is a positive integer divisible by 7, andif k < 90, what is the greatest possible valueof k ?

(A) 83

(B) 84(C) 87(D) 88(E) 89

10 . If a , b, and c are positive integers, and if (a − c)b=0, which of the following must betrue?

(A) a <b(B) b<c(C) a =b(D) a =c(E) b=c

11 . If p < − 5 or p > 5, which of the followingmust be true?

I. 2 p > 5

II. p > 5

III. 3 p > 5

(A) II only(B) I and II only(C) I and III only(D) II and III only(E) I, II, and III

12 . 3t =4

For how many values of t is the equationabove true?

(A) None(B) One(C) Two(D) Four(E) More than four

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13.

Which of the following inequalities is trueabout the lengths a and b of the sides of thetriangle above?

(A) 0 ≤ (a +b) 2 <20(B) 20 ≤ (a +b) 2 < 40(C) 40 ≤ (a +b) 2 < 100(D) 100 ≤ (a +b) 2 < 400(E) 400 ≤ (a +b) 2

14.

Which of the lettered points in the figureabove has coordinates ( x , y) such that

7 y x ?

(A) A(B) B(C) C (D) D(E) E

15. If 75 percent of m is equal to k percent of

25, where k > 0, what is the value of k

m?

(A)16

3

(B)3

1

(C)4

3

(D) 3

(E)3

16

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16. Marcus can spend no more than $120 on jeans and shirts for school. He buys 3 pairs of jeans at $32 each. If x represents the dollar

amount he can spend on shirts, which of thefollowing inequalities could be used todetermine the possible values for x ?

(A) (3) 32- x 120(B) (3) 32- x ≥ 120(C) (3) 32+ x 120(D) (3) 32+ x ≥ 120(E) x (3) 32

17. Each of the following inequalities is truefor some values of x EXCEPT

(A) x < x 2 < x 3 (B) x < x 3 < x 2 (C) x 2 <x 3 < x

(D) x 3

<x <x 2

(E) x 3 <x 2 <x

18. If 6 < 3 x < 7 and x< 0, what is one

possible value of x ?

19 . If x and y are integers, 7 < y < 16, and

5

2

y

x how many possible values are there for

x ?

(A) One(B) Two(C) Three(D) Four(E) Five

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1. 157

53

k

m

In the equations above, m < 0 and k < 0.What is the value of m – k?

(A) – 24(B) – 14(C) 8(D) 16(E) 20

2 .

66

1273

ky x

y x

For which of the following values for k willthe system of equations above have nosolution?

(A) − 14(B) − 7(C) 0(D) 7(E) 14

3 .174

852

ky x

y x

For which of the following values of k willthe system of equations above have nosolution?

(A) -10(B) -5(C) 0(D) 5(E) 1 0

4 .k wm

wxk

)1(

3

If k and m are defined by the equationsabove, what is the value of m when w = 4 andx = 1?

(A) 0(B) 3(C) 12(D) 24(E) 36

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5. If ba

y xthen

ba y x

101099

,32

A)109

B)23

10

C)27

10

D)3

2

E)5

3

6. If 5 y + 2 x = 23 and x = y + 1, what is thevalue of y?

7. If 2 x + z = 2y and 2 x + 2 y + z = 20, what isthe value of y?

(A) 5(B) 8(C) 10(D) 15(E) It cannot be determined from theinformation given.

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1. If x 2+ y2 = 73 and xy = 24, what is thevalue of ( x + y )2 ?

(A) 73(B) 97(C) 100(D) 121(E) 144

2.

The figure above shows the graphs of y = x 2 and y = a – x 2 for some constanta . If the length of PQ is equal to 6,what is the value of a ?

(A) 6(B) 9

(C) 12(D) 15(E) 18

3. The quadratic function g is given by g(x) = ax 2, + bx + c, where a and c arenegative constants. Which of the following

could be the graph of g ?

(A)

(B)

(C)

(D)

(E)

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3.

Which of the following could be the equationof the graph of function g , shown above?

(A) g (x ) = x 2 -3x +2

(B) g (x ) = x 2

-2x +1(C) g (x ) = x 2 +x + 3(D) g (x ) = x 2 +2 x -1(E) g (x ) = x 2 +3 x -2

5. If x 2 − 64 = 0, which of the following couldbe a value of x ?

(A) −8(B) −4(C) 0(D) 16(E) 32

6.

The quadratic function graphed above hasequation f (x ) = a − x 2 . Which of the followingmust be true ?

(A) a > 0(B) a < 0(C) a is even.(D) a is odd.(E) a is the square of an integer .

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1. The table above shows some values for thefunction f . If f is a linear function, what is thevalue of a + b ?

(A) 24 (B) 36(C) 48 (D) 72(E) It cannot be determined from theinformation given.

2 . The shaded region in the figureabove is bounded by the x – axis, the linex = 4, and the graph of y = f(x) .If the point

(a, b ) lies in the shaded region, which of thefollowing must be true?

I. a 4II. b a III. b f(a)

(A) I only (B) III only(C) I and II only (D) I and III only(E) I, II, and III

3.

The figure above shows the graph of y = g(x) . If the function h is defined by

h(x) = g( 2x) + 2, what is the value of h (1)?

4. A group of students washed cars to raisemoney. The net amount A , in dollars, raisedby washing k cars is given by the function

A(k) = 4 k – 30. If the group washed 15 cars,what is the net amount they raised?

(A) $10(B) $15(C) $20

(D) $25(E) $30

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5 . Let the function h be defined by

h(x) = 14 +4

2 x .If h ( 2m) = 9m , what is one

possible value of m ?

6. For which of the following functions is) f() f( 33 ?

(A) 24 x x f )(

(B) 4)( x f (C)

x x f

4)(

(D) 34 x x f )( (E) 44 x x f )(

7. The figure above shows the graph of thefunction h . Which of the following isclosest to h( 5 ) ?

(A) 1(B) 2(C) 3(D) 4(E) 5

8. The total daily cost c, in dollars, of producing x units of a certain product is

given by the function c(x) = x

x 200600+ k ,

where k is a constant and x 100. If 20 unitswere produced yesterday for atotal cost of $640, what is the value of k?

(A) 40(B) 50(C) 60(D) 590(E) 600

9. Let the function f be defined by f(x) = x + 1. If 2 f (p) = 20, what is the value of f ( 3 p) ?

\

10. The graph of y = g(x) is shown above.If g (k) = 1, which of the following is a

possible value of k?

(A) – 1.5(B) – 0.5(C) 1(D) 1.5(E) 2

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11. The table above gives values of thequadratic function f for selected values of x .Which of the following defines f ?

(A) f(x) = x 2 + 1(B) f(x) = x 2 + 2(C) f(x) = 2x 2 – 2(D) f(x) = 2x 2 – 1(E) f(x) = 2x 2 + 1

12. The graph of y = f(x) is shown above.Which of the following could be the graph of

y = f(x + 2 )?

(A)

(B)

(C)

(D)

(E)

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13. In the figure above, ABCD is a

rectangle. Points A and C lie on the graph of y = px 3, where p is a constant. If the area of ABCD is 4, what is the value of p ?

14. The total daily profit p , in dollars, fromproducing and selling x units of a certainproduct is given by the function

p (x) = 17 x – (10 x + b ), where b is a constant.If 300 units were produced and soldyesterday for a total profit of $1,900, what isthe value of b?

(A) – 200(B) – 100

(C) 0(D) 100(E) 200

15. The graph of y = g(x) is shown above.If g ( 2 ) = k , which of the following could bethe value of g (k) ?

(A) 2

(B) 2.5(C) 3(D) 3.5(E) 5

16. The figures above show the graphs of thefunctions f and g . The function f is defined by

f(x) = x 3 – 4x . The function g is defined by g(x) = f(x + h) + k , where h and k areconstants. What is the value of hk ?

(A) – 6(B) – 3(C) – 2(D) 3(E) 6

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17. If the function f is defined by f(x) = x 2 + b x + c, where b and c are positiveconstants, which of the following could be the

graph of f ?

(A)

(B)

(C)

(D)

(E)

18. The table above gives values of the linearfunction g for selected values of t . Which of the following defines g ?

(A) g(t)= 2

1t + 1

(B) g(t)= – 2

1t + 1

(C) g(t)= – t + 1(D) g (t)= – t + 2(E) g(t)= – 2t + 2

Questions 19 –20 refer to the following functions g and h .

nnnh

nnng2

2

)(

)(

19. g ( 5 ) – h( 4 ) =

(A) 0(B) 8(C) 10(D) 18(E) 32

20. Which of the following is equivalent toh (m + 1)?

(A) g (m)(B) g (m) + 1(C) g (m) – 1(D) h (m) + 1(E) h(m) – 1

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21. Let the function f be defined by f(x) = x 2 + 18. If m is a positive number suchthat f (2m ) = 2 f (m ), what is the value of m ?

22. Let the function h be defined byh (t) = 2( t3 – 3). When h (t) = – 60, what is thevalue of 2 – 3t?

(A) 35(B) 11

(C) 7(D) – 7(E) – 11

23. The table above represents a relationshipbetween x and y. Which of the followinglinear equations describes the relationship?

(A) y = x + 1(B) y = x + 4(C) y = 3x (D) y = 4x (E) y = 4x – 1

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1. Let the function f be defined by f(x) = 2x – 1.

If 2

1 f ( t ) = 4, what is the value of t?

(A)2

3

(B)2

7

(C)2

9

(D)4

49

(E)4

81

2. Based on the graph of the function f above,what are the values of x for which f(x) isnegative?

(A) – 6 < x < 0(B) 0 < x < 6(C) 6 < x < 7(D) – 6 < x < 6(E) – 6 < x < 0 and 6 < x < 7

3. Let the function f be defined by f(x) = x 2 + 18. If m is a positive number suchthat f (2m ) = 2 f (m ), what is the value of m ?

4. The rate for a telephone call between City A and City B is 50 cents for the first minuteand 30 cents for each additional minute orportion thereof. Which of the followingfunctions describes the cost, in dollars, of aphone call between these two cities that lastsfor n minutes, if n is a positive integer?

(A) f(n) = 0.80 n(B) f(n) = 0.50 + 0.30 n(C) f(n) = 0.50 + 0.30 ( n + 1)

(D) f(n) = 0.50 + 0.30 ( n – 1)(E) f(n) = 0.50 n + 0.30( n – 1)

5. For all numbers x , the function f is definedby f (x ) =( x +4) ( x +2). Which of the followinghas a negative value?

(A) f ( 5)(B) f ( 4)(C) f ( -3)(D) f ( -2)(E) f ( -1)

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6. A weather-watch camera is set so that itsshutter opens every 31 seconds. If g (h)represents the number of times the camera’s

shutter opens in h hours, which of thefollowing defines g?

(A) g (h) = 31h(B) g (h) = 31* 3600h(C) g (h) = 31h/3600(D) g (h) =3600h/31 (E) g (h) =31*3600/h

7. Let the function s be defined so that s(x) isthe area of a semicircle with diameter x. If s(6) +s (8) =s (b), what is the value of b?

8. The table above gives values of the linearfunction k for selected values of x. Which of the following defines k?

(A) k (x) = -2x +1(B) k (x) = -x +1

(C) k (x) =2

1

2

1 x

(D) k (x) = x -1(E) k (x) =2x-1

9. For all x ≥ -1, let the function f be definedas f (x ) = x +1. Which of the following is equalto f (15) f (8)?

(A) f ( 1)(B) f (0)(C) f (1)(D) f (7)(E) f ( 7 )

10. The table above shows some values forthe functions f and g. If f and g are linearfunctions, what is the value of a b?

(A) 0(B) 1(C) 2(D) 3(E) 4

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11. Rita’s dog weigh ed 5 pounds when shebought it. Over the next several years, thedog’s weight increased by 10 percent per

year. Which of the following functions givesthe weight, w, in pounds, of the dog after nyears of weight gain at this rate?

(A) w(n)=5+0.1n(B) w(n) = 5(0.1) n (C) w(n) = 5(0.9) n (D) w(n) = 5(1.1) n (E) w(n) = 5(n) 1.1

f x =kg(x) +2

12. The function f above is defined in termsof another function g for all values of x,

where k is a constant. If t is a number forwhich f (t) = 30 and g (t) = 8, what does kequal?

13. Which of the following could be theequation of the graph of function g , shownabove?

(A) g (x ) = x 2-3x +2(B) g (x ) = x 2 -2x +1(C) g (x ) = x 2 +x + 3(D) g (x ) = x 2 +2 x -1(E) g (x ) = x 2 +3 x -2

14. Let the function f be defined byf(x) =2x-1.

If 2

1f (t) = 10 what is the value of t?

(A) 9.5(B) 3(C) 3(D) 9.5(E) 10.5

15. For which of the following functions is ittrue that f (-2)= f(2)?

(A) f (x) =

(B) f (x) = 2 - x(C) f (x)=x+1(D) f (x)= x

2

+1(E) f (x)=2 x 3

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1.

The function f graphed above is defined for−3 ≤ x ≤ 6. For which of the following values

of x is f (x) < )( x f ?

(A) −3 (B) −2 (C) −1(D) 1 (E) 5

2. For all x, the function f is defined byf (x) = 3x, and the function g is defined byg(x) = f (x) + 2. What is the value of g (50)?

3. c (n ) = 35 + 12 n

To hold a birthday party for n people, theamount a party planner charges, in dollars,is given by the function c(n) above. How

much, in dollars, does the planner charge tohold a birthday party for 12 people?(Disregard the $ sign when gridding youranswer.)

4.2)(

)( 2

x xt

x xr

The functions r and t are defined above. Forhow many values of a is it true thatr (a) = t (a)?

(A) None(B) One(C) Two(D) Three(E) More than three

5.

The function y= f (x ), defined for −5≤ x ≤6, isgraphed above. Which of the following givesall values of x for which f (x ) is positive?

(A) 0< x ≤6(B) 5< x ≤6(C) −5≤ x <2(D) −4< x <1 and 5< x ≤6(E) −5≤ x < −4 and 1< x <5

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6. If the function f is defined by3

6)(

x x f ,

for what value of x does f(x) = 20?

7. If the function g is defined by g(x) =x 3 −3x,what is the value of g ( −3)?

(A) −36(B) −18(C) −3(D) 18(E) 36

8.

The table above gives values of the function f for several values of t . If the graph of f is aline, which of the following defines f (t )?

(A) f (t )=t-1(B) f (t )=t+1(C) f (t )=2 t+1(D) f (t )=2 t-1(E) f (t )=1-2 t

9.

Based on the graph of the function f above,what are the values of x for which f(x) ispositive?

(A) -2 x <1 or 8<x< 10(B) -2 x <1 or 4<x<8(C) 1<x<4 or 8<x 10(D) -2 x 10(E) 1<x<8

10. Let the function f be defined by f(x) = 5xfor all numbers x. Which of the following isequivalent to f(p + r)?

( A)5

r p

(B) 5p+r(C) 5p+5r

(D) 10 (p + r)(E) 25pr

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11. The graph of y= f(x) is shown above.If -3 x 6, for how many values of x doesf(x) = 2?


12.

The graph of y= f(x) is shown above.If -3 x 6, for how many values of x doesf(x) = 2?


13. If the function f is defined by f(x)=3x + 4,then 2f(x) +4=?

(A) 5x +4(B) 5x+ 8(C) 6x +4(D) 6x+ 8(E) 6x +12

14.

The graphs of the functions f and g are lines,as shown above. What is the value of f (3) +g (3)?

(A) 1.5(B) 2(C) 3(D) 4(E) 5.5

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15.

Based on the portions of the graphs of thefunctions f and g shown above, what are allvalues of x between -6 and 6 for whichg (x) >f (x)?

(A) 6< x< 3 only(B) 3 <x< 0 only(C) 0 <x< 3 only(D) 3 <x< 6 only

(E) 6 <x< 3 and 0< x< 3

16. Which of the following is the graph of afunction f such that f(x) =0 for exactly twovalues of x between- 5 and 5?

A.

B.

C.

D.

E.

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1. Let the operations ∆ and □ be definedfor all real numbers a and b as follows.

a ∆ b = a + 3b

a □ b = a + 4b

If 4 ∆ (5 y) = (5 y) □ 4, what is the valueof y?

2. Let the operation be defined by

bababa for all numbers a and b,

where a b . If 1 2 = 2 x , what isthe value of x ?

(A) 4(B) 3(C) 2(D) l(E) 0

3. For all the numbers x and y, let theoperation □ be defined byx □ y =xy – y. If a and b are positiveintegers, which of the following can beequal to zero?

I. a □ bII. (a + b) □ bIII . a □ (a + b)

(A) I only(B) II only(C) III only

(D) I and II(E) I and III

4. Let be defined as = x 2 – x

for all values of x . If whatis the value of a ?

(A) 1

(B)2

1

(C)2

3

(D)5

6

(E) 3

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5. For all positive integers j and k, let j ® k be defined as the whole number remainderwhen j is divided by k. If 13 ® k = 2, whatis the value of k?

6. Let be defined as

= y y z x for all positive integers x,

y, and z. What is the value of ?

Questions 7-9 refer to the following definition.

Let # be defined by a # b = ab + a + b for allnumbers a and b.

7. 2 # 5 =

(A) 7

(B) 10(C) 17(D) 20(E) 32

8. If 10 # h = 98, then h =

(A) 8

(B) 9(C) 10(D) 11(E) 12

9. For what value of x is the statement x # y = x always true?

(A) - 2(B) - 1(C) 0(D) 1(E) 2

10. For all values of y, let y be definedby y = y2- 1.Which of the followingis equal to ( y ) ?

(A) y4 − 1(B) y4 – y2 − 1(C) y4 + y2 − 1(D) y4 − 2 y2

(E) y4 − 2 y2 + 1

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11. For all positive integers a and b, let ▲be defined by a ▲b = a 2+ b 2 − 2.If c and d are positive integers, which

of the following CANNOT be the valueof c▲d ?

(A) 0(B) 2(C) 3(D) 6(E) 8

12. For all positive integers w and y,where w > y, let the operation be

defined by w y= yw

yw

2

2.

For how many positive integers w is w1 equal to 4 ?

(A) None(B) One(C) Two(D) Four(E) More than four

13. For all numbers x and y, let x y be

defined as x y = x 2 + xy + y2. What is

the value of (3 1) 1 ?

(A) 5(B) 13(C) 27(D) 170(E) 183

14. Let x be defined as x+ x

1

for all nonzero integers x . If x = t , where t is an integer, which of the following is a possible value of t ?

(A) 1(B) 0(C) −1(D) −2(E) −3

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1. In the xy – plane, the equation of line l is y = 2 x + 5. If line m is the reflectionof line l in the x – axis, what is the

equation of line m ?

(A) y = – 2x – 5(B) y = – 2x + 5(C) y = 2 x – 5

(D) y = 2

1x – 5

(E) y =2

1x + 5

2. In the xy – plane, line l passes through theorigin and is perpendicu1ar to the line

k y x4 where k is a constant. If the twolines intersect at the point ( t , t + 1), what is

the value of t?

(A)3

4

(B)4

5

(C)4

3

(D)4

5

(E)34

3. In the figure above, what is the slope of line ℓ ?(A)

(B)

(C)

(D)

(E)

4. In the coordinate plane, the points Fand H lie on a circle with

center P.What are the coordinates of point P ?

(A (B)(C)(D)(E)

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5. Which of the following is the graph of a linear function with a negative slopeand a positive y – intercept?

(A)

(B)

(C)

(D)

(E)

6. In the figure above, the scale on thex – axis is different from the scale onthe y – axis. If the area of ∆ABC is 18,what is the value of k?

(A)10

3

(B)4

3

(C)5

6

(D)2

3

(E) 3

7. In the xy – plane, the center of a circlehas coordinates (3, – 7). If one endpointof a diameter of the circle is ( – 2, – 7),

what are the coordinates of the otherendpoint of this diameter?

(A) ( – 7, – 7)(B) ( – 2, – 2)(C) (3, – 2)(D) (8, – 2)(E) (8, – 7)

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8. In the figure above, RS = ST andthe coordinates of S are ( k , 3).What is the value of k?

(A) – 3(B) 3

(C) 0(D) 3 (E) 3

9. If the areas of the two rectangles in thefigure above are equal, which of the followingcould be the coordinates of point P ?

(A) ( −5, −3)(B) ( −5, 3)(C) (5, − 5)(D) (5, − 3)(E) (5, 3)

10. What is an equation of line in the figureabove?

(A) y=

(B) y=

(C) y=

(D) y=

(E) y=

11. In the xy -plane, an equation of line ℓ isy=3x −1. If line m is the reflection of line ℓ inthe y -axis, what is an equation of line m ?

(A) y = − 3x −1(B) y = − 3x+1(C) y=3x+1(D) y=

(E) y=

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12. In the xy-coordinate plane, the graph of y= intersects line ℓ at (p, 5) and(t, -7). What is the least possible value of the

slope of ℓ?

(A) 6(B) 2(C) -2(D) -6(E) -10

13. In the xy – coordinate system above,which of the following line segmentshas a slope of – 1?

(A) OA (B) OB (C) OC (D) OD

(E) DC

14. In the figure above, line l passesthrough the origin. What is the value

of h

k ?

(A) 3(B) 2

(C)2

3

(D)2

3

(E) – 3

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15. The figure above shows the graphof the line y = mx + b , where m and b are constants. Which of the followingbest represents the graph of the line

y = – 3mx + b ?

(A)

(B)

(C)

(D)

(E)

16. The figure above shows the graph of theline y = ax + b , where a and b are constants.Which of the following best represents thegraph of the line y = 2ax + b ?

(A)

(B)

(C)

(D)

(E)

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17. Rectangle ABCD lies in thexy – coordinate plane so that its sidesare not parallel to the axes. What is

the product of the slopes of all foursides of rectangle ABCD ?

(A) – 2(B) – 1(C) 0(D) 1(E) 2

18. In the xy – plane above, points Q andS are the centers of the circles, whichare tangent to the x – axis. What is theslope of line QS (not shown)?

(A)8

1

(B)4

1

(C)2

1

(D)87

(E) 1

19. Which of the lettered points in thefigure above has coordinates ( x, y ) such that

3 y x ?

(A) A (B) B (C) C (D) D(E) E

20. In the figure above, if the legs of triangle ABC are parallel to the axes, whichof the following could be the lengths of thesides of triangle ABC ?

(A) 2, 5, and 29 (B) 2, 5,and 7(C) 3, 3, and 23 (D) 3, 4,and 5(E) 4, 5,and 41

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21. In the figure above, the slope of line ℓ is .What is the value of k ?

(A) 3

(B)

(C)

(D) 2

(E)

22. If the areas of the two rectangles in thefigure above are equal, which of the followingcould be the coordinates of point R ?

(A)(B)(C)(D)(E)

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1. In the figure above, line ℓ (not shown) isperpendicular to and bisects . Which of the following points lies on line ℓ?

(A)(B)(C)(D)(E)

2. In the figure above, the coordinates of Pare (10 -2a, 0) - and the coordinates of Q are(10, a). A point in square ORST is to bechosen at random. If the probability that thepoint will be in the shaded triangle is whatis the value of a?

(A)(B)(C) 2(D) 2(E) 5

3. Point P is the point with the greatest y-coordinate on the semicircle shown above.What is the x-coordinate of point Q ?

(A) -3.5(B) -3(C) -2.5(D)-2(E)-1.5

4. Point S is the point with the greatest y -coordinate on the semicircle shown above.What is the x – coordinate of point R ?

(A) −5.5

(B) −4(C) −3.5(D) −3(E) −2.5

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5. What is an equation of the line parallel tothe x – axis and two units above the x -axis?

(A) x = − 2(B) x = 2(C) y = − 2(D) y = 0(E) y = 2

6. Which of the lettered points in the figureabove has coordinates (x,y) such thaty =5?

(A) A

(B) B(C) C(D) D(E) E

7. In the figure above, if line ℓ has a slope of -2, what is the y-intercept of ℓ?

(A) 7(B) 8(C) 9(D) 10(E) 12

8. If x is the coordinate of the indicated pointon the number line above, which of thelettered points has coordinate -2x ?

(A) A (B) B(C) C(D) D(E) E

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Questions 9-10 refer to the following figureand information.

The grid above represents equally spacedstreets in a town that has no one-way streets.F marks the corner where a firehouse islocated. Points W, X, Y, and Z represent thelocations of some other buildings. The firecompany defines a building’s m-distance asthe minimum number of blocks that a firetruck must travel from the firehouse to reachthe building. For example, the building at Xis an m-distance of 2, and the building at Y

is an m-distance of from the firehouse.

9. What is the m-distance of the building atW from the firehouse?

(A) 2

(B) 2

(C) 3

(D) 3

(E) 4

10. What is the total number of differentroutes that a fire truck can travel the m-distance from F to Z ?

(A) Six(B) Five(C) Four(D) Three(E) Two

11. All of the buildings in the town that arean m-distance of 3 from the firehouse mustlie on a

(A) circle(B) square(C) right isosceles triangle(D) pair of intersecting lines(E) line

12. In the figure above, line ℓ intersects thex-axis at x = -2 and the y-axis at y = -3. If linem (not shown) passes through the origin andis perpendicular to line ℓ, what is the slope of line m ?

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13. In the xy – coordinate plane, the distancebetween point B(10, 18) and point A(x, 3)is 17. What is one possible value of x?

14. In a rectangular coordinate system, thecenter of a circle has coordinates (5, 12),and the circle touches the x – axis at onepoint only. What is the radius of thecircle?

15. In the figure above, PQRS is a rectangle,and points Q and. R lie on the graph of y= ax 2, where a is a constant. If theperimeter of PQRS is 10, what is thevalue of a ?

16. In the figure above, ABCD is a

rectangle. Points A and C lie on thegraph of y = px 3, where p is a constant.If the area of ABCD is 4, what is thevalue of p ?

17. Point P lies on the line with equation y – 4 = 3( x – 2). If the x – coordinate of P is4, what is the y – coordinate of P ?

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18. Line m (not shown) passes through Oand intersects AB between A and B.What is one possible value of the slopeof line m ?

19. In the xy-plane above, the area of ∆ OSTis 8. What is the value of a ?

20. In the xy -coordinate plane, the distancebetween points P(10,y) and Q(70, 14) is 61.What is one possible value of y ?

21. In the xy -coordinate plane above, AC =3, BC = 5, and is perpendicular to . If the coordinates of point A are (1, 0), what isthe y -intercept of line ℓ ?

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1. In the figure above, PS and TR intersectat O and ON is perpendicular to PS . Whatis the value of y – x?

(A) 20(B) 70(C) 90(D) 100(E) 140

2. In the figure above, l n and x > 90. Whichof the following must be true?

(A) y < 90

(B) y > 90(C) y = 90(D) n m(E) l//m

3. In the figure above, if l // m , then the sumof the measures of angles 2 and 4 must equalthe sum of the measures of which of thefollowing pairs of angles?

(A) 5 and 6(B) 5 and 7(C) 6 and 7(D) 6 and 8(E) 7 and 8

4.

In the figure above, three line segments meetat a point to form three angles. What is thevalue of x ?

(A) 20(B) 36(C) 40(D) 45(E) 60

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5. What is the value of x in the figure above?

6. In the figure above, l //m and r = 50.What is the value of s + t + u ?

(A) 230(B) 240(C) 250(D) 270

(E) 310

7. Three lines intersect in a point as shown

in the figure above. Which of the followingpairs of angle measures is NOT sufficient fordetermining all six angle measures?

(A) t and z(B) t and y(C) s and x (D) r and t (E) r and s

Note: Figure not drawn to scale.

8. In the figure above, m // n and l bisects<ABC . If 45 < y < 55, what is one possiblevalue for x ?

9. In the figure above, if z = 30, what is thevalue of x + y ?

(A) 60(B) 150(C) 180(D) 210(E) 330

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10. In the figure above, if AB is a line, whatis the value of y?

(A) 108(B) 114

(C) 117(D) 120(E) 135

11. In the figure above, l // m . If x = 80 and y= 70, what is the value of z?

(A) 30

(B) 60(C) 75(D) 90(E) 150

12 . In the figure above, y + z =?

(A) 180(B) 195(C) 215(D) 230(E) 245

.

13 . In the figure above, if x = 70 and y = 40and the dotted lines bisect the angles withmeasures x ° and y°, what is the value of z°?

(A) 30

(B) 40(C) 45(D) 50(E) 55

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14 . In the figure above, AD , BE , and CF intersect at point O. If the measure of < AOB

is 80° and CF bisects < BOD , what is themeasure of < EOF ?

(A) 40°(B) 50°(C) 60°(D) 70°(E) 80°

15. In the figure above, if l // m , what does z equal in terms of x and y?

(A) x + y(B) x – y (C) 180 – x (D) 180 – x + y(E) 180 – x – y

16. In the figure above l // m. If v = 2w,which of the following must be equal to q?

(A) v + t(B) v - t(C) t(D) 2v(E) s + t

.

17. In the figure above, AE and BG intersectat C . If x = 80 and CF bisects ECG , what isthe value of y?

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18 . In the figure above, l // m . If p (notshown) is another line in the plane, what is

the least number of points at which p canintersect these four lines?

(A) None(B) One(C) Two(D) Three(E) Four

19 . In the figure above, OA OC and OBOD. If x = 35, what is the value of z?

(A) 55(B) 45(C) 35(D) 30(E) 25

20.

In the figure above, the measure of SQR is

5

2the measure of PQR . If the

measure of PQR is3

2the measure of a

right angle, what is the measure of SQR?

(A) 24(B) 36(C) 48(D) 60(E) 96

.

21. In the figure above, lines k, l, and m areparallel. If y = 125, what is the value of x + z?

(A) 90(B) 95(C) 100(D) 105(E) 110

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TRIANGLES

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1. In the equilateral triangle RST above,what is the value of y ?

(A) 60(B) 70(C) 75(D) 80(E) 85

2. In the figure above, N lies on MO . Interms of x , which of the following mustbe equivalent to y ?

(A) x2 (B) 52 x (C) 53 x (D) x90 (E) x3180

Note: Figure not drown to scale.

3. In the xy-plane above, the area of OST is 8. What is the value of a ?

4. In the figure above, what is the valueof x + y ?

(A) 90(B) 100(C) 110(D) 120(E) 130

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Note: Figure not drown to scale.

5. In the figure above, 90 x and 1 z y .If z is an integer, what is the greatestpossible value of y ?

(A) 30(B) 45(C) 60(D) 61(E) 89

6. If the length of AB is 5 and the lengthof BC is 6, which of the following couldbe the length of AC ?

(A) 10(B) 12

(C) 13(D) 15(E) 16

7. In triangle ABC above, if AD = 6, DC = 3, and BC = 4, what is the areaof triangle ABD?

(A) 36(B) 18(C) 12(D) 6(E) 3

8. In ABC above, what is the length of AD ?

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9. In ABC above, AB = 3, and D is themidpoint of AC . What is the length of BC ?

(A) 33 (approximately 5.20)

(B) 24 (approximately 5.66)(C) 34 (approximately 6.93)(D) 26 (approximately 8.49)(E) 35 (approximately 8.66)

10. In isosceles triangle ABC , the measureof angle A is 80 . If another angle of the triangle measures x , where

80 x , what is one possible value of x ?

11. In the triangle above, x =

(A) 59(B) 60(C) 61(D) 62(E) 63

12. In the figure above,the coordinates of P are )0,210( a and the coordinates of Q are ),10( a .A point in square ORST isto be chosen at random. If theprobability that the point will be in the

shaded triangle is51 , what is the value

of a ?(A) 5 (B) 10 (C) 52 (D) 102 (E) 5

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13. In the figure above, if the area of triangle CAF is equal to the area of rectangle CDEF , what is the length of segment AD ?

(A)2

7

(B) 5(C) 7

(D)2

15

(E) 15

14. In the figure above, side AC of ABC is on line ℓ . What is x in terms of k ?

(A) k 60 (B) k (C) k 60 (D) k 120 (E) k 2120

15. If the length of LM is 7 and the lengthof MN is 8, which of the followingcould be the length of LN ?

(A) 23(B) 22(C) 17(D) 16(E) 14

16. A circle (not drawn) passes throughpoint A in the figure above. Whatcould be the total number of points of intersection of this circle and Δ ABC ?

I. 1

II. 3III. 4

(A) I only(B) II only(C) I and II only(D) II and III only(E) I, II, and III

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17. In triangle XYZ above, XW = 2,WZ = 8, and XY = 6. What is the areaof triangle WYZ ?

(A) 6(B) 12(C) 18(D) 24(E) 30

18. In the figure above, Δ ABC is similar to Δ DEF . What is the length of side EF ?

19. In the figure above, ABDE is a square, Δ BCD is a right triangle, and AB = BC . If a point is chosen atrandom from polygon ACDE , what isthe probability that the chosen point isin the shaded region?

(A)2

1

(B)3

1

(C)4

1

(D)5

1

(E)6

1

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20. The figure above is a right triangle.What is the value of 225 x ?

(A) 32

(B) 34(C) 39(D) 50(E) 64

21. In the figure above, a < 40 andb = c + 1. If c is an integer, what is theleast possible value of b ?

(A) 30(B) 39(C) 50(D) 61(E) 71

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6. In the figure above, triangles ABC andCDE are equilateral and line segment AE has length 25. What is the sum of the perimeters of the two triangles?

7. In the figure above, which of thefollowing is greatest?

(A) a(B) b(C) c(D) d(E) e

8. In PQR above, PR = QR . Which of the following must be true?

(A) u = x (B) x = v

(C) x = z(D) y = x (E) y = z

9. In the figure above, 6 AC and 3 BC .Point P (not shown) lies on AB between A and B such that ABCP .Which of the following could be thelength of CP ?

(A) 2(B) 4(C) 5(D) 7(E) 8

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(E) 100

14. In the right triangle above, if x = 3,what is the value of y?

(A) 13 (approximately 3.61)

(B) 15 (approximately 3.87)(C) 4(D) 17 (approximately 4.12)(E) 5

15.

Each angle of ∆ ABC above has thesame measure as angle in ∆ XYZ (notshown). If the length of one side of ∆ XYZ is 24, what is one possible

perimeter of ∆ XYZ ?

16.

In the figure above, ∆ PQR isequilateral and SR and TV intersectat point P . What is the value of y?

17.

In the figure above, AD = 1 and DC = 3 . What is the value of z?

(A) 15(B) 20(C) 25(D) 30(E) 35

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1.

In the figure above, JLKN and JL LM . If the lengths of LN and

LM are equal, what is the value of x ?

2.

In the figure above, what is the valueof t + u ?

(A) 80(B) 90(C) 100(D) 110(E) 120

3.

In the figure above, AB = BC and DE = EF = DF . If the measure of < ABC is 30° and the measure of < BDE is 50°, what is the measure of < DFA ?

(A) 30°(B) 35°(C) 40°(D) 45°(E) 50°

4.

In the figure above, what is the sum,in terms of n , of the degree measures

of the four angles marked witharrows?

(A) n (B) 2 n (C) 180 – n (D) 360 – n(E) 360 – 2n

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5.

In ∆ XYZ above, XZ is7

6of h , the

length of the altitude. What is the areaof ∆ XYZ in terms of h ?

(A)3

2h

(B)7

3 2h

(C)7

3 h

(D)7

6 2h

(E)7

12 2h

6. P(3, 2)Q(7, 2)R(7, 4)

The coordinates of points P, Q, and R in the xy – plane are given above. Whatis the perimeter of ∆ PQR ?

(A) 12(B) 14(C) 6 + 20 (approximately 10.47)(D) 6 + 32 (approximately 11.66)(E) 164 (approximately 12.81)

7.

In the figure above, what is the valueof z?

(A) 55(B) 60(C) 65(D) 70

(E) 75

8.

If AB = BC and BD bisects AC in thefigure above, which of the followingCANNOT be concluded?

(A) w = x (B) w = z(C) x = y(D) AD = DC (E) AC BD

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9.

In the figure above, if z = 30, what isthe value of x + y ?

(A) 60(B) 150(C) 180(D) 210(E) 330

10.

In the figure above, AE and CD areeach perpendicular to CE . If x = y , the

length of AB is 4, and the length of BD is 8, what is the length of CE ?

(A) 23 (approximately 4.24)(B) 26 (approximately 8.49)(C) 28 (approximately 11.31)(D) 210 (approximately 14.14)(E) 212 (approximately 16.97)

11.

For the triangles above, the perimeterof ∆ ABC equals the perimeter of ∆ DEF . If ∆ ABC is equilateral, what isthe length of AB ?

(A) 4

(B) 5(C) 7(D) 9(E) 15

12.

In the triangles above, what is theaverage (arithmetic mean) of u, v, w, x,and y?

(A) 21(B) 45(C) 50(D) 52(E) 54

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13.

In the figure above, points P, A, and B are equally spaced on line l and points

P, Q, and R are equally spaced on linem . If PB = 4, PR = 6, and AQ = 4, whatis the perimeter of quadrilateral

QABR ?

(A) 13(B) 14(C) 15(D) 16(E) 17

14.

In the figure above, the perimeter of the triangle is 4 + 2 2 . What is thevalue of x ?

(A) 2

(B) 4(C) 2 (D) 2 2 (E) 2 + 2

15.

In the figure above, y + z = ?

(A) 180(B) 195(C) 215(D) 230(E) 245

16. A square and an equilateral trianglehave equal perimeters. If the squarehas sides of length 3, what is thelength of one side of the triangle?

(A) 2

(B) 3(C) 4(D) 5(E) 6

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17. The perimeter of equilateral triangle ABC is 3 times the perimeter of equilateral triangle DEF . If the

perimeter of ∆ DEF is 10, what is thelength of one side of ∆ ABC ?

(A)3

13 (B) 10 (C) 15

(D) 30 (E) 40

18.

In ∆ ABC above, what is the value of x ?

(A) 25 (B) 30 (C) 35(D) 40 (E) 60

19.

The figure above is a right triangle.What is the value of 49 + x 2?

(A) 50 (B) 51 (C) 72(D) 98 (E) 100

20.

In the figure above, if the legs of triangle ABC are parallel to the axes,which of the following could be thelengths of the sides of triangle ABC ?

(A) 2, 5, and 29 (B) 2, 5,and 7(C) 3, 3, and 23 (D) 3, 4,and 5(E) 4, 5,and 41

21. If the degree measures of the angles of a triangle are in the ratio 2:3:4, by howmany degrees does the measure of thelargest angle exceed the measure of the smallest angle?

(A) 2 0°(B) 30°(C) 40°(D) 5 0°(E) 60°

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1. In the figure above, a small square isinside a larger square. What is the area, interms of x , of the shaded region?

(A) 2 x – 10(B) 10 – 2x (C) 25 – 2x

(D) x 2

– 25(E) 25 – x 2

2. In the figure above, rectangle ABCD ismade up of seven non-overlappingrectangles. The two smallest rectangles havethe same area. Each of the other rectangleshas twice the area of the next smallerrectangle. The area of the shaded rectangle iswhat fraction of the area of rectangle ABCD?

(A)128

1

(B)641

(C)32

1

(D)16

1

(E)7

1

3. In the figure above, the circle is tangent tosides BC and AD of the 8-by-12 rectangle,

ABCD . What is the area of the circle?

(A) 16 (B) 20 (C) 36

(D) 64

(E) 96

4. What is the perimeter of the figure above?

(A) 24(B) 25(C) 28

(D) 30(E) 36

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5. In the figure above, ABCD is a rectanglewith BC = 4 and AB = 6. Points P, Q, and R are different points on a line (not shown) thatis parallel to AD . Points P and Q aresymmetric about line AB and points Q and R

are symmetric about line CD . What is thelength of PR ?

(A) 6(B) 8(C) 10(D) 12(E) 20

.

6. The pattern shown above is composed of rectangles. This pattern is used repeatedly tocompletely cover a rectangular region 12 L

units long and 19 L units wide. How manyrectangles of dimension L by W are needed?

(A) 30(B) 36(C) 100(D) 150(E) 180

7. In rectangle PQRS above, arcs QT and RT are quarter circles with centers at P and S ,respectively. If the radius of each quartercircle is 1, what is the area of the shadedregion?

(A)4

1

(B)2

2

(C)4

2

(D)4

(E)3

2

8. If the areas of two regions are equal andthe sum of the areas of the regions is 5, whatis the average (arithmetic mean) of the areasof the two regions?

(A) 0

(B) 2

5

(C)4

5

(D) 5(E) 10

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9. The smallest squares in Figure A and Figure B are all equal in size. If the area of Figure A is 26 squarecentimeters, what is the area of Figure

B ?

(A) 12 sq cm(B) 14 sq cm(C) 16 sq cm(D) 18 sq cm(E) 20 sq cm

10. In the figure above, arc SBT is onequarter of a circle with center R and radius6. If the length plus the width of rectangle

ABCR is 8, then the perimeter of the shadedregion is

(A) 8 + 3 (B) 10 + 3 (C) 14 + 3 (D) 1 + 6 (E) 12 + 6

11. In the figure above, ABCDEF is a regularhexagon, and its center is point O. What isthe value of x?

(A) 80(B) 60(C) 40(D) 30(E) 20

12. If the five line segments in the figureabove are all congruent, what is the ratio of

the length of AC (not shown) to the length of BD ?


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13. The figures above represent three piecesof cardboard. All angles of the cardboardpieces are right angles, all short sides havelength 1, and all long sides have length 2.Which of the following figures could be madefrom only the three pieces of cardboardwithout over – lapping or cutting them?

(A) None (B) I only (C) II only(D) III only (E) I and II

14. If there is no waste, how many squareyards of carpeting is needed to cover arectangular floor that is 12 feet by 18 feet?(1 yard = 3 feet)

(A) 8(B) 16(C) 24(D) 30(E) 216

15. In rectangle ABCD , point E is themidpoint of BC . If the area of quadrilateral

ABED is3

2, what is the area of rectangle

ABCD ?

(A)2

1

(B)4

3

(C)9

8

(D) 1

(E)38

=

16. In the figure above, EF divides square ABCD into two rectangles, and CD bisectsEF. If AB is 4, what is the area of ∆DCF?

(A) 9(B) 8

(C) 7(D) 6(E) 5

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17. If the perimeter of the rectangle above is72, what is the value of x?

(A) 9(B) 15 ππ (C) 18(D) 21(E) 36

18. In the figure above, a square with sides of length 6 units is divided into 9 squares. Whatis the area of the circle (not shown) thatpasses through the points A, B, C, and D,which are the centers of the four cornersquares?

(A) 6π square units(B) 8 π square units(C) 9 π square units(D) 10 π square units(E) 18 π square units

19. In the figure above, the length of CD is 4,and the length of each side of quadrilateral

ABCE is 5. What is the area of quadrilateral ABCD?

(A) 32(B) 28

(C) 27(D) 26(E) 22

20. If all four interior angles of quadrilateralP have the same measure, which of thefollowing statements must be true?

I. All sides of P have equal length.II. The diagonals of P are perpendicular.III. The measure of each interior angle of P is

.

(A) None(B) I only(C) II only(D) III only(E) I, II, and III

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1. In the figure above, a small square isinside a larger square. What is the area, interms of x , of the shaded region?

(A) 2 x – 10(B) 10 – 2x (C) 25 – 2x

(D) x 2

– 25(E) 25 – x 2

2. In the figure above, rectangle ABCD ismade up of seven non-overlappingrectangles. The two smallest rectangles havethe same area. Each of the other rectangleshas twice the area of the next smallerrectangle. The area of the shaded rectangle iswhat fraction of the area of rectangle ABCD?

(A)128

1

(B)641

(C)32

1

(D)16

1

(E)7

1


ABCD . What is the area of the circle?

(A) 16 (B) 20 (C) 36

(D) 64

(E) 96

4. What is the perimeter of the figure above?

(A) 24(B) 25(C) 28

(D) 30(E) 36

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5. In the figure above, ABCD is a rectanglewith BC = 4 and AB = 6. Points P, Q, and R are different points on a line (not shown) thatis parallel to AD . Points P and Q aresymmetric about line AB and points Q and R

are symmetric about line CD . What is thelength of PR ?

(A) 6(B) 8(C) 10(D) 12(E) 20

.

6. The pattern shown above is composed of rectangles. This pattern is used repeatedly tocompletely cover a rectangular region 12 L

units long and 19 L units wide. How manyrectangles of dimension L by W are needed?

(A) 30(B) 36(C) 100(D) 150(E) 180

7. In rectangle PQRS above, arcs QT and RT are quarter circles with centers at P and S ,respectively. If the radius of each quartercircle is 1, what is the area of the shadedregion?

(A)4

1

(B)2

2

(C)4

2

(D)4

(E)3

2

8. If the areas of two regions are equal andthe sum of the areas of the regions is 5, whatis the average (arithmetic mean) of the areasof the two regions?

(A) 0

(B) 2

5

(C)4

5

(D) 5(E) 10

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9. The smallest squares in Figure A and Figure B are all equal in size. If the area of Figure A is 26 squarecentimeters, what is the area of Figure

B ?

(A) 12 sq cm(B) 14 sq cm(C) 16 sq cm(D) 18 sq cm(E) 20 sq cm



(A) 8 + 3 (B) 10 + 3 (C) 14 + 3 (D) 1 + 6 (E) 12 + 6

11. In the figure above, ABCDEF is a regularhexagon, and its center is point O. What isthe value of x?

(A) 80(B) 60(C) 40(D) 30(E) 20

12. If the five line segments in the figureabove are all congruent, what is the ratio of

the length of AC (not shown) to the length of BD ?


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13. The figures above represent three piecesof cardboard. All angles of the cardboardpieces are right angles, all short sides havelength 1, and all long sides have length 2.Which of the following figures could be madefrom only the three pieces of cardboardwithout over – lapping or cutting them?

(A) None (B) I only (C) II only(D) III only (E) I and II

14. If there is no waste, how many squareyards of carpeting is needed to cover arectangular floor that is 12 feet by 18 feet?(1 yard = 3 feet)

(A) 8(B) 16(C) 24(D) 30(E) 216

15. In rectangle ABCD , point E is themidpoint of BC . If the area of quadrilateral

ABED is3

2, what is the area of rectangle

ABCD ?

(A)2

1

(B)4

3

(C)9

8

(D) 1

(E)38

=

16. In the figure above, EF divides square ABCD into two rectangles, and CD bisectsEF. If AB is 4, what is the area of ∆DCF?

(A) 9(B) 8

(C) 7(D) 6(E) 5

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17. If the perimeter of the rectangle above is72, what is the value of x?

(A) 9(B) 15 ππ (C) 18(D) 21(E) 36

18. In the figure above, a square with sides of length 6 units is divided into 9 squares. Whatis the area of the circle (not shown) thatpasses through the points A, B, C, and D,which are the centers of the four cornersquares?

(A) 6π square units(B) 8 π square units(C) 9 π square units(D) 10 π square units(E) 18 π square units

19. In the figure above, the length of CD is 4,and the length of each side of quadrilateral

ABCE is 5. What is the area of quadrilateral ABCD?

(A) 32(B) 28

(C) 27(D) 26(E) 22

20. If all four interior angles of quadrilateralP have the same measure, which of thefollowing statements must be true?

I. All sides of P have equal length.II. The diagonals of P are perpendicular.III. The measure of each interior angle of P is

.

(A) None(B) I only(C) II only(D) III only(E) I, II, and III

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5. In the figure above, ABDE is a square,Δ BCD is a right triangle, and AB=BC. If apoint is chosen at random from polygon

ACDE, what is the probability that the

chosen point is in the shaded region?

(A)

(B)

(C)

(D)(E)

6. The length of a rectangular garden is 3feet more than its width. If the length of thegarden is 9 feet, what is the area of thegarden in square feet?

(A) 27(B) 36(C) 54(D) 81(E) 108

7. In the figure above, regular pentagon ABCDE is divided into three nonoverlappingtriangles. Which of the following is trueabout the three triangles?

(A) They have equal areas.

(B) They have equal perimeters.(C) They are similar.(D) They are isosceles.(E) They each have at least one angle of measure 60 ° .

8. Triangles ABC and ACD in the figureabove are equilateral. What is the ratio of BDto AC ?

(A) to 1(B) to 1(C) to 2(D) to 2(E) to 2

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9. The length of a rectangular rug is 2 feetmore than its width. If the length of the rugis 8 feet, what is the area of the rug in square

feet?

(A) 16(B) 48(C) 66(D) 80(E) 96

10. In rectangle ABCD above, the area of the

shaded region is given by . If the area of

the shaded region is 7 π , what is the totalarea, to the nearest number, of the unshadedregions of rectangle ABCD?

(A) 4(B) 6(C) 8(D) 9(E) 10

11. What is the perimeter of the trapezoidabove?

(A) 52(B) 72(C) 75(D) 80(E) 87

12. In the figure above, CDE is an equilateraltriangle and ABCE is a square with an area

of 1. What is the perimeter of polygon ABCDE?

(A) 4(B) 5(C) 6(D) 7(E) 8

13. The perimeter of a rectangular plot of land is 250 meters. If the length of one side of the plot is 40 meters, what is the area of theplot, in square meters?

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14. In the figure above, the lengths andwidths of rectangles A, B, C, and D are wholenumbers. The areas of rectangles A, B, and Care 35, 45, and 36, respectively. What is thearea of the entire figure?

15. In the figure above, what is the area of the shaded square?

16. In the figure above, PQST is a rectangleand URST is a square. PU = 5 and UT is apositive integer. If the area of PQST must bemore than 10 but less than 30, what is onepossible value of UT.

17. In the figure above, EBCD is a squareand AE = 8. What is the area of EBCD?

18. In the figure above, PQRS is a rectangle.The area of ∆ RST is 7 and

PT ═ PS. What is the area of PQRS

19. In the figure above, points A, D, and E lieon the same line. What is the value of x?

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1. The circle above has center O anddiameter AB. The two semicircles havediameters OA and OB. If thecircumference of the circle is 36 , what isthe length of the curved path from A to Bthrough O?

(A) 6

(B) 9 (C) 18 (D) 24 (E) 36


ABCD. What is the area of the circle?

(A) 16

(B) 20 (C) 36 (D) 64 (E) 96

3. Senai customized his bicycle byexchanging the front wheel for a wheelthat had one half the diameter of the back

wheel. Now when Senai rides the bicycle,how many revolutions does the front wheelmake for each revolution of the backwheel?

(A) 8(B) 4(C) 2

(D)2

1

(E) 4

1

4. In the figure above, ∆ XYZ is equilateral,with side of length 2. If WY is a diameterof the circle with center O, then the area of the circle is

(A) 4

3

(B)3

2

(C)4

3

(D)

(E)2

3

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5. In rectangle PQRS above, arcs QT andRT are quarter circles with centers at

P and S , respectively. If the radius of each quarter circle is 1, what is thearea of the shaded region?

(A)4

1

(B)2

2

(C)4

2

(D)4

(E)3

2

6. In the figure above, point O is thecenter of the circle. If x = 40, what is

the value of y?

(A) 40(B) 50(C) 60(D) 70(E) 80

7. The figure above shows part of circlewhose circumference is 45. If arcs of length 2 and length b continue toalternate around the entire circle so thatthere are 18 arcs of each length, what isthe degree measure of each of the arcs of

length b?

(A) 4° (B) 6°(C) 10°(D) 16°(E) 20°



(A) 8 + 3 π (B) 10 + 3 π (C) 14 + 3 π (D) 1 + 6 π (E) 12 + 6 π

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9. In the xy – plane above, points Q and S arethe centers of the circles, which are tangentto the x – axis. What is the slope of line QS (not shown)?

(A)8

1

(B)4

1

(C)2

1

(D)8

7

(E) 1

10. In the figure above, the two circles aretangent at point B and AC = 6. If thecircumference of the circle with center A istwice the circumference of the circle with

center C , what is the length of BC ?

(A) 1(B) 2(C) 3(D) 4(E) 6

11. In the figure above, the radius of thecircle with center R is twice the radius of thecircle with center P. What is the radius of thecircle with center R?

(A) 5

(B) 6(C) 7(D) 8(E) 10

12. A circular piece of cardboard is cut in half along a diameter. If the diameter is 12inches, what is the perimeter, in inches, of one of the semicircular pieces?

(A) 6p+6(B) 6p+12(C) 12p+6(D) 12p+12(E) 12p+24

13. What is the ratio of the radius r of acircle to the circumference of the circle?

(A) 1:2 π (B) 1: π (C) 1: π r(D) π :1(E) 2 π :1

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1. What is the radius of a circle whosecircumference is π ?

(A)(B) 1(C) 2(D) π (E) 2 π

2. If three different circles are drawn on apiece of paper, at most how many points canbe common to all three?

(A) None(B) One(C) Two(D) Three(E) Six

3. The circle above has an area of 25 π and isdivided into 8 congruent regions. What is theperimeter of one of these regions?

(A) 10 - 25 π (B) 10 +

C) 10+(D) 10+5 π (E) 10+25 π

4. In the figure above, O is the center of thecircle and segment AC is tangent to the circleat point B. If the measure of ∠ ABO is x ° ,how many possible valuesare there for x ?

(A) One

(B) Two(C) Three(D) Four(E) More than four

5. A circle was cut into two pieces, and one of the pieces is shown above, with the dashedline indicating the path of the cut. Which of the following could be theother piece of the circle?

(A)

(B)

(C)

(D)

(E)

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6. The circle above has an area of 49 π and isdivided into 6 congruent regions. What is theperimeter of one of these regions?

(A) 14 − 49 π (B) 14+ π

(C) 14+ π (D) 14 + 7 π (E) 14 + 49 π

7. The circumference of the circle with centerO shown above is 2 π . What is the area of theshaded region?

(A)

(B)

(C) 1

(D)

(E)

8. What is the ratio of the diameter d of acircle to half the circumference of the circle?

(A) 1 : 2π

(B) 1 : π (C) 2 : π (D) π : 1(E) 2 π :1

9. Six points are placed on a circle. What isthe greatest number of different lines thatcan be drawn so that each line passesthrough two of these points?

(A) 12(B) 15(C) 25(D) 30(E) 36

10. In the figure above, the smaller circleseach have radius 3. They are tangent to thelarger circle at points A and C, and aretangent to each other at

point B, which is the center of the largercircle. What is the perimeter of the shadedregion?

(A) 6 π (B) 8 π (C) 9 π (D) 12 π (E) 15

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11. In the figure above, triangle ABC isinscribed in the circle with center O anddiameter AC. If AB AO, what is the degreemeasure of ABO?

(A) 15 ° (B) 30 ° (C) 45 ° (D) 60 ° (E) 90 °

12. Tameka cut a circular pizza into wedge – shaped pieces, one of which is shown above.The tip of each piece is at the center of thepizza and the angle at the tip is alwaysgreater than 20°, but less than 30°. What isone possible value for the number of piecesinto which the pizza is cut?

13. If a circle has circumference 7 π , what isthe radius of the circle?

Note: Figure not drawn to scale.

14. The figure above consists of two circlesthat have the same center. If the shaded areais 64 square inches and the smaller circlehas a radius of 6 inches, what is the radius,in inches, of the larger circle?

15. Naomi makes silver jewelry. For onestyle of earrings, she cuts wedges from asilver disk, as shown in the figure above.Each wedge makes a 40° angle at the centerof the disk. If the weight of each uncut disk isa uniformly distributed 2.5 grams, how manygrams does each wedge weigh?

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SOLID GEOMETRY

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1. Which of the following has the samevolume as the cylinder shown above withradius x and height 2 x ?

(A) A cylinder with radius 2 x and height x (B) A cylinder with radius 2 x and height x (C) A cube with edge 2 x (D) A cube with edge 2 x (E) A rectangular solid with dimensions x , 2 x ,

x

2. Ahmad has containers of two differentsizes. The total capacity of 16 containers of

one size is x gallons, and the total capacity of 8 containers of the other size is also x gallons, and x > 0. In terms of x , what is thecapacity, in gallons, of each of the largercontainers?

(A) 4 x (B) 2 x

(C)2

x

(D) 8

x

(E) 16

3. If the rectangular box with no lid shownabove is cut along the vertical edges andflattened, which of the following figuresbest represents the result?

(A)

(B)

(C)

(D)

(E)

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4. How many cubical blocks, each with edgesof length 4 centimeters, are needed to fill arectangular box that has inside dimensions

20 centimeters by 24 centimeters by 32centimeters?

(A) 38(B) 96(C) 192(D) 240(E) 384

5. The three – dimensional figure above hastwo parallel bases and 18 edges. Linesegments are to be drawn connecting vertex V with each of the other 11 vertices in thefigure. How many of these segments will not lie on an edge of the figure?

(A) Two

(B) Three(C) Four(D) Seven(E) Nine

6. The cube shown above has edges of length2, and A and B are midpoints of two of theedges. What is the length of AB (not shown)?

(A) 2 (B) 3 (C) 5 (D) 6 (E) 10

7. The three – dimensional figure representedabove consists of rectangular and triangularfaces. Each rectangular face has area r andeach triangular face has area t . What is thetotal surface area of the figure, in terms of r and t?

(A) 2 r + t (B) 3 r + 2 t(C) 4 r + 3 t(D) 6 rt (E) r 3t 2

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8. In the cube shown above, points B, C, and E are midpoints of three of the edges. Whichof the following angles has the leastmeasure?

(A) < XAY (B) < XBY (C) < XCY (D) <XDY (E) <XEY

9. The pyramid above has a square base andfour congruent triangular faces. The heightof the pyramid is 5 inches and each edge of the base is 4 inches long.What is the length of AB , in inches?

(A) (approximately 5.39)(B) (approximately 5.74)(C) (approximately 6.24)(D) (approximately 6.56)(E) (approximately 7.55)

10. If the volume of a cube is 8, what is theshortest distance from the center of the cubeto the base of the cube?

(A) 1(B) 2(C) 4(D) 2 (E) 22

11. In a windowless, cube-shaped storageroom, the ceiling and 4 walls, including adoor, are completely painted. The floor is notpainted. If the painted area is equal to 80square meters, what is the volume of theroom, in cubic meters?

(A) 16(B) 20(C) 64(D) 256

(E) 400

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12. The tin can in the figure above is acylinder that is 8 inches high and has a baseof radius 3 inches. Of 5 pencils with lengths 6

inches, inches, 9 inches, inches, and

12 inches, how many CANNOT fit entirelyinside the can?

(A) One(B) Two(C) Three(D) Four(E) Five

13. Of the labeled points on the cube shownabove, which is farthest from point P ?

(A) A (B) B(C) C(D) D(E) E

14. Which of the rectangular solids shownabove has a volume closest to the volume of aright circular cylinder with radius 2 andheight 4 ?

(A) A (B) B(C) C(D) D(E) E

15. The height of a right circular cylinder is 5and the diameter of its base is 4. What is thedistance from the center of one base to apoint on the circumference of the other base?

(A) 3(B) 5(C) 29 (approximately 5.39)(D) 33 (approximately 5.74)(E) 41 (approximately 6.40)

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16. Two spheres, one with radius 7 and onewith radius 4, are tangent to each other. If Pis any point on one sphere and Q is any point

on the other sphere, what is the maximumpossible length of PQ ?

(A) 7(B) 11(C) 14(D) 18(E) 22

17. The interior dimensions of a rectangularfish tank are 4 feet long, 3 feet wide, and 2feet high. The water level in the tank is 1foot high. All of the water in this tank ispoured into an empty second tank. If theinterior dimensions of the second tank are 3feet long, 2 feet wide, and 4 feet high, what isthe height of the water in the second tank?

(A) 0.5 ft(B) 1 ft

(C) 1.5 ft(D) 2 ft(E) 4 ft

18. Point O is the center of both circles in thefigure above. If the circumference of the largecircle is 36 and the radius of the small circleis half of the radius of the large circle, whatis the length of the darkened arc?

(A) 10(B) 8(C) 6(D) 4(E) 2

19. The figure above shows the dimensions of a pedestal constructed of 4 layers of marble.Each layer is a rectangular solid that is 1foot high and has a square base. How manycubic feet of marble make up the pedestal?

(A) 14(B) 16(C) 30(D) 36(E) 80

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20. What is the total number of right anglesformed by the edges of a cube?

(A) 36(B) 24(C) 20(D) 16(E) 12

21. A large solid cube is assembled by gluingtogether identical unpainted small cubicblocks. All six faces of the large cube are thenpainted red. If exactly 27 of the small cubicblocks that make up the large cube have nored paint on them, how many small cubicblocks make up the large cube?

22. The sphere above has radius 6 inches.What is the volume, in cubic inches, of thesmallest cube that can contain the entiresphere?

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Questions 1-2 refer to the following graph:

1. Which of the following regions in Africahad an elephant population in 1989 that wasapproximately of its elephant population in1979 ?

I. CentralII. Eastern

III. Southern

(A) I only(B) II only(C) III only(D) I and III only(E) I, II, and III

2. From 1979 to 1989, the total elephantpopulation in

the four regions of Africa decreased byapproximatelywhat percent?

(A) 10% (B) 30% (C) 50%(D) 70% (E) 90%

3.

The pictograph above shows the results of asurvey in which 150 people were asked toindicate which of four hot beverages theydrink. How many more responses did Coffeereceive than Hot cider?

(A) 15 (B) 30 (C) 40(D) 45 (E) 60

4.

In a survey, 3,400 people responded to thefollowing question: “How many weeks of vacation did you take last year?” Theirresponses to the question are summarized inthe chart above, where n equals the numberof vacation weeks indicated. How manyrespondents took more than 2 weeks of vacation last year?

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5.

The depth of a lake is the difference betweenthe altitude at the surface and at the lowestpoint of the lake. If the five lakes in thegraph above were listed in order from thegreatest depth to the least depth, which lakewould be third in the list?

(A) Erie (B) Huron (C) Michigan(D) Ontario (E) Superior

6.

The graph above shows various temperaturesfrom 10 A.M. to 6 P.M. of a given day. Whichof the following situations best fits thenformation on the graph?

(A) It rained a little, and then the Sun cameout and warmed things up.(B) The mild temperature was lowered by aheavy rain in the morning, and thetemperature dropped lower by evening.(C) It was more windy in the morning than itwas in the evening, and the temperature wasmild throughout.(D) The morning was cold, but the Sun later

came out and raised the temperature.(E) The temperature decreased at a constantrate from 10 A.M. to 6 P.M.

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7.

Some common nail sizes and theircorresponding lengths are shown in the tableabove. If nail sizes from 2d up to 10d increaseby a constant length for each increase of 1din size, what would be the length, in inches,of a 6d nail?

(A) 2 (B) 2 (C) 2

(D) 1 (E) 1

8.

According to the chart above, Company XYZ

experienced its largest increase in monthlyprofits between which two consecutivemonths?

(A) January and February(B) February and March(C) March and April(D) April and May(E) May and June

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9.

Which of the following graphs bestrepresents the information in the tableabove?

10.

The Lyndhurst High School twelfth gradersare represented in the circle graph in Figure1. Figure 2 is another way to illustrate theuse of computers by these twelfth graders. If the same 200 twelfth graders are representedin both figures, what is the total number of twelfth graders represented by the shadedcircle in Figure 2 ?

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11.

According to the graph above, for whichmonth was sales minus cost greatest?(A) June (B) July (C) August(D) September (E) October

12.

It took Kia 6 hours to drive from Ashton toFarley, passing through Belville, Clinton,Dryden, and Edgewood on the way. Thegraph above shows where she was along theroute during the 6 hours of the trip.

According to the graph, approximately howlong, in hours, did it take Kia to drive fromDryden to Edgewood?

(A) 1 (B) 2 (C) 3

(D) 3 (E) 4

13.

For 12 bottles of shampoo of various brands,the cost and volume of each are displayed inthe scatterplot above, and the line of best fitfor the data is shown. Of the following, whichis closest to the average (arithmetic mean)cost per ounce for the 12 bottles?

(A) $0.06 (B) $0.09 (C) $0.12(D) $0.15 (E) $0.18

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14.

Company R makes cars in many locationsaround the world. The graph above showswhere its cars were made in 2003. If thecompany made 5,000,000 cars in 2003, howmany of these cars were made in South

America?

(A) 50 (B) 500 (C) 5,000(D) 50,000 (E) 500,000

15.

The graph above shows the monthly sales forCompany A and Company B for the secondhalf of 2004. What was the largest one-monthdecrease in sales for Company B during thisperiod of time?(A) $45,000 (B) $30,000 (C) $25,000(D) $20,000 (E) $15,000

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16.

Which of the following graphs bestrepresents the information in the tableabove?

17.

The table above shows the number of items

100 customers purchased from a hardwarestore over a 4 -hour period. Which of thefollowing can be determined from theinformation in the table?

I. The average (arithmetic mean) number of items purchased per customerII. The median number of items purchasedper customerIII. The mode of the number of itemspurchased per customer

(A) None(B) I and II only(C) I and III only(D) II and III only(E) I, II, and III

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18.

The incomplete table above is an expensesheet for Carmen’s business trip. If her hotelexpenses were the same each day, what wereher total expenses for Friday, in dollars?

(Disregard the $ sign when gridding youranswer.)

19.

Table 1 above shows the number of juniorsand seniors taking Physics and Statistics atMidland High School. The partiallycompleted Table 2 above gives the enrollmentfor these classes in periods 1 and 2, whichare the only periods Physics and Statistics

are taught. If only juniors and seniors takethese classes, what is the total number of students who take Physics or Statistics inperiod 2?

20.

Graphed above is the amount that acomputer shop charges for a repair job as afunction of the number of hours required todo the job. Which of the following is mostconsistent with the information in the graph?

(A) The shop charges the same amount forany job of any length.

(B) The shop charges at an hourly rate forwork with no fixed initial amount.

(C) The shop charges a fixed initial amount

plus an hourly rate for work, starting atthe beginning of the first hour.

(D) The shop charges a fixed amount for thefirst 2 hours or less of work. The shopcharges at an hourly rate for work beyond2 hours.

(E) The shop charges at an hourly rate forwork beginning at the start of the firsthour. This rate decreases after 2 hours of work.

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1.

An amusement park awards tickets that canbe exchanged for prizes to reward high scoresat an arcade game. Some scores and thecorresponding number of prize ticketsawarded are shown in the table above. Forscores from 100 up to 200, the number of tickets awarded increases by a constantamount for each10 -point score increase. How many ticketswould be awarded for a score of 180 ?

(A) 4

(B) 4

(C) 4

(D) 5

(E) 5

2.

A furniture company makes one style of tables and chairs. The chart on the left abovegives the prices of these tables and chairs inthree different years. The chart on the rightgives the maximum number of tables and

chairs that can be stocked in each of threewarehouses, X , Y , and Z . Based on the pricesshown, what was the maximum possiblevalue of the table and chair inventory inwarehouse Y in 1995 ?

(A) $23,950

(B) $26,500

(C) $27,200

(D) $28,400

(E) $29,500

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3.

Students at Northern High School arerepresented in Figure 1 above. Figure 2above is another way to show which petsthese students have. If the same 500students are represented in both figures,what is the total number of studentsrepresented by the shaded circle in Figure 2 ?

4.

The scatterplot above shows, for each of 10

students, the amount of time the studentspent on homework plotted against theamount of time the student spent on after-school activities last week. According to thescatterplot, which of the following statementsis true?

(A) Each of the students spent the sameamount of time on homework as on after-school activities.

(B) Each of the students spent more time onhomework than on after-school activities.

(C) Each of the students spent less time onhomework than on after-school activities.

(D) Exactly 3 students spent 4 hours onhomework.

(E) Exactly 4 students spent 3 hours on after-school activities.

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5.

According to the graph above, if there are6,000 registered voters aged 60 and over inWashington County, how many registeredvoters are under the age of 30 ?

(A) 1,000 (B) 2,000 (C) 3,000(D) 4,000 (E) 5,000

6.

The table above shows the total number of copies of Book B that were sold by the end of each of the first 5 weeks of its publication.How many copies of the book were soldduring the 3rd week of its publication?

7.

The graph above shows the monthly sales forCompany A and Company B for the secondhalf of 2004. What was the largest one-monthdecrease in sales for Company B during thisperiod of time?

(A) $45,000

(B) $30,000

(C) $25,000

(D) $20,000

(E) $15,000

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8.

The grid above shows the number of hoursworked last week by 12 students of variousages at after-school jobs. Which of thefollowing is true, according to this grid?

(A) Half of the students worked more than 12

hours each.

(B) One student worked exactly 15 hours.

(C) One 16 year old worked more than 11

hours.

(D) More 18 year olds than 17 year olds

worked at least 13 hours each.

(E) Most of the students were under 16 years

old.

9. Mark began a 4-mile bicycle trip by ridingslowly uphill for 1 mile. He rested for 10minutes and then rode quickly downhill forthe rest of the trip. Which of the followinggraphs could correctly represent his trip?

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10.

In a certain game, each person threw abeanbag at a target until the person missedthe target. The table shows the results forthe 25 people who played the game. Forexample, 4 people hit the target on their first3 throws and missed on their 4th throw.Based on the information in the table, whichof the following must be true?

I. More than half the people hit the target ontheir first throw.II. For all of the throws attempted, more hitthe target than missed the target.III. No one hit the target 5 times.

(A) I only

(B) II only

(C) I and III only

(D) II and III only

(E) I, II, and III

11.

In the schedule above, each session is to be 1hours long, each break is to be hour long,

and lunch is to be 1 hour long. If session IV isto end at 4:30 P.M., at what time shouldsession I begin?

(A) 8:15 A.M.

(B) 8:30 A.M.

(C) 8:45 AM.

(D) 9:00 A.M.

(E) 9:15 A.M

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15.

The table above shows the number of employees at Company X classified accordingto work shift and salary. If a second-shiftemployee will be picked at random, what isthe probability that the employee’s salary isover $30,000?

(A) (B) (C)

(D) (E)

16.

The circle graph above shows how David’smonthly expenses are divided. If Davidspends $450 per month for food, how muchdoes he spend per month on his car?

(A) $200 (B) $320 (C) $360(D) $400 (E) $450

17.

The first table above shows the number of premium members at two video rental stores,

A and B, during the years 2000 – 2002. Thesecond table shows the average (arithmeticmean) number of video rentals per premiummember at store B during each of thoseyears. Based on this information, which of the following best approximates the total

number of video rentals by premiummembers at Store B during the years 2000 – 2002?

(A) 24,000

(B) 46,000

(C) 58,000

(D) 70,000

(E) 130,000

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18.

The graph above shows how the Jacksonfamily continued to grow between 1991 and

1998 by indicating the total number of children in the family at the end of each year.The Jacksons have one set of twins who wereborn to Mrs. Jackson one year in July.During what year were the twins born?

(A) 1993 (B) 1994 (C) 1996(D) 1997 (E) 1998

19.

The graph above shows Elina’s height ininches from the age of 6 to the age of 12.Elina’ s height at the age of 12 was what

percent greater than her height at the age of 6?

(A) 15% (B) 25% (C) 33%(D) 50% (E) 66 %.

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1.

The table above shows the noontemperatures for seven cities designated A through G. If the median noon temperatureof these cities is 40°F, then the noontemperature for City D could be any of thefollowing EXCEPT

(A) 29°F

(B) 35°F

(C) 39°F

(D) 40°F

(E) 42°F

2.

The table above, describing the Preston Cityworkforce, is partially filled in. Based on theinformation in the table, how many womenin the Preston City workforce are

unemployed?

(A) 500

(B) 1,000

(C) 1,500

(D) 2,000

(E) 2,500

3.

A merchant sells three types of clocks thatchime as indicated by the check marks in thetable above. What is the total number of chimes of the inventory of clocks in the 90 – minute period from 7: 15 to 8:45?

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4. Of the following, which is the closestapproximation of the cost per donut whenone purchases a box of 6?

(A) $0.20

(B) $0.30

(C) $0.40

(D) $0.50

(E) $0.60

5. What would be the least amount of moneyneeded to purchase exactly 21 donuts?

(A) $5.88

(B) $6.68

(C) $7.19(D) $7.38

(E) $8.40

6.

The bar graph above shows where fraud iscommitted on the Internet. Which of thefollowing circle graphs most accuratelydisplays the same data?

(A) (B)

(C) (D)

(E)

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7.

According to the graph above, between whichtwo consecutive years was there the greatest

change in the price of coffee?

(A) 1981 and 1982 (B) 1982 and 1983(C) 1983 and 1984 (D) 1984 and 1985(E) 1985 and 1986

8.

According to the graph above, during which

of the following two – month periods didEllen’s Bookstore sell the least number of books?

(A) June and July(B) July and August(C) August and September(D) September and October(E) October and November

9.

Doug’ s biology experiment involved timing12 hamsters in a maze. Each hamsterreceived at least one practice before beingtimed. The scatter-plot above shows the timeeach hamster took to complete the maze andthe corresponding number of practices thateach hamster received. Based on the data,

which of the following functions best modelsthe relationship between t, the number of seconds to complete the maze, and p, thenumber of practices?

(A) t(p) = 44

(B) t(p) = p

(C) t(p) = 44p

(D) t(p) =

(E) t(p) = p+44

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10. For which student was the change inscores from test I to test II the greatest’?

(A) A

(B) B

(C) C

(D) D

(E) E

11. What was the average (arithmetic mean)of the scores of the 5 students on test II?

(A) 60

(B) 65

(C) 68

(D) 70

(E) 72

12.

The table above gives the voter registrationdata for the town of Bridgeton at the time of a recent election. In the election, 40 percentof the voting – age population actually voted.If the turnout for an election is definedto be the fraction

votersregisteredof numberotedactually vnumber who

What was the turnout for this election?

13.

The table above shows how many students ina class of 12 preschoolers had 0, 1, 2, or 3siblings. Later, a new student joined theclass, and the average (arithmetic mean)number of siblings per student became equalto the median number of siblings perstudent. How many siblings did the newstudent have?

(A) 0 (B) 1 (C) 2(D) 3 (E) 4

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14.

According to the graph above, whichsalesperson had the greatest increase in thenumber of units sold from 1998 to 1999?

(A) Albert(B) Goldberg(C) Patel(D) Smith(E) Wang

15.

In the table above, each letter represents thenumber of students in that category. Whichof the following must be equal to z?

(A) k + s(B) m + x(C) r + s(D) r + s + t(E) k + n + r + s

16.

According to the graph above, which of thefollowing is closest to the decrease per yearin the number of homes sold between 1987and 1990?

(A) 7,000 (B) 11,500 (C) 14,000(D) 17,500 (E) 42,000

17.

The circle graph above represents all the jeans that were sold by a retail store in 2001,according to their brands. If the store sold900 pairs of jeans other than brands J, K, L,M, and N, how many pairs of jeans did it sellaltogether?

(A) 1,500 (B) 2,250 (C) 3,000(D) 3,600 (E) 4,500

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18.

The results of a survey of 16 students atThompson High School are given in the gridabove. It shows the distance, to the nearest

mile, that students at various grade levelstravel to school. According to this grid, whichof the following is true?

(A) There is only one student who travels 2miles to school.(B) Half of the students travel less than 4miles to school.(C) More 12th graders than 11th graderstravel 6 or more miles to school.(D) The students who travel less than 3 miles

to school are all 12th graders.(E) Of the students who travel 7 or moremiles to school, half are 9th graders.

19.

According to the table above, car engine oilwith a rating of 5W flows how many times asfast as car engine oil with a rating of 20W?

(A) 2 (B) 4 (C) 8 (D) 16 (E) 32

20.

The scores on Tuesday’s history test for 16students are shown in the table above. Sam,who was the only student absent on Tuesday,will take the test next week. If Sam receivesa score of 95 on the test, what will be themedian score for the test?

(A) 90 (B) 87.5 (C) 85(D) 82.5 (E) 80

21.

Outdoor Sneaker Company manufacturesonly white sneakers and black sneakers, bothof which are available as either high – tops orlow – tops. On the basis of the information inthe table above, how many black sneakersdid Outdoor Sneaker Company manufacturein July?

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22. Josephine’s daily exercise routineconsists of swimming, cycling, and running,in that order. She runs faster than she swimsand cycles faster than she runs. If she doesnot rest between the activities, which of thefollowing could be the graph of the distanceshe covers during the entire time of herexercise routine?

(A) (B)

(C) (D)

(E)

23.

The chart above shows the results when1,000 people were asked, “How old are you?”The age they gave is represented by x. Howmany people said that their age was less

than 40?

(A) 200(B) 300(C) 450(D) 500(E) 550

24.

The table above shows student enrollment atWeston High School from 1992 through 1996.If the median enrollment for the five yearswas 1351, and no two years had the sameenrollment, what is the greatest possiblevalue for x?

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1. How many positive four-digit integershave 1 as their first digit and 2 or 5 as theirlast digit?

(A) 144(B) 180(C) 200(D) 300(E) 720

2.

Marble 1 was red.Marble 2 was not red.Marble 3 was blue.Marble 4 was the same color as marble

1.Marble 5 was the same color as marble2.

A jar contained 10 marbles — some red, somewhite, and some blue. The information aboveis about 5 marbles that were drawn from the

jar. If x is the total number of blue marblesdrawn, which of the following statementsmust be true?

(A) The only possible value of x is 1.

(B) The only possible value of x is 2.(C) The only possible value of x is 3.(D) The only possible values of x are 1 and 2.(E) The only possible values of x are 1 and 3.

3. A , B , C , D , E , F , G

A list consists of all possible three-letter

arrangements formed by using the lettersabove such that the first letter is D and oneof the remaining letters is A . If no letter isused more than once in an arrangement inthe list and one three-letter arrangement israndomly selected from the list, what is theprobability that thearrangement selected will be DCA ?

(A) (B) (C) (D) (E)

4. If a number is chosen at random from theset{-12,-6, 0, 6, 12}, what is the probability thatit is a member of the solution set of both2x – 3 < 7 and x + 5 > -6 ?

(A) 0 (B) (C) (D) (E)

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5. A box contains 2,900 solid-colored marblesthat are either orange, blue, or green. If 29percent of the marbles are orange and 29

percent of the marbles are blue, what percentare green?

(A) 29%(B) 42%(C) 52%(D) 58%(E) 71%

6.

A snack machine has buttons arranged asshown above.If a selection is made by choosing a letterfollowed by a one-digit number, what is thegreatest number of different selections thatcould be made?

7.

The figure above shows, on the left, the callbuttons for the 12 floors of an apartmentbuilding, and on the right, the 9 buttonslabeled A through I for the 9 apartments oneach floor of the building. How manydifferent apartments can be called bypressing one button on the left and onebutton on the right?

8. The digits of the positive three-digitinteger n are 7, 8 and 9. How many possiblevalues are there for n ?

(A) Three (B) Four (C) SixD) Eight (E) Nine

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9.

On the disk shown above, a player spins thearrow twice. The fraction is formed, where

a is the b number of the sector where thearrow stops after the first spin and b is the

number of the sector where the arrow stopsafter the second spin. On every spin, each of the numbered sectors has an equalprobability of being the sector on which thearrow stops. What is the probability that thefraction is greater than 1?

(A) (B) (C)

(D) (E)

10. A special lottery is to be held to select thestudent who will live in the only deluxe roomin a dormitory. There are 100 seniors, 150

juniors, and 200 sophomores who applied.Each senior’s name is placed in the lottery 3times; each junior’s name, 2 times; and eachsophomore’s name, 1 time. If a student'sname is chosen at random from the names inthe lottery, what is the probability that asenior's name will be chosen?

(A) (B) (C)

(D) (E)

11.

There are five houses on each side of astreet, as shown in the figure above. No twohouses next to each other on the same side of the street and no two houses directly acrossfrom each other on opposite sides of thestreet can be painted the same color. If thehouses labeled G are painted gray, how manyof the seven remaining houses cannot bepainted gray?

(A) Two (B) Three (C) Four(D) Five (E) Six

12.

In the figure above, a path from point A topoint D is determined by moving upward or

to the right along the grid lines. How manydifferent paths can be drawn from A to Dthat do not include either B or C?

(A) Two (B) Four (C) Six(D) Eight (E) Sixteen

13.

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The figure above shows the top view of anopen square box that is divided into 6compartments with walls of equal height.Each of the rectangles D, E, and F has twicethe area of each of the equal squares A, B,and C. When a marble is dropped into thebox at random, it falls into one of thecompartments. What is the probability thatit will fall into compartment F?

(A) (B) (C)

(D) (E)

14.

The tables above show the different colorsand sizes of T-shirts that are available atIndependence High School. How many

different combinations of color and size arepossible?

(A) 7(B) 12(C) 15(D) 25(E) 64

15. For a class ring, each senior can choosefrom 4 types of stones and 3 types of metals.How many combinations of a stone and a

metal are there?

(A) 7 (B) 8 (C) 10(D) 12 (E) 16

16. There are 6 red, 6 brown, 6 yellow, and 6gray scarves packaged in 24 identical,

unmarked boxes, 1 scarf per box. What is theleast number of boxes that must be selectedin order to be sure that among the boxesselected 3 or more contain scarves of thesame color?

(A) 3 (B) 6 (C) 7(D) 8 (E) 9

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1. A bag contains only red marbles, bluemarbles, and yellow marbles. The probabilityof randomly selecting a red marble from this

bag is , and the probability of randomly

selecting a blue marble is . Which of the

following could be the total number of marbles in the bag?

(A) 10 (B) 12 (C) 18(D) 20 (E) 30

2. If 6 cars out of 10 on an assembly line arered, what is the probability that a carselected at random from the assembly linewill be red?

(A) (B) (C)

(D) (E)

3. How many different positive three – digitintegers can be formed if the three digits 4, 5,and 6 must be used in each of the integers?

(A) Three (B) Four (C) Six(D) Eight (E) Nine

4. A piece of fruit is to be chosen at randomfrom a basket of fruit. The probability that

the piece of fruit chosen will be an apple is .Which of the following could NOT be thenumber of pieces of fruit in the basket?

(A) 20 (B) 35 (C) 52(D) 70 (E) 80

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5. A restaurant menu lists 8 dinners and 3desserts. How many different dinner – dessertcombinations are possible from this menu?

(A) 24 (B) 12 (C) 11(D) 8 (E) 3

6. A clerk accidentally threw a valuabledocument into one of 90 trash cans. It isequally likely that the document is in any of

these 90 trash cans. If exactly 15 of these 90trash cans are blue, what is the probabilitythat the document will be in a blue trashcan?

(A) (B) (C)

(D) (E)

7.

The figure above shows the remaining piecesof a paper chain from which a section hasbeen removed. The first link of the originalchain was red and the colors of the linksformed the repeating pattern of red (R),yellow (Y), green (G), white (W), and blue (B)from left to right. Which of the followingcould be the number of links in the sectionthat was removed?

(A) 60 (B) 61 (C) 62(D) 63 (E) 64

8.

Above are the four houses on a block of OakRoad. Each house is painted a different color.There is a red house, which is next to a bluehouse. There is a green house, which is nextto the red house and a yellow house. Whichhouse could be painted red?

(A) 1 only (B) 2 only (C) 3 only(D) 2 or 3 (E) 1 or 4

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9.

The figure above represents four offices thatwill be assigned randomly to four employees,one employee per office. If Karen and Tinaare two of the four employees, what is theprobability that each will be assigned anoffice indicated with an X ?

(A) (B) (C)

(D) (E)

10.

In the figure above, three wires are braided.That is, by starting in the order A, B, C, theouter left wire A is brought over wire B to themiddle position, forming the order shown instep 1 , then the outer right wire C is broughtto the new middle position shown in step 2,and so on, alternately bringing each new leftand each new right wire to the middle. Atwhat numbered step does the braid firstrepeat the original order A, B, C?

(A) 3 (B) 4 (C) 5 (D) 6 (E) 7

11. A complete cycle of a traffic light takes 80seconds. During each cycle, the light is greenfor 40 seconds, amber for 10 seconds, and red

for 30 seconds. At a randomly chosen time,what is the probability that the light will notbe red?

(A) (B) (C)

(D) (E)

12. The first person ordered a salad.The second person did not order a

salad.The third person ordered a

hamburger.

The fourth person ordered the samething as the first

person.The fifth person ordered the same

thing as the secondperson.

A lunch stand has three choices: hamburger,hot dog, or salad. Five people from an officeordered one choice each from the lunchstand. The statements above are about whatthese five people ordered. If n is the numberof people who ordered a hamburger, which of the following statements is true?

(A) n must be 1.(B) n must be 2.(C) n must be 3.(D) n must be 1 or 2.(E) n must be 1 or 3.

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13.

A circle was cut into two pieces, and one of the pieces is shown above, with the dashedline indicating the path of the cut. Which of

the following could be the other piece of thecircle?

14.

The figure above shows four apartments in abuilding. In this building, each apartment isoccupied by only one person. Alice lives nextto Sam, and Paul lives next to Alice andDara. In which apartment could Alice live?

(A) 1 only(B) 2 only(C) 3 only(D) 2 or 3(E) 1 or 4

15. The Acme Plumbing Company will send ateam of 3 plumbers to work on a certain job.The company has 4 experienced plumbersand 4 trainees. If a team consists of 1experienced plumber and 2 trainees, howmany different such teams are possible?

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ANSWER

SAT Practice Book

2009-2010

111

01. PROPERTIES OFINTEGERS I

1 D

2 E

3 C

4 E

5 C

6 A

7 D

8 D

9 E10 E

02. NUMBER LINES ANDFRACTIONS I

1 B

2 4/9, 0.4443 D

4 C

5 D

6 D

7 D

8 B

9 D

10 C11 E

12 E

13 A

14 C

15 E

03. ELEMANTARYNUMBER THEORY

(DIVISIBILITY) I

1 D

2 D

3 C

4 B

5 C

6 D

7 990

8 C9 D

10 D

11 C

12 125

13 12

14 B

15 D

16 D17 10

18 1600

19 C

20 2491

04. SEQUENCE I

1 C2 D3 C4 C5 E6 B7 C8 C9 B

10 A

11 20212 D13 514 B15. A 16 C17 D18 3919 E20 D21. 12.522 2123 6/25

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ANSWER

2009-2010

2

05. SETS I

1 C

2 A 3 A 4 335 1806 D7 B8 2759 C

10 A 11 A 12 1113 E14 B15 B16 E17 E18 E19 A 20 E

06. RATIO, PROPORTION,PERCENTS I

1 D2 D

3 C

4 B

5 E

6 B

7 C

8 E

9 7/15, 0.466, 0.467

10 3

11 A

12 B

13 A

14 8, 10, 12

15 A

16 D

17 D

18 B

06. RATIO, PROPORTION,PERCENTS II

1 1202 A

3 E

4 B

5 E

6 C

7 D

8 B

9 D

10 B

11 C

12 5/2 OR 2.5

13 2380

14 B

15 A

16 3.4 OR 17/5

17 E

18 E

189



ANSWER

2009-2010

3

06. RATIO, PROPORTION,PERCENTS III

1 32 0.53 OR 8/15

3 B

4 B

5 A

6 A

7 175

8 4

9 C

10 E

11 B

12 C

13 A

14 B

15 E

16 C

17 A

18 E

07. EXPONENTS,SQUARES, SQUARE

ROOTS I

1 B

2 A

3 1404

4 C

5 D

6 B

7 E

8 D

9 B

10 A

11 B

12 E

13 C

14 C

15 A

16 D

17 518 C

19 B

20 A

21 B

07. EXPONENTS,SQUARES, SQUARE

ROOTS II

1 C

2 A

3 B

4 A

5 A

6 A

7 25

8 E

9 A

10 C

11 D

12 C

13 A

14 B

15 D

16 E

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ANSWER

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4

08. WORD PROBLEMS I

1 D2 E3 D4 C5 18 mile6 D7 C8 D9 C

10 B11 A

12 D13 7 packages14 7/1515 C16 E17 E18 A 19 45020 12821 70

22 D23 C24 A 25 A 26 B

08. WORD PROBLEMS II

1 n+42 B3 D4 C5 B6 C7 3 1/38 369 1 3/7

10 B11 A

12 E13 45 mile14 B15 E16 B17 D18 32.519 B20 A 21 D

22 B23 D24 D

08. WORD PROBLEMS III

1 C2 1003 A 4 E5 C6 B7 C8 D9 C

10 C11 7.5

12 2213 102414 A 15 A 16 8917 A 18 C19 E20 115

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ANSWER

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5

09. FACTORING I

1 B2 D3 E4 B5 A 6 D7 B8 29 D

10 A 11 10312 A 13 A 14 C15 E16 15/717 A 18 C

10. MEAN, MEDIAN, MODEI

1 C2 A

3 46

4 C

5 D

6 D

7 A

8 71

9 12.5, 25/2

10 C

11 A

12 3.4 OR 17/5

13 C

14 E

15 A

16 C

17 D

18 109

19 D

20 C

21 A

22 B

23 D

24 A

11. EQUATIONS I

1 B2 C3 B4 C5 D6 2/57 C8 C9 C

10 B11 B12 D13 A 14 A 15 A 16 B17 C18 E19 320 B21 B22 15/7

23 E24 C25 C26 C27 E28 A

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ANSWER

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6

12. VARIATIONS I

1 D2 B3 D4 D5 D6 8/157 E

13. INEQUALITIES I

1 D2 B3 E4 D5 C6 B

7 A 8 E9 13

10 D11 E12 C13 E14 B15 B16 C

17 E18 B19 D20 D

13. INEQUALITIES II

1 A 2 E3 C4 E5 A 6 A 7 D8 A 9 B

10 D11 A 12 C13 E14 D15 B16 A 17 D18 9.519 B

14. LINEAR EQUATIONS I

1 E2 A 3 A 4 E

5 E6 37 A

15. QUADRATICEQUATIONS I

1 D2 E3 A 4 B5 A 6 A

16. FUNCTIONS I

1 E2 E3 34 E5 2 or 76 D7 C8 B9 28

10 B11 A 12 C13 1614 E15 B16 E17 D18 E

19 D20 A 21 322 B23 E

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ANSWER

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7

16. FUNCTIONS II

1 A 2 B3 3, -34 D5 C6 E7 108 D9 D

10 C11 D12 3.513 B14 E15 D16 B17 D

16. FUNCTIONS III

1 D2 1523 1794 C5 D6 667 B8 D9 C

10 C11 D12 D13 E14 E15 B16 D

17. OPERATIONS I

1 1.22 A 3 E4 C5 116 8757 C8 A 9 B

10 D11 B

12 E13 E14 D

18. COORDINATEGEOMETRY I

1 B2 A

3 A

4 B

5 A

6 E

7 E

8 A

9 D10 B

11 B

12 D

13 E

14 A

15 C

16 B

17 D18 B

19 B

20 A

21 E

22 C

194



ANSWER

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8

18. COORDINATEGEOMETRY II

1 D2 C

3 C

4 E

5 E

6 E

7 D

8 E

9 D10 A

11 D

12

13 8

14 12

15 5

16 16

17 10

18 0 < m <

19 4

20 3

21

19. PARALLEL LINES AND ANGLES I

1 C2 A 3 D4 C5 1356 A 7 A 8 22.5<x<27.59 D

10 A 11 A 12 E13 E14 B15 E16 E17 4018 C19 C20 A 21 E

22 D23 A 24 D25 A

20. TRIANGLES I

1 D

2 B3 2

4 B

5 B

6 A

7 B

8 9

9 A

10 20 or 5011 D

12 C

13 C

14 A

15 E

16 E

17 E

18 10.519 E

20 A

21 E

195



ANSWER

2009-2010

9

20. TRIANGLES II

1 E

2 B3 B

4 3 or 6 or 9 or 12

5 8

6 75

7 D

8 E

9 A

10 C11 C

12 B

13 B

14 A

15 52 or 78 or 104

16 40

17 D

18 E

19

20 B

21 C

20. TRIANGLES III

1 70

2 C3 B

4 B

5 B

6 C

7 C

8 A

9 D

10 B11 C

12 E

13 E

14 A

15 E

16 C

17 B

18 C19 A

20 A

21 C

21. POLYGONS I

1 E

2 B3 A

4 D

5 B

6 180

7 B

8 B

9 B

10 B11 B

12 B

13 C

14 C

15 C

16 B

17 D

18 B19 D

20 D

196



ANSWER

2009-2010

10

21. POLYGONS II

1 A

2 A 3 C

4 C

5 B

6 C

7 D

8 B

9 B

10 B11 D

12 B

13 B

14 28

15 5

16 3

17 192

18 70/319 105

22. CIRCLES I

1 B

2 A 3 C

4 C

5 C

6 B

7 A

8 B

9 B

10 B11 B

12 B

13 A

22. CIRCLES II

1 A

2 B3 C

4 A

5 B

6 C

7 B

8 B

9 B

10 D11 D

12 7

13 7/2

14 10

15 5/18

23. SOLID GEOMETRY I

1 E

2 D3 D

4 D

5 D

6 D

7 B

8 D

9 B

10 A 11 C

12 C

13 C

14 C

15 C

16 B

17 D

18 D19 C

20 B

21 125

22 1728

197



ANSWER

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11

24. STATISTICS, GRAPHS& TABLES I

1 B2 C3 D4 23805 D6 B7 C8 C9 B

10 180

11 D12 A 13 C14 E15 E16 B17 E18 9619 3920 D

24. STATISTICS, GRAPHS& TABLES II

1 D2 C3 2754 D5 E6 13007 E8 D9 B

10 E

11 D12 A 13 1/314 C15 B16 C17 B18 D19 C20 D

24. STATISTICS, GRAPHS& TABLES III

1 E2 A 3 1494 B5 B6 D7 D8 C9 A

10 E

11 C12

13 D14 B15 E16 C17 E18 C19 C

20 C21 240022 E23 D24 1350

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ANSWER

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12

25. PROBABILITY I

1 C2 E3 D4 C5 B6 547 1088 C9 A

10 A 11 E

12 B13 E14 B15 D16 E

25. PROBABILITY I

1 B2 B3 C4 C5 A 6 C7 B8 D9 E

10 D11 B

12 E13 B14 D15 24

199

SAT Practice Book 2009 2010

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