sat practice book

TABLE of CONTENTS

SAT Practice Book

2009-2010

1 1

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

2009-2010

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

xxy1

, which of the following must be

true?

I. y x

II. y is an integer.

III. xy > x2

(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 odd

integers, where y > x, which of the

following is y2 – x2?

(A) 2x

(B) 4x

(C) 2x + 2

(D) 2x + 4

(E) 4x + 4

3. If x, y, and z are positive integers such

that the value of x + y is even and the

value 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) 2

n

(B) 2n

(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 the

following?

(A) 10

(B) 20

(C) 30

(D) 40

(E) 50

6. Which of the following must be true for

all integers a,b, and c ?

I. a- 0 =a

II. a-b=b-a

III. (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

SAT Practice Book

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7. If a, b, and c are positive integers, and if

(a−c)b=0, which of the following must

be 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 even

integer, which of the following is an odd

integer?

(A) 3b

(B) a+3

(C) 2(a+b)

(D) a+2b

(E) 2a+ b

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

the value of t?

(A) -3

(B) -1

(C) 0

(D) 1

(E) 3

10. If 2

3x is 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

3

NUMBER LINES & FRACTIONS

SAT Practice Book

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1.

Which of the lettered points on the

number line above could represent the

result when the coordinate of point P

is multiplied by the coordinate of point

Q?

(A) A

(B) B

(C) C

(D) D

(E) E

2.

On the number line above, there are 9

equal 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 the

indicated points. Which of the

following 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 is

5 less than the denominator. 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

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7.

In the figure above, AC = 24 and

AB = BC. Point D (not shown) is on the

line 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

xx?

(A) –4

(B) 0

(C) 1

(D) 2

(E) 3

9. Which of the following numbers is

between 5

1and

4

1?

(A) 0.14

(B) 0.15

(C) 0.19

(D) 0.21

(E) 0.26

10.

If x, x2, and x3 lie on a number line in

the order shown above, which of the

following 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 tick

marks are equally spaced. What is the

value of w – p ?

(A) 3/4

(B) 2/3

(C) 1/2

(D) 1/3

(E) 1/4

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12.


marks 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 best

estimate of the length of segment AB on

the number line above?

(A) 4

(B) 3.5

(C) 3

(D) 1.5

(E) 1

14.

In the figure above, if the coordinates

of points X and Y are added together,

the result will be the coordinate of a

point between which two consecutive

integers?

(A) −3 and −2

(B) −2 and −1

(C) −1 and 0

(D) 0 and 1

(E) 2 and 3

15.


marks are equally spaced. What is the

value 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 line

above are equally spaced, which of the

lettered points A through E is between

1/4 and 3/8?

(A) A

(B) B

(C) C

(D) D

(E) E

17.

If x is the coordinate of the indicated point

on the number line above, which of the

lettered 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.


marks are equally spaced and their

coordinates are shown. Of these

coordinates, which has the smallest

positive value?

(A) a

(B) b

(C) c

(D) d

(E) e

7

DIVISIBILITY

SAT Practice Book

2009-2010

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1. There are 8 sections of seats in an

auditorium. Each section contains at

least 150 seats but not more than 200

seats. Which of the following could be

the number of seats in this

auditorium?

(A) 800

(B) 1,000

(C) 1,100

(D) 1,300

(E) 1,700

2. “All numbers that are divisible by both

2 and 6 are also divisible by 4.”

Which of the following numbers can be

used to show that the statement above

is FALSE?

(A) 4

(B) 8

(C) 12

(D) 18

(E) 24

3. If m is the greatest prime factor of 38

and 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 the

remainder when 2p + 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 positive

integer k, the remainder is 3. For how

many different values of k is this true?

(A) One

(B) Two

(C) Three

(D) Four

(E) Five

6. How many cubical blocks, each with

edges of length 4 centimeters, are

needed to fill a rectangular box that

has inside dimensions 20 centimeters

by 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–digit

integer that has a factor of 10?

8. If there is no waste, how many square

yards of carpeting is needed to cover a

rectangular floor that is 12 feet by 18

feet?

(1 yard = 3 feet)

(A) 8

(B) 16

(C) 24

(D) 30

(E) 216

9.

If x is divisible by 3 and y is divisible

by 5, which of the following must be

divisible by 15?

I. xy

II. 3x + 5y

III. 5x + 3y

(A) I only

(B) III only

(C) I and II only

(D) I and III only

(E) I, II, and III

10. How many integers greater than 20

and less than 30 are each the product

of 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, the

remainder is 5. What is the remainder

if 4m is divided by 6 ?

(A) 0

(B) 1

(C) 2

(D) 4

(E) 5

12. A large solid cube is assembled by

gluing together identical unpainted

small cubic blocks. All six faces of the

large cube are then painted red. If

exactly 27 of the small cubic blocks

that make up the large cube have no

red paint on them, how many small

cubic blocks make up the large cube?

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DIVISIBILITY

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13. When the positive integer n is divided

by 6, the remainder is 2. What is the

remainder when 24n is divided by 36 ?

14. If k is a positive integer divisible by 7,

and if k < 90, what is the greatest

possible 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 125

books but not more than 160 books.

Which of the following could be the

total number of books in all 6

bookcases?

(A) 500

(B) 625

(C) 725

(D) 925

(E) 1,000

16. Which of the following is divisible by 3

and by 5 but is not divisible by 10 ?

(A) 30

(B) 35

(C) 40

(D) 45

(E) 60

17. When the positive integer m is

divided by 5, the remainder is 3. What

is the remainder when 20m is divided

by 25?

18. For what positive number is the

square root of the number the same as

the number divided by 40?

19. The result when a number is divided

by 2 is equal to the result when that

same number is divided by 4. What is

that number?

(A) -4

(B) -2

(C) 0

(D) 2

(E) 4

20. What is the product of the smallest

prime number that is greater than 50

and the greatest prime number that is

less than 50?

10

SEQUENCES

SAT Practice Book

2009-2010

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1. –1, 0, 1, 2

A sequence is formed by repeating the

4 numbers above in the same order

indefinitely. What is the sum of the

first 28 terms of the sequence?

(A) 12

(B) 13

(C) 14

(D) 15

(E) 16

2. Rita’s dog weighed 5 pounds when she

bought it. Over the next several years,

the dog’s weight increased by 10

percent per year. Which of the

following functions gives the weight,

w, in pounds, of the dog after n years

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

3. Each month, a telephone service

charges a 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 much does the telephone

service charge for a month in which 50

calls are made?

(A) $12.20

(B) $12.80

(C) $13.60

(D) $14.40

(E) $17.60

y, 2y + 7, y + 6 . . .

4. In the increasing sequence above, the

first term is y and the difference

between any two consecutive terms is

3. What is the value of the fourth term

in the sequence?

(A) –4

(B) 2

(C) 5

(D) 13

(E) 19

5. In a sequence of numbers, the first

number is 4 and each number after the

first is 1 more than 5 times the

preceding number. What is the third

number in the sequence?

(A) 16

(B) 21

(C) 94

(D) 96

(E) 106

6. The first term of a sequence is 3, and

each term after the first is 2 more than

the previous term. Which of the

following is an expression for the nth

term of the sequence for any positive

integer n?

(A) 2n

(B) 1+2n

(C) 2+2n

(D) 3+2n

(E) 2+3n

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SEQUENCES

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7. The nth term of a sequence is defined

to be 4n + 3. The 50th term is how

much 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 each

term to the term immediately

preceding it is 2 to 1. What is the ratio

of the 8th term in this sequence to the

5th 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 7

more 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 the

previous term and each odd–numbered

term, after the first, is –1 times the

previous term. For example, the

second term is 3 + 2, and the third

term is (–1) × 5. What is the 55th term

of the sequence?

(A) –5

(B) –3

(C) –1

(D) 3

(E) 5

11. The sum of 5 consecutive integers is

1,000. What the value of the greatest

of these integers?

12. 5.101001000100001 …

The decimal number above consists of

only 1 ‘ s and 0’s to the right of the

decimal point. The first 1 is followed

by one 0, the second 1 is followed by

two 0’ s, the third 1 is followed by

three 0’ s, and so on. What is the total

number of 0’s between the 98th and

the 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 3

times the preceding term. If the sum of

the first 5 terms is 605, what is the

value of a?

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

The first term in the sequence above is

7, and each term after the first is

determined by multiplying the

preceding 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 in

either of two ways. Either two

adjacent letters may be interchanged

or the entire sequence may be

reversed. What is the least number of

such changes needed to put the letters

into alphabetical order from left to

right?

(A) 2

(B) 3

(C) 4

(D) 5

(E) 6

16. After the first term, each term in a

sequence is 3 greater than 3

1 of the

preceding term. If t is the first term of

the sequence and t ≠ 0, what is the

ratio of the second term to the first

term?

(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 are

shown above. Each term after the first

is found by adding 9 to the term

immediately preceding it. Which term

in this sequence is equal to

8 + (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 consecutive

integers if the sum of these integers

equals 185?

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

In the sequence above, the first term

is 2. Each number after the first is

obtained by adding 1 to the

preceding number and then doubling

the result. What is the sixth number

in the sequence?

(A) 122

(B) 123

(C) 124

(D) 125

(E) 126

20. “The sum of three consecutive odd

integers is 111. “

If n represents the least of the three

integers, which of the following

equations represents the statement

above?

(A) 3n = 111

(B) 3n + 2 = 111

(C) 3n + 4 = 111

(D) 3n + 6 = 111

(E) 3n + 9 = 111

21. The first term of a sequence is 20 and

the second term is 8. The third term

and each term thereafter is the

average (arithmetic mean) of the two

terms immediately preceding it. What

is the value of the first term in the

sequence that is not an integer?

22. The nth term of a sequence is given by

the formula .22 nn How much larger

is the 10th term of the sequence than

the 9th term?

23. 150, 30, 6,…

In the sequence above, each term after

the 1st term is 5

1of the term preceding

it. What is the 5th term of this

sequence?

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SETS

SAT Practice Book

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1. How many positive four-digit integers

have 1 as their first digit and 2 or 5 as

their 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 shirts

with buttons, and circular region R

represents shirts with collars. What is

represented by the shaded region?

(A)Shirts with pockets, buttons, and

collars

(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 a

member of set P and y is a member of

set Q, which of the following CANNOT

be equal to the product xy ?

(A) 16

(B) 18

(C) 20

(D) 21

(E) 24

4. How many positive integers less than

1,000 are multiples of 5 and are equal

to 3 times an even integer?

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SETS

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5. The Lyndhurst High School twelfth

graders are represented in the circle

graph in Figure 1. Figure 2 is another

way to illustrate the use of computers

by these twelfth graders. If the same

200 twelfth graders are represented in

both figures, what is the total number

of twelfth graders represented by the

shaded circle in Figure 2 ?

6. A set has property X if tt 2 is in the

set 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 integers

and 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 are

represented in Figure 1 above. Figure

2 above is another way to show which

pets these students have. If the same

500 students are represented in both

figures, what is the total number of

students represented by the shaded

circle in Figure 2 ?

9. Some integers in set X are even.

If the statement above is true, which

of 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

4A , 7,4,

4

7,

7

4B

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

B above, which of the following must

be 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 B

is the set of two-digit positive integers

whose 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 the

cafeteria. Each tray contains a cup

only, a plate only, or both a cup and a

plate. If 15 of the trays contain cups

and 21 of the trays contain plates, how

many contain both a cup and a plate?

13. The least integer of a set of

consecutive integers is –25. If the sum

of 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 all

members that are in either set X or set

Y with the exception of the k common

members (k > 0). Which of the

following 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) 2x + 2y – 2k

15. If E is the set of even integers, P is the

set of positive integers, and F is the set

of integers less than 5, which of the

following integers will be in all three

sets?

(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 all

possible values of xy?

(A) xy = 4

(B) 240 xy

(C) 111 xy

(D) 241 xy

(E) 248 xy

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17. How many integers in the set of all

integers from 1 to 100, inclusive, are

not 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 number

only

(D) Decreasing the largest number

only

(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. How

many numbers in set X are also in

set Y ?

(A) Two

(B) Three

(C) Four

(D) Seven

(E) Nine

20. If k is a positive integer, let be

defined as the set of all multiples of k.

All of the numbers in which of the

following sets are also in all three of

the sets , and ?

(A)

(B)

(C)

(D)

(E)

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RATIO, PROPORTION & PERCENTS

SAT Practice Book

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1. Which of the following tables shows a

relationship in which w is directly

proportional to x?

(A) (B)

(C) (D)

(E)

2. Dwayne has a newspaper route for

which he collects k dollars each day.

From this amount he pays out 3

k

dollars per day for the cost of the

papers, and he saves the rest of the

money. In terms of k, how many days

will it take Dwayne to save $1,000?

(A) 5001,

k (B)

0001,

k

(C) k

0001, (D)

k

5001,

(E) 1,500k

3. 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

4. If 30 percent of 40 percent of a positive

number is equal to 20 percent of w

percent of the same number, what is

the value of w?

(A) 80

(B) 60

(C) 50

(D) 15

(E) 10

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SAT Practice Book

2009-

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2009-2010

2

5. There are 75 more women than men

enrolled in Linden College. If there are

n men enrolled, then, in terms of n,

what percent of those enrolled are

men?

(A) 75n

n%

(B) 752n

n%

(C) )( 752100 n

n%

(D) 75

100

n

n%

(E) 752

100

n

n%

6. The eggs in a certain basket are either

white or brown. If the ratio of the

number of white eggs to the number of

brown eggs is 3

2 , each of the following

could be the number of eggs in the

basket EXCEPT

(A) 10

(B) 12

(C) 15

(D) 30

(E) 60

7. The price of a telephone was first

increased by 10 percent and then the

new price was decreased by 25

percent. The final price was what

percent of the initial price?

(A) 78%

(B) 80%

(C) 82.5%

(D) 85%

(E) 87.5%

8. The force required to stretch a spring

beyond its natural length is

proportional to how far the spring is

being stretched. If a force of 15 pounds

stretches a spring 8 centimeters

beyond its natural length, what force,

in pounds, is needed to stretch this

spring 20 centimeters beyond its

natural length?

(A) 23

(B) 27

(C) 30.5

(D) 35

(E) 37.5

21


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2009-2010

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9. A measuring cup contains 5

1of a cup of

orange juice. It is then filled to the 1

cup mark with a mixture that contains

equal 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 4b,

what is the value of b

a ?

11. In a poll, 35 people were in favor of

building a new library, 14 people were

against it, and 1 person had no

opinion. What fraction of those polled

were in favor of building a new

library?

(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 in

terms 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 nonzero

numbers, then all of the following

proportions are equivalent EXCEPT

(A) c

b

f

a

(B) a

b

c

f

(C) b

f

a

c

(D) f

b

c

a

(E) 1

1

bc

af

14. When the positive even integer n is

increased by 50 percent of itself, the

result is between 10 and 20. What is

one possible value of n?

22


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2009-2010

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15. If a

xx 2

4 and 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. What

is the ratio of the area of the larger

circle 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 15

percent of m?

(A) 15

(B) 20

(C) 25

(D) 30

(E) 35

23


SAT Practice Book

2009-2010

1 1

1. If 12

10 b

a, what is the value of ab?

2. The price of ground coffee beans is d

dollars for 8 ounces and each ounce

makes c cups of brewed coffee. In

terms of c and d, what is the dollar

cost of the ground coffee beans

required to make 1 cup of brewed

coffee?

(A) c

d

8 (B)

8

cd

(C) d

c8 (D)

c

d8

(E) 8cd

3.

The circle graph above represents all

the jeans that were sold by a retail

store in 2001, according to

their brands. If the store sold 900

pairs of jeans other than brands J, K,

L, M, and N, how many pairs of jeans

did it sell altogether?

(A) 1,500 (B) 2,250

(C) 3,000 (D) 3,600

(E) 4,500

4. The Smith Metal Company’s old

machine makes 300 bolts per hour. Its

new machine makes 450 bolts per

hour. If both machines begin running

at the same time, how many minutes

will it take the two machines to make

a 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 and2

1

2

1n

n,

then n =?

(A) 1

(B) 2

(C) 3

(D) 4

(E) 5

24


SAT Practice Book

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2009-2010

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7. If y is directly proportional to x2 and

8

1y when

2

1x what is the positive

value of x when 2

9y ?

(A) 4

3

(B) 2

3

(C) 4

9

(D) 3

(E) 9

8.

If the five line segments in the figure

above are all congruent, what is the

ratio of the length of AC (not shown) to

the 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 results

when 1,000 people were asked, “How

old are you?” The age they gave is

represented by x. How many people

said that their age was less than 40?

(A) 200

(B) 300

(C) 450

(D) 500

(E) 550

10. 37

39

2x

x, then x = ?

(A) 37

(B) 39

(C) 41

(D) 74

(E) 78

25


SAT Practice Book

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2009-2010

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11. From 1979 to 1989, the total elephant

population in the four regions of Africa

decreased by approximately what

percent?

(A) 10%

(B) 30%

(C) 50%

(D) 70%

(E) 90%

12. If n

1 =

5

2, what is the value of n ?

13.

In a survey, 3,400 people responded to the

following question: “How many weeks of

vacation did you take last year?” Their

responses to the question are summarized in

the chart above, where n equals the number

of vacation weeks indicated. How many

respondents took more than 2 weeks of

vacation last year?

14. A box contains 2,900 solid-colored

marbles that are either orange, blue,

or green. If 29 percent of the marbles

are orange and 29 percent of the

marbles are blue, what percent are

green?

(A) 29%

(B) 42%

(C) 52%

(D) 58%

(E) 71%

15. What is the ratio of the radius r of a

circle to the circumference of the

circle?

(A) 1: 2

(B) 1:

(C) 1: r

(D) :1

(E) 2 :1

16. Fifty percent of the songs played on a

certain radio station are 3 minutes

long, 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 on

this radio station

26

Jai Sahni

Highlight


SAT Practice Book

2009-

2010

4

2009-2010

4

17. If tr

tr =

2

5 what 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, what

percent of (q + 1) is r ?

(A) )1(100

1

qr %

(B) r

q

100

1 %

(C)r

q )1(100 %

(D) ( q

r100 + 1 ) %

(E) 1

100

q

r %

27


SAT Practice Book

2009-2010

1 1

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

2 when 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 4,600

staples that are either silver, black, or

red. If 46 percent of the staples are

silver and 46 percent are black, what

percent are red?

(A) 8%

(B) 18%

(C) 46%

(D) 54%

(E) 92%

6. The original price of a book was b

dollars. 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 following

represents the price, in dollars,

that James paid for the book?

(A) b 100

1x

1001

t

(B) b100

)1)(1( tx

(C) b100

1tx

(D) b100

1xt

(E) b100

x

100

t

28


SAT Practice Book

2009-

2010

2

2009-2010

2

7.

Students at Northern High School are

represented in Figure 1 above. Figure 2

above is another way to show which pets

these students have. If the same 500

students are represented in both figures,

what is the total number of students

represented by the shaded circle in

Figure 2 ?

8. If the value of -t

1 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 the

circle?

(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

29


SAT Practice Book

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2009-2010

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11. Flour, water, and salt are mixed by

weight 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, in

pounds, 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 3

percent 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 her

average speed, in miles per hour?

(A) t

n (B)

n

t

(C)nt

1 (D) nt

(E) n 2 t

14. 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

15. If ba

yx =

3

2, then

ba

yx

1010

99= ?

(A) 10

9

(B) 23

20

(C) 27

20

(D) 3

2

(E) 5

3

16. 30


SAT Practice Book

2009-

2010

4

2009-2010

4

The circle graph above shows how

David’s monthly expenses are divided.

If David spends $450 per month for

food, how much does he spend per

month on his

car?

(A) $200

(B) $320

(C) $360

(D) $400

(E) $450

17. In a certain store, the regular price of

a refrigerator is $600. How much

money is saved by buying this

refrigerator at 20 percent off the

regular price rather than buying it on

sale at 10 percent off the regular price

with an additional discount of 10

percent off the sale price?

(A) $6

(B) $12

(C) $24

(D) $54

(E) $60

18.

According to the graph above, if there are

6,000 registered voters aged 60 and over

in Washington County, how many

registered 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 ROOTS

SAT Practice Book

2009-2010

1 1

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

(A) 2

(B) 3

(C) 4

(D) 5

(E) 6

2. If 24x = 16, then x =?

(A) 1

(B) 2

(C) 4

(D) 8

(E) 12

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

4. If tr1818 , where r and t are

positive integers and r > t, which of the

following 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

equations 3

12

1

x and 16zy . If z > y

what is the value of x + z?

(A) 5

(B) 7

(C) 11

(D) 13

(E) 15

6. 22 33 )( xx

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




(A) 2x

(B) 4x

(C) 2x + 2

(D) 2x + 4

(E) 4x + 4

32


SAT Practice Book

2009-

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2

2009-2010

2

8. If m and k are positive and

mkm 10010 12 , what is 1m in terms of

k?

(A) 10

k

(B) 90

k

(C) 10

k

(D) k10

1

(E) k90

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 positive

integers 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 yy

x?

(A) 5

(B) 8

(C) 10

(D) 12

(E) 20

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

(A) y

(B) y2

(C) y3

(D) y6

(E) y12

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SAT Practice Book

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2009-2010

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14. 39 xx

For all values of x greater than 3, the

equation above is equivalent to which

of the following?

(A) x = x2

(B) x = x2 + 18

(C) x = x2 – 6x

(D) x = x2 – 6x + 9

(E) x = x2 – 6x + 18

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

satisfying 23

4

kx and 23

4

ny ,

what is 3

2

)(xy in terms of n and k?

(A) nk

1

(B) k

n

(C) n

k

(D) nk

(E) 1

16. If 287 mmm x and 155 mm y)( , what is

the value of x + y?

(A) 7

(B) 12

(C) 14

(D) 24

(E) 31

17. If 722222 xxxx , what is the value

of x?

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

least value of k for which 3

5k 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

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2009-2010

4

20. If x and y are positive integers andyx 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

1 1

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

x in

terms of z ?

(A) z

(B) z + 1

(C) 5 z

(D) 5 z +1

(E) 5 1z

2. If k is a positive integer, which of the

following is equivalent to 3 k + 3 k ?

(A) 2 3 k

(B) 3 k2

(C) 6 k

(D) 6 k2

(E) 9 k2

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

x what is the value

of x ?

(A) 6

(B) 5

(C) 4

(D) 3

(E) 2

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

could be a value of x?

(A) −8

(B) −4

(C) 0

(D) 16

(E) 32


9(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, and

3 y − 7 = 8, what is the value of y ?

8. If a 2 = 4, which of the following could

be 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 following

could 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 following

could be true?

I. x = 8

II. y = -4

III. 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 terms

of 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

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3

2009-2010

3

13. If x is a positive integer satisfying

x 7 = k and x 9 = m, which of the following

must be equal to x 11 ?

(A) k

m2

(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

= 2 k , 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

1 1

1. There are 8 sections of seats in an

auditorium. Each section contains at

least 150 seats but not more than 200

seats. Which of the following could be

the number of seats in this

auditorium?

(A) 800

(B) 1,000

(C) 1,100

(D) 1,300

(E) 1,700

2. If 4 less than 3 times a certain number

is 2 more than the number, what is the

number?

(A) –1

(B) –3

(C) 1

(D) 2

(E) 3

3. During a game, the blue team scored

one–sixth of its points in the first

quarter, one–fourth in the second

quarter, one–third in the third

quarter, and the remaining points in

the fourth quarter. If its total score

was 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 fills

a bottle with spring water and

machine 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, which

of the following describes all possible

values of n?

(A) 8

112n

(B) 8

112n

(C) 8

112n

(D) 8

112n

(E) 8

112n

5. Esther drove to work in the morning

at an average speed of 45 miles per

hour. She returned home in the

evening along the same route and

averaged 30 miles per hour. If Esther

spent a total of one hour commuting to

and 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

t

h

e

s

c

hedule above, each session is to be 2

11

hours long, each break is to be 4

1 hour

long, and lunch is to be 1 hour long. If

session IV is to end at 4:30 P.M., at

what 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 on

Monday, 4 times as many packages on

Tuesday as on Monday, and 3 more

packages on Wednesday than on

Monday. What is the average

(arithmetic mean) number of packages

he delivered per day over the three

days?

(A) 2n – 3

(B) 2n – 1

(C) 2n + 1

(D) 2n + 3

(E) 6n + 1

8. 5.101001000100001 …

The decimal number above consists of

only 1 ‘ s and 0’s to the right of the

decimal point. The first 1 is followed

by one 0, the second 1 is followed by

two 0’ s, the third 1 is followed by

three 0’ s, and so on. What is the total

number of 0’s between the 98th and

the 101st 1 in this decimal number?

(A) 288

(B) 291

(C) 294

(D) 297

(E) 300

9. There is the same number of boys and

girls on a school bus when it departs

from school. At the first stop, 4 boys

get off the bus and nobody gets on.

After the first stop, there are twice as

many 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 both

the12th tallest and the 12th shortest

students in her class. If everyone in

the class is of the different height, how

many students are in the class?

(A) 22

(B) 23

(C) 24

(D) 25

(E) 34

Event Beginning

Time

Ending

Time

Session I ?

Break

Session II

Lunch

Session III

Break

Session 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 a

bus trip. Each of the n buses that were

used to transport the passengers could

seat a maximum of x passengers. If

one bus had 3 empty seats and the

remaining buses were filled, which of

the following expresses the

relationship 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 certain

fraction is 5 less than the

denominator. 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–day

camping trip. Each person will need to

bring 1 bottle of water for each day of

the trip. If the water is sold only in 3–

bottle packages, how many packages

must the family buy for the trip?

14. A measuring cup contains 5

1of a cup of

orange juice. It is then filled to the 1 cup

mark with a mixture that contains equal

amounts of orange, grapefruit, and pineapple

juices. What fraction of the final mixture is

orange juice?

15. When Ms. Yun arrived at the grocery

store, there were 5 packages of hot dog rolls

left on the shelf. One package contained 12

rolls, and each of the others

contained 8 rolls. If Ms. Yun bought all 5

packages, how many hot dog rolls did she

purchase at the store?

(A) 32

(B) 36

(C) 44

(D) 48

(E) 52

16. How old was a person exactly 1 year ago

if exactly x years ago the person was y years

old?

(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 standard

time (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 in

San Francisco at 4:00 P.M. PST on the

same day. If a second plane left San

Francisco at noon PST and took exactly

the same amount of time for the trip,

what was the plane’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 but

younger than Susan. If t, m, and s

represent the ages, in years, of Todd,

Marta, and Susan, respectively, which

of 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 light

bulbs. Some of the light bulbs cost $1

each and the others cost $2 each. If

twice as many $1 bulbs as $2 bulbs

were ordered, how many light bulbs

were ordered altogether?

20. When twice a number is decreased

by 3, the result is

253. What is the number?

21. h(t) = c – (d – 4t)2

At time t = 0, a ball was thrown upward

from an initial height of 6 feet. Until the

ball hit the ground, its height, in feet,

after t seconds was given by the

function h above, in which c and d are

positive constants. If the ball reached

its 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 he

does during the week, plus a weekly

allowance of $10. If Bobby receives no

other money, which of the following

expressions represents the total dollar

amount Bobby receives for a week in

which he has done n chores?

(A) 10 + n

(B) (10 + 2)n

(C) 10n + 2

(D) 10 + 2n

(E) (10 + n)2

42

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SAT Practice Book

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2010

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2009-2010

5

23. A computer program randomly

selects a positive two–digit integer. If

the integer selected is odd, twice that

integer is printed. If the integer selected

is even, the integer itself is printed. If

the integer printed is 26, which of the

following could have been the integer

selected?

I. 13

II. 26

III. 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) 60m + s

(B) m + 60s

(C) 60(m + s)

(D) 60

sm

(E) sm

60

25. Kyle’s lock combination consists of 3

two–digit numbers. The combination

satisfies the three conditions below.

One number is odd.

One number is a multiple of 5.

One number is the day of the

month of Kyle’s birthday.

If each number satisfies exactly one

of the conditions, which of the

following could be the combination to

the 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 tape

was wasted, which of the following

represents the number feet of masking

tape that was left on the roll after he

put up n posters? (12 inches = 1 foot)

(A) 300 – 6n

(B) 300 – 2n

(C) 300 – n

(D) 300 – n2

1

(E) 300 – n4

1

43

WORD PROBLEMS

SAT Practice Book

2009-2010

1 1

1. A number n is increased by 5 and the

result is multiplied by 5. This result is

decreased by 5. Finally, that result is

divided by 5. In terms of n, what is the

final result?

2. In a certain game, points are assigned to

every word. Each q, x, and z in a word is

worth 5 points, and all other letters are

worth 1 point each. What is the sum of the

points assigned to the word “exquisite”?

(A) 21

(B) 17

(C) 16

(D) 13

(E) 9

3. A certain scale only registers weights

that are greater than 6 pounds. A person

who wanted to know the weights of a

puppy, a kitten, and a bunny weighed

them in pairs and got the following

results.

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 her

office is 5 kilometers longer than the direct

route. When she goes by the scenic route and

returns by the direct route, the round trip is

35 kilometers. How many kilometers is the

direct route?

(A) 5

(B) 2

112

(C) 15

(D) 20

(E) 2

122

5. For a certain hot–water heater, the

increase in heating expenses is directly

proportional to the increase in water–

temperature setting. If heating expenses

increase by $24 when the water–

temperature setting is increased by 20

degrees Fahrenheit, by how much will

heating expenses increase when the

water–temperature setting is increased

by 15 degrees Fahrenheit?

(A) $16

(B) $18

(C) $19

(D) $20

(E) $21

6. If Peg traveled 10 miles in 2 hours and

Linda traveled twice as far in half the

time, 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 is

equal to 1, what is the number?

8. A company sells boxes of balloons in

which the balloons are red, green, or

blue. Luann purchased a box of balloons

in which 3

1of them were red. If there

were half as many green balloons in the

box as red ones and 18 balloons were

blue, how many balloons were in the box?

9. Alice and Corinne stand back-to-back.

They each take 10 steps in opposite

directions away from each other and

stop. Alice then turns around, walks

toward Corinne, and reaches her in 17

steps. 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 are

the same length and all of Corinne’s

steps are the same length.)

10. If 3 more than n is a negative number

and if 5 more than n is a positive

number, which of the following could be

the value of n?

(A) –5

(B) –4

(C) –3

(D) 0

(E) 4

11. If all men in the Williams family are over

six feet tall, which of the following

statements must be true?

(A) No man under six feet tall is a

member of the Williams family.

(B) All men over six feet tall are

members of the Williams family.

(C) All men who are not members of the

Williams, family are under six feet tall.

(D) Every member of the Williams family

over six feet tall is a man.

(E) There is one man in the Williams

family under six feet tall.

12. The total cost of 3 equally priced

mechanical pencils is $4.50. If the cost

per pencil is increased by $0.50, how

much will 5 of these pencils cost at the

new rate?

(A) $7.50

(B) $8.00

(C) $9.00

(D) $9.50

(E) $10.00

13. Car A traveled 60 miles and averaged 20

miles per gallon of gasoline. If car B

traveled 15 miles

for each gallon of gasoline it used, how

many miles had car B traveled

when it had used the same amount of

gasoline that car A used to travel 60

miles?

45

WORD PROBLEMS

SAT Practice Book

2009-

2010

3

2009-2010

3

14. At Maple Creek High School, some

members of the chess club are on the

swim team and no members of the swim

team are tenth graders. Which of the

following must also be true?

(A) No members of the chess club are

tenth graders.

(B) Some members of the chess club

are tenth graders.

(C) Some members of the chess club

are not tenth graders.

(D) More tenth graders are on the

swim team than are in the chess

club.

(E) More tenth graders are in the

chess club than are on the swim

team.

15. To celebrate a colleague’s graduation, the

m coworkers in an office agreed to

contribute equally to a catered lunch that

costs a total of y dollars. If p of the

coworkers fail to contribute, which of the

following represents the additional

amount, in dollars, that each of the

remaining coworkers must contribute to

pay for the lunch?

(A)m

y

(B) pm

y

(C) pm

py

(D) m

pmy )(

(E) )( pmm

py

16. While driving on a 500-mile trip, Mr.

Smith averages 60 miles per hour for the

first t hours. In terms of t, where

t < 8, how many miles remain to be

traveled?

(A) 60t − 500

(B) 500 − 60t

(C) 30,000 − t

(D) 500 − t

60

(E) t60

500

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

1 of the junior class had

arrived at a school dance. By 8:00 P.M.,

30 more juniors had arrived, raising

attendance to 2

1 of 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 sum

of

(1) a basic fixed charge for using the

taxicab, and

(2) an additional charge for each 4

1 of a

mile that is traveled.

If the total cost to ride 4

3 mile is $4.00

and the total cost to ride 12

1 miles is

$5.50, what is the total cost, in dollars, of

a 3-mile ride?

(Disregard the $ sign when gridding your

answer. If, for example, your answer is

$1.37, grid 1.37)

19. Classified ads cost $2.50 per 30 words at

CityNewspaper. What is the least

number of words that must be deleted

from the text of a 75-word classified ad to

reduce the cost to $5.00 or less?

(A) 5

(B) 15

(C) 20

(D) 30

(E) 60

20. Which of the following represents the total

cost, in dollars, of k compact discs at $15

each and p compact disc cases at $25 each?

(Disregard sales tax.)

(A) 15k + 25p

(B) 25k + 15p

(C) 40(k + p)

(D) 0.40(k + p)

(E) (15 + k)(25 + p)

21. If x and y are two different integers and

the product 35xy is the square of an

integer, 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 for

an adult’s admission than for a child’s

admission. If a group of 4 adults and 3

children spent $119 on admission, what

is the price of admission for one child?

(A) $11

(B) $13

(C) $16

(D) $17

(E) $18

47

WORD PROBLEMS

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2009-2010

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23. The figure above shows four apartments

in a building. In this building, each

apartment is occupied by only one

person. Alice lives next to Sam, and Paul

lives next to Alice and Dara. In which

apartment 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 activity

fee of $4.00 per student and has a

student body of 8,200 students. If every

student pays the fee, what is the total

amount in activity fees collected from the

students?

(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

1 1

1. Each month, a telephone service charges

a 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 much

does the telephone service charge for a

month in which 50 calls are made?

(A) $12.20

(B) $12.80

(C) $13.60

(D) $14.40

(E) $17.60

2. How many 4

1-pound sticks of butter

together weigh as much as 25 pounds of

butter?

3. The total cost of 5 equally priced

notebooks is $12.50. If the cost per

notebook is reduced by $1, how much will

3 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 added

to k. What is the value of 4k?

(A) 5

4

(B) 1

(C) 4

5

(D) 4

(E) 5

5. The bus fare from city A to city B is $5

more for adults than for children. If a

group of 5 adults and 6 children pay a

total of $124 to travel by bus from city A

to city B, what is the cost of the ticket for

one adult?

(A) $11

(B) $12

(C) $14

(D) $16

(E) $17

6. Which of the following represents the

total cost, in dollars, of x rolls of

wrapping paper that cost $6 each and y

greeting cards that cost $2 each?

(A) 2x + 6y

(B) 6x + 2y

(C) 8(x + y)

(D) 0.8(x + y)

(E) (2 + x) (6 + y)

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WORD PROBLEMS

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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 are

dated earlier than 2000. Which of the

following must be true?

(A) None of the coins in Jamal’s pocket

are 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 pocket

are dated 2000 or later.

(D) Most of the coins in Jamal’s pocket

are either quarters or dated earlier than

2000.

(E) Most of the coins in Jamal’s pocket

are not quarters.

8. There are 6 bookcases in a house. Each

bookcase contains at least 125 books but

not more than 160 books. Which of the

following 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’s

books 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 a

book and the rest of the students take 5

books each, there will be no books left.

How many books were donated to the

class?

(A) 120

(B) 140

(C) 160

(D) 175

(E) 185

10. Bernardo drives to work at an average

speed of 50 miles per hour and returns

along the same route at

an average speed of 25 miles per hour. If

his total travel time is 3 hours, what is

the 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

1 and the product is then multiplied by

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

50

WORD PROBLEMS

SAT Practice Book

2009-

2010

3

2009-2010

3

12. An object thrown upward from a height

of h feet with an initial velocity of v feet

per second will reach a maximum height

of h+ 64

2v feet. If the object is thrown

upward from a height of 6 feet with an

initial velocity of 32 feet per second, what

will be its maximum height, in feet?

13. On Monday morning Mr. Smith had a

certain amount of money that he planned

to spend during the week. On each

subsequent morning, he had one fourth

the amount of the previous morning. On

Saturday morning, 5 days later, he had

$1. How many dollars did Mr. Smith

originally start with on Monday

morning?

(Disregard the $ sign when gridding

your answer.)

14. Ali, Ben, and Carla made a total of 20

sandwiches. Ben made 3 times as many

as Ali, and Carla made twice as many as

Ben. How many sandwiches did Ali

make?

(A) Two

(B) Four

(C) Five

(D) Six

(E) Ten

15. If Marisa drove n miles in t hours, which

of the following represents her average

speed, in miles per hour?

(A) t

n

(B) n

t

(C) nt

1

(D) nt

(E) n2t

16. Morgan’s plant grew from 42

centimeters to 57 centimeters in a year.

Linda’s plant, which was 59 centimeters

at the beginning of the year, grew twice

as many centimeters as Morgan’s plant

did during the same year. How tall, in

centimeters, was Linda’s plant at the end

of the year?

17. Since the beginning of 1990, the number

of squirrels in a certain wooded area has

tripled during every 3-year period of

time. If there were 5,400 squirrels in the

wooded area at the beginning of 1999,

how many squirrels were in the wooded

area at the beginning of 1990?

51

WORD PROBLEMS

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2009-2010

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18. The result when a number is divided by 2

is equal to the result when that same

number 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 the

following must also be true?

(A) If Fred cannot swim, then he is not

Kay’s brother.

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

brother.

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

brother.

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

swim.

(E) If Mark is not Kay’s brother, then he

cannot swim.

20. When her son’s class held its magazine

drive, Dr. Nelson bought 7 one-year

magazine subscriptions for the waiting room

in 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 per

year. Altogether, how many magazines will

her office receive from these subscriptions?

52

FACTORING

SAT Practice Book

2009-2010

1 1

1. If a + 2(x + 1) = s, what is x + 1, in

terms of s and a?

(A) a

s

2

(B) 2

as

(C) 2

as

(D) as

2

(E) as

2

2. If x2+y2 = 73 and xy = 24, what is the

value of (x + y)2?

(A) 73

(B) 97

(C) 100

(D) 121

(E) 144

3. If 2

1

2

1

)()( baba , which of the


(A) b = 0

(B) a + b = 1

(C) a – b = 1

(D) a2 + b2 = 1

(E) a2 – b2 = 1

4. If x2 – y2 = 77 and x + y = 11, what is

the value of x?

(A) 10

(B) 9

(C) 8

(D) 7

(E) 6

5. If a, b, and c are different positive

integers and 64222 cba , then

?cba 222

(A) 14

(B) 17

(C) 21

(D) 28

(E) 34

6. If (2x – 2)(2 – x) = 0, what are all the

possible values of x?

(A) 0 only

(B) 1 only

(C) 2 only

(D) 1 and 2 only

(E) 0, 1, and 2

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FACTORING

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a2 – b2 = 7, what is the value of a?

(A) 3

(B) 4

(C) 5

(D) 6

(E) 7

8. If x2 – y2 = 10 and x + y = 5, what is the

value of x – y?

9. If xy = 7 and x – y = 5, then

x2y – xy2 =?

(A) 2

(B) 12

(C) 24

(D) 35

(E) 70

10. If 2x + z = 2y and 2x + 2y + z = 20,

what is the value of y?

(A) 5

(B) 8

(C) 10

(D) 15

(E) It cannot be determined from the

information given.

11. if

dcxbxaxxxx 2323

90

1

30

1

10

1

for all values of x, where a,b,c, and d are

constants, what is the value of

a+b+c+d ?

12. 3(x-7)(x-2)=k

In the equation above, k is a constant. If the

roots of the equation are 7 and 2, what is the

value of k?

(A) 0

(B) 2

(C) 3

(D) 7

(E) 14

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FACTORING

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3

13. If 2x − 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 the

following?

(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 possible

value of 22 yx ?

(A) 0

(B) 9

(C) 18

(D) 81

(E) 162

16. If (x+5) y= 2x −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


information given.

18. If x 2 +x=30, which of the following is a

possible value of x 2 x?

(A) -30

(B) 10

(C) 20

(D) 30

(E) 870

55

MEAN, MEDIAN & MODE

SAT Practice Book

2009-2010

1 1

1. Carlos delivered n packages on

Monday, 4 times as many packages on

Tuesday as on Monday, and 3 more

packages on Wednesday than on

Monday. What is the average

(arithmetic mean) number of packages

he delivered per day over the three

days?

(A) 2n – 3

(B) 2n – 1

(C) 2n + 1

(D) 2n + 3

(E) 6n + 1

2. If the average (arithmetic mean) of x

and y is k, which of the following is the

average 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 consecutive

integers 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 equal

and the sum of the areas of the regions

is 5, what is the average (arithmetic

mean) of the areas of the two regions?

(A) 0

(B) 2

5

(C) 4

5

(D) 5

(E) 10

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MEAN, MEDIAN & MODE

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6. When the sum of a list of prices is

divided by the average (arithmetic

mean) 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 Class

Number

of Siblings

Number

of Students

0 3

I 6

2 2

3 1

The table above shows how many

students in a class of 12 preschoolers

had 0, 1, 2, or 3 siblings. Later, a new

student joined the class, and the

average (arithmetic mean) number of

siblings per student became equal to

the median number of siblings per

student. How many siblings did the

new student have?

(A) 0

(B) 1

(C) 2

(D) 3

(E) 4

8. Each of 5 people had a blank card on

which they wrote a positive integer. If

the average (arithmetic mean) of these

integers is 15, what is the greatest

possible integer that could be on one of

the cards?

9. The first term of a sequence is 20 and

the second term is 8. The third term

and each term thereafter is the

average (arithmetic mean) of the two

terms immediately preceding it. What

is the value of the first term in the

sequence that is not an integer?

10. If the average (arithmetic mean) of x

and 3x is 12, what is the value of x?

(A) 2

(B) 4

(C) 6

(D) 12

(E) 24

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2009-2010

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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

c a

(B) 3

c a

(C) 2

a - c

(D) 3

a - c

(E) ac

12. Fifty percent of the songs played on a

certain radio station are 3 minutes

long, 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 on

this radio station?

13. If the average (arithmetic mean) of 5

and r is 7 and the average of 3 and s is

3, what is the average of r and s ?

(A) 3

(B) 5

(C) 6

(D) 9

(E) 12

14. a, 2a, b

If the average (arithmetic mean) of the

3 numbers above is 2a, what is b in

terms of a ?

(A) a

(B) 2

3 a

(C) 2a

(D) 2

5a

(E) 3a

15. For which of the following lists of 7

numbers is the average (arithmetic

mean) 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

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MEAN, MEDIAN & MODE

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2010

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2009-2010

4

16. For 12 bottles of shampoo of various

brands, the cost and volume of each

are displayed in the scatterplot above,

and the line of best fit for the data is

shown. Of the following, which is

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

17.

The table above shows the number of items

100

customers purchased from a hardware store

over a 4 -hour period. Which of the following

can be determined from the information in

the table?

I. The average (arithmetic mean) number of

items purchased per customer

II. The median number of items purchased

per

customer

III. The mode of the number of items

purchased 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

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2010

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2009-2010

5

18. The median of a list of 99 consecutive

integers is 60. What is the greatest

integer 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 t

and t 2 is x and if the average of t

and t 2 is y, what is the average of x

and y ?

(A) 1

(B) 2

t

(C) t

(D) t 2

1

(E) 2t

21.

The bar graph above shows the number of

tons of beans produced on a large farm for

the years 1985 through 1991. For which of

the following two-year periods was the

average (arithmetic mean) bean production

closest 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 t

and y is 15, and the average of w and x

is 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 & MODE

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2009-

2010

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2009-2010

6

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

If x is the median of the 7 numbers

listed above, which of the following

could be the value of x ?

(A) 5

(B) 8

(C) 9

(D) 14

(E) 16

24. If 2x – 5, x + 1, and 3x – 8 are all

integers and x + 1 is the median of

these integers, which of the following

could be a value for x?

(A) 5

(B) 7

(C) 9

(D) 10

(E) 11

61

EQUATIONS

SAT Practice Book

2009-2010

1 1

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

4x – 3?

(A) 5

(B) 9

(C) 15

(D) 18

(E) 21

2. If 3

2

y


y

x

2

3?

(A) 3

1

(B) 3

2

(C) 1

(D) 2

3

(E) 4

9

3. If 5t = 45 and tk = 1, what is the value

of k?

(A) 45

1

(B) 9

1

(C) 5

1

(D) 5

(E) 9

4. If 3

2

y


y

x

2

3?

(A) 3

1

(B) 3

2

(C) 1

(D) 2

3

(E) 4

9

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

x?

(A) 1

(B) 2

(C) 3

(D) 4

(E) 8

6. If 2(x – 3) = 8, what does 3

3

x

xequal?

62

EQUATIONS

SAT Practice Book

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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 2x – 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) k2 – k

(B) k2 – 3k

(C) k2 – 2k + 1

(D) k2 + 2k + 1

(E) k2 – 1

10. 37

39

2x

x, then x =

(A) 37

(B) 39

(C) 41

(D) 74

(E) 78

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

z, what is the value of n when z =1 ?

(A) 1

(B) 0

(C) 1

(D) 2

(E) 3

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

(A) 20

(B) 10

(C) 5

(D) 10

(E) 20

63

EQUATIONS

SAT Practice Book

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2010

3

2009-2010

3

15. Which of the following represents the

total cost, in dollars, of k compact discs at

$15 each and p compact disc cases at $25

each? (Disregard sales tax.)

(A) 15k 25p

(B) 25k 15p

(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 be

true?

(A) x 4

(B) x 5

(C) t 4

(D) t 5

(E) t 5x

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

x in terms of z ?

(A) z

(B) z + 1

(C) 5 z

(D) 5 z +1

(E) 5 1z

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

(A) z4

3

(B) z

(C) z3

4

(D) 7z

(E) 12z

19. 64

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

20. if thenxxx ,24642 x=?

A) -288

B) -2

C) -2

1

D) 2

1

E) 2

21. if 2

1

1

1

x, What is the value of x?

A) 2

B) 1

C) 0

D) -1

E) -2

22. if 13)5( 2 xxyx 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

yxthen

ba

yx

A) 10

9

B) 23

20

C) 27

20

D) 3

2

E) 5

3

24. If 10 + x is 5 more than 10, what is the

value of 2x?

(A) -5

(B) 5

(C) 10

(D) 25

(E) 50

25. The result when a number is divided by 2

is equal to the result when that same

number is divided by 4. What is that

number?

(A) -4

(B) -2

(C) 0

(D) 2

(E) 4

26. If a positive integer n is picked at

random from the positive integers less than

or 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 (2m)k =6, then mk =?

(A) 3

(B) 4

(C) 5

(D) 6

(E) 12

65

VARIATIONS

SAT Practice Book

2009-2010

1 1

1. Which of the following tables shows a

relationship in which w is directly

proportional to x?

(A)

(B)

(C)

(D)

(E)

2. If 5t = 45 and tk = 1, what is the value

of 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 the

following is equal to k?

(A) 1

(B) x

1

(C) x – 1

(D) x

(E) x + 1

4. If y is directly proportional to x2 and 8

1y

when 2

1x what is the positive value of x

when2

9y ?

(A) 4

3

(B) 2

3

(C) 4

9

(D) 3

(E) 9

66

VARIATIONS

SAT Practice Book

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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 y

when x = 9?

(A) 3

10

(B) 3

40

(C) 23

(D) 27

(E) 30

67

INEQUALITIES & ABSOLUTE VALUE

SAT Practice Book

2009-2010

1 1

1. If rstv = 1 and stuv = 0, which of the


(A) r < 1

(B) s < 1

(C) t > 2

1

(D) u = 0

(E) v = 0

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

greatest?

(A) –2x

(B) –(2x + y)

(C) 2x

(D) 0

(E) –y

3. If 3b + 1 < 10, which of the following

CANNOT 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

xxy1

, which of the following must

be true?

I. y x

II. y is an integer.

III. xy > x2

(A) I only

(B) III only

(C) I and II only

(D) I and III only

(E) I, II, and III

5. At a bottling company, machine A fills

a bottle with spring water and

machine 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, which

of the following describes all possible

values of n ?

(A) 8

112n

(B) 8

112n

(C) 8

112n

(D) 8

112n

(E) 8

112n

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SAT Practice Book

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2010

2

2009-2010

2

6. 22 33 )( xx

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 positive

integers (x, y) is 2x + 3y < 6?

(A) One

(B) Two

(C) Three

(D) Five

(E) Seven




(A) 2x

(B) 4x

(C) 2x + 2

(D) 2x + 4

(E) 4x + 4

9. 85

310

k

k

What is the value of k that satisfies

both equations above?

10. A regulation for riding a certain

amusement park ride requires that a

child be between 30 inches and 50

inches tall. Which of the following

inequalities can be used to determine

whether 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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2009-2010

3

11. If 0 < x < 1, which of the following

statements must be true?

I. x2 > x3

II. x > 2

x

III. x> x3

(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 the

indicated points. Which of the

following 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 following

gives the correct ordering of n , n,

and n2 ?

(A) n < n < n2

(B) n < n2 < n

(C) n < n < n2

(D) n < n2 < n

(E) n2 < n < n

14. If 80 x and 31 y , which of

the following gives the set of all

possible 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


(A) y > 0

(B) y < 22

(C) y = 22

(D) y > 22

(E) x < 30

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2009-2010

4

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 4x = 6u = 5v = 7w > 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 the

following has the greatest value?

(A) 2kx

(B) 4kx2

(C) 6kx3

(D) 8kx4

(E) l0kx5

71


SAT Practice Book

2009-2010

1 1

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 be

true?

(A) 2x < 9

(B) 3x > 9

(C) x < 9

(D) 2x >7

(E) 9x <9

4. If 8

1

7

11

8

1

7

1

6

1

x then x could be

which of the following?

(A) 3

(B) 4

{C) 5

(D) 6

(E) 7

5. If m>0, then m

m

m

mm2

(A) 0

(B) 1

{C) m

(D) 12m

(E) 2m

6. . If y

1

6

1

5

1

7

1

6

1

5

1 then y could be

which of the following?

(A) 6

(B) 7

{C) 8

(D) 9

(E) 10

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SAT Practice Book

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2010

2

2009-2010

2

7. If a+b= 40 and a < 15, which of the


(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

xx

(A) 0

(B) 1

{C) x

(D) 2x

(E) 1x

9. If k is a positive integer divisible by 7, and

if k < 90, what is the greatest possible value

of 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 be

true?

(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 following

must be true?

I. 2p > 5

II. p > 5

III. 3p > 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 equation

above true?

(A) None

(B) One

(C) Two

(D) Four

(E) More than four

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2010

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2009-2010

3

13.

Which of the following inequalities is true

about the lengths a and b of the sides of the

triangle 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 figure

above has coordinates (x,y) such that

7yx ?

(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

74


SAT Practice Book

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2010

4

2009-2010

4

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 the

following inequalities could be used to

determine 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 true

for 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 < 3x <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

75

LINEAR EQUATIONS

SAT Practice Book

2009-2010

1 1

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

kyx

yx

For which of the following values for k will

the system of equations above have no

solution?

(A) −14

(B) −7

(C) 0

(D) 7

(E) 14

3. 174

852

kyx

yx

For which of the following values of k will

the system of equations above have no

solution?

(A) -10

(B) -5

(C) 0

(D) 5

(E) 1 0

4. kwm

wxk

)1(

3

If k and m are defined by the equations

above, what is the value of m when w = 4 and

x = 1?

(A) 0

(B) 3

(C) 12

(D) 24

(E) 36

76

LINEAR EQUATIONS

SAT Practice Book

2009-

2010

2

2009-2010

2

5. If ba

yxthen

ba

yx

1010

99,

3

2

A) 10

9

B) 23

10

C) 27

10

D) 3

2

E) 5

3

6. If 5y + 2x = 23 and x = y + 1, what is the

value of y?

7. If 2x + z = 2y and 2x + 2y + z = 20, what is

the value of y?

(A) 5

(B) 8

(C) 10

(D) 15


information given.

77

QUADRATIC EQUATIONS

SAT Practice Book

2009-2010

1 1

1. If x2+y2 = 73 and xy = 24, what is the

value of (x + y)2 ?

(A) 73

(B) 97

(C) 100

(D) 121

(E) 144

2.

The figure above shows the graphs of

y = x2 and y = a – x2 for some constant

a. 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) = ax2, + bx + c, where a and c are

negative constants. Which of the following

could be the graph of g?

(A)

(B)

(C)

(D)

(E)

78

QUADRATIC EQUATIONS

SAT Practice Book

2009-

2010

2

2009-2010

2

3.

Which of the following could be the equation

of 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 +2x -1

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

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

be a value of x?

(A) −8

(B) −4

(C) 0

(D) 16

(E) 32

6.

The quadratic function graphed above has

equation f(x) = a − x 2 . Which of the following

must be true?

(A) a > 0

(B) a < 0

(C) a is even.

(D) a is odd.

(E) a is the square of an integer.

79

FUNCTIONS

SAT Practice Book

2009-2010

1 1

1. The table above shows some values for the

function f. If f is a linear function, what is the

value of a + b?

(A) 24 (B) 36

(C) 48 (D) 72


information given.

2. The shaded region in the figure

above is bounded by the x–axis, the line

x = 4, and the graph of y = f(x).If the point

(a, b) lies in the shaded region, which of the


I. a 4

II. 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 raise

money. The net amount A, in dollars, raised

by washing k cars is given by the function

A(k) = 4k – 30. If the group washed 15 cars,

what is the net amount they raised?

(A) $10

(B) $15

(C) $20

(D) $25

(E) $30

80

FUNCTIONS

SAT Practice Book

2009-

2010

2

2009-2010

2

5. Let the function h be defined by

h(x) = 14 + 4

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

possible value of m?

6. For which of the following functions is

)f() f( 33 ?

(A) 24xxf )(

(B) 4)(xf

(C) x

xf4

)(

(D) 34 xxf )(

(E) 44xxf )(

7. The figure above shows the graph of the

function h. Which of the following is

closest 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 units

were produced yesterday for a

total 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 2f (p) = 20, what is the value of

f (3p)?

\

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 the

quadratic function f for selected values of x.

Which of the following defines f?

(A) f(x) = x2 + 1

(B) f(x) = x2 + 2

(C) f(x) = 2x2 – 2

(D) f(x) = 2x2 – 1

(E) f(x) = 2x2 + 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 = px3, 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, from

producing and selling x units of a certain

product is given by the function

p(x) = 17x – (10x + b), where b is a constant.

If 300 units were produced and sold

yesterday for a total profit of $1,900, what is

the 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 be

the value of g (k)?

(A) 2

(B) 2.5

(C) 3

(D) 3.5

(E) 5

16. The figures above show the graphs of the

functions f and g. The function f is defined by

f(x) = x3 – 4x. The function g is defined by

g(x) = f(x + h) + k, where h and k are

constants. 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) = x2 + bx + c, where b and c are positive

constants, which of the following could be the

graph of f?

(A)

(B)

(C)

(D)

(E)

18. The table above gives values of the linear

function 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

nnng

2

2

)(

)(

19. g (5) – h(4) =

(A) 0

(B) 8

(C) 10

(D) 18

(E) 32

20. Which of the following is equivalent to

h (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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f(x) = x2 + 18. If m is a positive number such

that f (2m) = 2f (m), what is the value of m?

22. Let the function h be defined by

h (t) = 2(t3 – 3). When h (t) = –60, what is the

value of 2 – 3t?

(A) 35

(B) 11

(C) 7

(D) –7

(E) –11

23. The table above represents a relationship

between x and y. Which of the following

linear 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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f(x) = 2x – 1.

If 2

1f ( 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) is

negative?

(A) –6 < x < 0

(B) 0 < x < 6

(C) 6 < x < 7

(D) –6 < x < 6

(E) –6 < x < 0 and 6 < x < 7


f(x) = x2 + 18. If m is a positive number such

that f (2m) = 2f (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 minute

and 30 cents for each additional minute or

portion thereof. Which of the following

functions describes the cost, in dollars, of a

phone call between these two cities that lasts

for n minutes, if n is a positive integer?

(A) f(n) = 0.80n

(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) = 0.50n + 0.30(n – 1)

5. For all numbers x, the function f is defined

by f(x) =(x+4) (x+2). Which of the following

has 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 its

shutter opens every 31 seconds. If g (h)

represents the number of times the camera’s

shutter opens in h hours, which of the

following 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) is

the 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 linear

function 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

1x

(D) k (x) = x -1

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

9. For all x ≥ -1, let the function f be defined

as f(x) = x+1. Which of the following is equal

to 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 for

the functions f and g. If f and g are linear

functions, 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 weighed 5 pounds when she

bought it. Over the next several years, the

dog’s weight increased by 10 percent per

year. Which of the following functions gives

the weight, w, in pounds, of the dog after n

years 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 terms

of another function g for all values of x,

where k is a constant. If t is a number for

which f (t) = 30 and g (t) = 8, what does k

equal?

13. Which of the following could be the

equation of 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 +2x -1

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


f(x) =2x-1.

If2

1 f (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 it

true that f (-2)= f(2)?

(A) f (x) =

(B) f (x) = 2 - x

(C) f (x)=x+1

(D) f (x)= x2+1

(E) f (x)=2 x 3

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16. The graph of a quadratic function and the

graph of a linear function in the xy -plane

can intersect in at most how many points?

(A) One

(B) Two

(C) Three

(D) Four

(E) More than four

17. Which of the following could be the graph

in the xy -plane of the function f (x) = 2x + 3?

A.

B.

C.

D.

E.

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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) < )(xf ?

(A) −3 (B) −2 (C) −1

(D) 1 (E) 5

2. For all x, the function f is defined by

f (x) = 3x, and the function g is defined by

g(x) = f (x) + 2. What is the value of g (50)?

3.

c (n) = 35 + 12n

To hold a birthday party for n people, the

amount a party planner charges, in dollars,

is given by the function c(n) above. How

much, in dollars, does the planner charge to

hold a birthday party for 12 people?


answer.)

4. 2)(

)( 2

xxt

xxr

The functions r and t are defined above. For

how many values of a is it true that

r (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, is

graphed above. Which of the following gives

all 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)(

xxf ,

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 a

line, which of the following defines f (t)?

(A) f (t)=t-1

(B) f (t)=t+1

(C) f (t)=2t+1

(D) f (t)=2t-1

(E) f(t)=1-2t

9.

Based on the graph of the function f above,

what are the values of x for which f(x) is

positive?

(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) = 5x

for all numbers x. Which of the following is

equivalent to f(p + r)?

(A)5

rp

(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 does

f(x) = 2?

(A) None

(B) One

(C) Two

(D) Three

(E) More than three

12.

The graph of y= f(x) is shown above.

If -3 x 6, for how many values of x does

f(x) = 2?

(A) None

(B) One

(C) Two

(D) Three

(E) More than three

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 the

functions f and g shown above, what are all

values of x between -6 and 6 for which

g (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 a

function f such that f(x) =0 for exactly two

values of x between- 5 and 5?

A.

B.

C.

D.

E.

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1. Let the operations ∆ and □ be defined

for all real numbers a and b as follows.

a ∆ b = a + 3b

a □ b = a + 4b

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

of y?

2. Let the operation be defined by

ba

baba for all numbers a and b,

where a b. If 1 2 = 2 x, what is

the value of x?

(A) 4

(B) 3

(C) 2

(D) l

(E) 0

3. For all the numbers x and y, let the

operation □ be defined by

x □ y =xy – y. If a and b are positive

integers, which of the following can be

equal to zero?

I. a □ b

II. (a + b) □ b

III. 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 = x2 – x

for all values of x. If what

is 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 remainder

when j is divided by k. If 13 ® k = 2, what

is the value of k?

6. Let be defined as

= yy zx 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 all

numbers 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 defined

by y = y2- 1.Which of the following

is 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+ b2 − 2.

If c and d are positive integers, which

of the following CANNOT be the value

of 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 w

1 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 = x2 + 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 = 2x + 5. If line m is the reflection

of line l in the x–axis, what is the

equation of line m ?

(A) y = –2x – 5

(B) y = –2x + 5

(C) y = 2x – 5

(D) y = 2

1x – 5

(E) y = 2

1x + 5

2. In the xy–plane, line l passes through the

origin and is perpendicu1ar to the line

kyx4 where k is a constant. If the two

lines 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) 3

4

3. In the figure above, what is the slope of

line ℓ ?

(A)

(B)

(C)

(D)

(E)

4. In the coordinate plane, the points F

and 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 slope

and a positive y–intercept?

(A)

(B)

(C)

(D)

(E)

6. In the figure above, the scale on the

x–axis is different from the scale on

the 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 circle

has coordinates (3, –7). If one endpoint

of a diameter of the circle is (–2, –7),

what are the coordinates of the other

endpoint 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 and

the 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 the

figure above are equal, which of the following

could 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 figure

above?

(A) y=

(B) y=

(C) y=

(D) y=

(E) y=

11. In the xy -plane, an equation of line ℓ is

y=3x−1. If line m is the reflection of line ℓ in

the 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 segments

has a slope of –1?

(A) OA

(B) OB

(C) OC

(D) OD

(E) DC

14. In the figure above, line l passes

through 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 graph

of the line y = mx + b, where m and b

are constants. Which of the following

best represents the graph of the line

y = –3mx + b?

(A)

(B)

(C)

(D)

(E)

16. The figure above shows the graph of the

line y = ax + b, where a and b are constants.

Which of the following best represents the

graph of the line y = 2ax + b?

(A)

(B)

(C)

(D)

(E)

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17. Rectangle ABCD lies in the

xy–coordinate plane so that its sides

are not parallel to the axes. What is

the product of the slopes of all four

sides of rectangle ABCD?

(A)–2

(B) –1

(C) 0

(D) 1

(E) 2

18. In the xy–plane above, points Q and

S are the centers of the circles, which

are tangent to 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

19. Which of the lettered points in the

figure above has coordinates (x, y) such that

3yx ?

(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, which

of the following could be the lengths 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

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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 the

figure above are equal, which of the following

could be the coordinates of point R ?

(A)

(B)

(C)

(D)

(E)

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1. In the figure above, line ℓ (not shown) is

perpendicular 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 P

are (10 -2a, 0) - and the coordinates of Q are

(10, a). A point in square ORST is to be

chosen at random. If the probability that the

point will be in the shaded triangle is what

is 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 to

the 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 figure

above has coordinates (x,y) such that

y=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 point

on the number line above, which of the

lettered 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 figure

and information.

The grid above represents equally spaced

streets in a town that has no one-way streets.

F marks the corner where a firehouse is

located. Points W, X, Y, and Z represent the

locations of some other buildings. The fire

company defines a building’s m-distance as

the minimum number of blocks that a fire

truck must travel from the firehouse to reach

the building. For example, the building at X

is 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 at

W from the firehouse?

(A) 2

(B) 2

(C) 3

(D) 3

(E) 4

10. What is the total number of different

routes 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 are

an m-distance of 3 from the firehouse must

lie 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 the

x-axis at x = -2 and the y-axis at y = -3. If line

m (not shown) passes through the origin and

is perpendicular to line ℓ, what is the slope of

line m ?

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13. In the xy–coordinate plane, the distance

between point B(10, 18) and point A(x, 3)

is 17. What is one possible value of x?

14. In a rectangular coordinate system, the

center of a circle has coordinates (5, 12),

and the circle touches the x–axis at one

point only. What is the radius of the

circle?

15. In the figure above, PQRS is a rectangle,

and points Q and. R lie on the graph of y

= ax2, where a is a constant. If the

perimeter of PQRS is 10, what is the

value of a?

16. In the figure above, ABCD is a

rectangle. Points A and C lie on the

graph of y = px3, where p is a constant.

If the area of ABCD is 4, what is the

value of p?

17. Point P lies on the line with equation y

– 4 = 3(x – 2). If the x–coordinate of P is

4, what is the y–coordinate of P ?

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18. Line m (not shown) passes through O

and intersects AB between A and B.

What is one possible value of the slope

of line m?

19. In the xy-plane above, the area of ∆OST

is 8. What is the value of a ?

20. In the xy -coordinate plane, the distance

between 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 is

the y -intercept of line ℓ ?

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1. In the figure above, PS and TR intersect

at O and ON is perpendicular to PS . What

is 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. Which

of 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 sum

of the measures of angles 2 and 4 must equal

the sum of the measures of which of the

following 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 meet

at a point to form three angles. What is the

value 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 following

pairs of angle measures is NOT sufficient for

determining 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 possible

value for x?

9. In the figure above, if z = 30, what is the

value 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, what

is 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 = 40

and the dotted lines bisect the angles with

measures 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 the

measure 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 intersect

at C. If x = 80 and CF bisects ECG, what is

the value of y?

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18. In the figure above, l // m. If p (not

shown) is another line in the plane, what is

the least number of points at which p can

intersect these four lines?

(A) None

(B) One

(C) Two

(D) Three

(E) Four

19. In the figure above, OA OC and OB

OD. 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

2 the measure of PQR. If the

measure of PQR is 3

2 the 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 are

parallel. If y = 125, what is the value of x + z?

(A) 90

(B) 95

(C) 100

(D) 105

(E) 110

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22. In the figure above, lines l and m

intersect. If y = 44, what is the value of x?

(A) 127

(B) 128

(C) 130

(D) 132

(E) 134

23. The figure above shows five lines. If

l // m, which of the following is NOT equal to

90?

(A) r

(B) s

(C) t

(D) u

(E) v

24. In the figure above, what is the value of

y?

(A) 40

(B) 45

(C) 50

(D) 60

(E) 72

.

25. In the figure above, if l // m and r = 91,

then t + u =

(A) 178

(B) 179

(C) 180

(D) 181

(E) 182

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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 . In

terms of x, which of the following must

be equivalent to y ?

(A) x2

(B) 52x

(C) 53x

(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 value

of 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, 90x and 1zy .

If z is an integer, what is the greatest

possible value of y ?

(A) 30

(B) 45

(C) 60

(D) 61

(E) 89

6. If the length of AB is 5 and the length

of BC is 6, which of the following could

be 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 area

of 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 the

midpoint 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 measure

of angle A is 80 . If another angle of

the triangle measures x , where

80x , 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 is

to be chosen at random. If the

probability that the point will be in the

shaded triangle is5

1, 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) k60

(B) k

(C) k60

(D) k120

(E) k2120

15. If the length of LM is 7 and the length

of MN is 8, which of the following

could be the length of LN ?

(A) 23

(B) 22

(C) 17

(D) 16

(E) 14

16. A circle (not drawn) passes through

point A in the figure above. What

could be the total number of points of

intersection of this circle and ΔABC ?

I. 1

II. 3

III. 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 area

of triangle WYZ ?

(A) 6

(B) 12

(C) 18

(D) 24

(E) 30

18. In the figure above, ΔABC is similar to

ΔDEF. What is the length of side EF ?

19. In the figure above, ABDE is a square,

ΔBCD is a right triangle, and

AB = BC. If a point is chosen at

random from polygon ACDE, what is

the probability that the chosen point is

in 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 and

b = c + 1. If c is an integer, what is the

least possible value of b ?

(A) 30

(B) 39

(C) 50

(D) 61

(E) 71

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1. Which of the following inequalities is

true about the lengths a and b of the

sides of the triangle above?

(A) 20)(0 2ba

(B) 40)(20 2ba

(C) 100)(40 2ba

(D) 400)(100 2ba

(E) 2)(400 ba

2. Triangles ABC and ACD in the figure

above are equilateral. What is the

ratio of BD to AC ?

(A) 2 to 1

(B) 3 to 1

(C) 2 to 2

(D) 3 to 2

(E) 3 to 2

3. A triangle has a perimeter of 13 and

one side of length 3. If the lengths of

the other two sides are equal, what is

the length of each of them?

(A) 4

(B) 5

(C) 6

(D) 7

(E) 8

4. The three angles of a triangle have

measures of x , x2 , and y° , where

x > 55. If x and y are integers, what is

one possible value of y ?

5. In ΔABC above, AC=5, PC=3, and BP

= 34 .What is the length of AB ?

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6. In the figure above, triangles ABC and

CDE 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 the

following is greatest?

(A) a

(B) b

(C) c

(D) d

(E) e

8. In PQR above, PR = QR. Which of


(A) u = x

(B) x = v

(C) x = z

(D) y = x

(E) y = z

9. In the figure above, 6AC and 3BC .

Point P (not shown) lies on AB

between A and B such that ABCP .

Which of the following could be the

length of CP ?

(A) 2

(B) 4

(C) 5

(D) 7

(E) 8

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10. What is the greatest possible area of a

triangle with one side of length 7 and

another side of length 10 ?

(A) 17

(B) 34

(C) 35

(D) 70

(E) 140

11. In the figure above, AB ,CD , and EF

intersect at P. If r= 90, s=50, t= 60,

u= 45, and w= 50,

what is the value of x ?

(A) 45

(B) 50

(C) 65

(D) 75


information given.

12. In ABC above, ACAB , E is the

midpoint of AB , and D is the midpoint

of AC . If xAE and 4ED , what is

length BC ?

(A) 6

(B) 8

(C) 2x

(D) 4x

(E) 24x

13. If x = 20 and y = 30 in the figure above,

what is the value of z ?

(A) 60

(B) 70

(C) 80

(D) 90

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(E) 100

14. In the right triangle above, if x = 3,

what is the value of y?



(C) 4


(E) 5

15.

Each angle of ∆ABC above has the

same measure as angle in ∆XYZ (not

shown). If the length of one side of

∆XYZ is 24, what is one possible

perimeter of ∆XYZ?

16.

In the figure above, ∆PQR is

equilateral and SR and TV intersect

at 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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18.

In the figure above, what is the value

of c in terms of a and b?

(A) a + 3b – 180

(B) 2a + 2b – 180

(C) 180 – a – b

(D) 360 – a – b

(E) 360 – 2a – 3b

19.

.

In ∆PQR above,3

1

QV

QS and

4

3

PR

PT .

What is the value of the fraction

PQR

PST

area

area?

20. The lengths of the sides of a right

triangle are consecutive even integers,

and the length of the shortest side is x.

Which of the following equations could

be used to find x?

(A) x + x + 1 = x + 2

(B) x2 + (x + 1)2 = (x + 2)2

(C) x2 + (x + 2)2 = (x + 4)2

(D) x + x + 2 = x + 4

(E) x2 = (x + 2)(x + 4)

21.

If y = 60 in ∆DEF above, how much

greater is the perimeter of ∆ABC than

the perimeter of ∆DEF?

(A) 0

(B) 3

(C) 6

(D) 8

(E) 9

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1.

In the figure above, JLKN and

JLLM . If the lengths of LN and

LM are equal, what is the value of x?

2.


of 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 with

arrows?

(A) n

(B) 2n

(C) 180 – n

(D) 360 – n

(E) 360 – 2n

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5.

In ∆XYZ above, XZ is 7

6of h, the

length of the altitude. What is the area

of ∆XYZ in terms of h?

(A) 3

2h

(B) 7

3 2h

(C) 7

3h

(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. What

is the perimeter of ∆PQR?

(A) 12

(B) 14

(C) 6 + 20 (approximately 10.47)

(D) 6 + 32 (approximately 11.66)


7.


of z?

(A) 55

(B) 60

(C) 65

(D) 70

(E) 75

8.

If AB = BC and BD bisects AC in the

figure above, which of the following

CANNOT be concluded?

(A) w = x

(B) w = z

(C) x = y

(D) AD = DC

(E) ACBD

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9.

In the figure above, if z = 30, what is

the value of x + y?

(A) 60

(B) 150

(C) 180

(D) 210

(E) 330

10.

In the figure above, AE and CDare

each perpendicular to CE . If x = y, the

length of AB is 4, and the length of

BD is 8, what is the length ofCE ?






11.

For the triangles above, the perimeter

of ∆ABC equals the perimeter of

∆DEF. If ∆ABC is equilateral, what is

the length of AB ?

(A) 4

(B) 5

(C) 7

(D) 9

(E) 15

12.

In the triangles above, what is the

average (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 line

m. If PB = 4,PR = 6, and AQ = 4, what

is 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 the

value 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 triangle

have equal perimeters. If the square

has sides of length 3, what is the

length 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 the

length 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 + x2?

(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 the

lengths 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 how

many degrees does the measure of the

largest angle exceed the measure of

the smallest angle?

(A) 20°

(B) 30°

(C) 40°

(D) 50°

(E) 60°

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1. In the figure above, a small square is

inside a larger square. What is the area, in

terms of x, of the shaded region?

(A) 2x – 10

(B) 10 – 2x

(C) 25 – 2x

(D) x2 – 25

(E) 25 – x2

2. In the figure above, rectangle ABCD is

made up of seven non-overlapping

rectangles. The two smallest rectangles have

the same area. Each of the other rectangles

has twice the area of the next smaller

rectangle. The area of the shaded rectangle is

what fraction of the area of rectangle ABCD?

(A) 128

1

(B) 64

1

(C) 32

1

(D) 16

1

(E) 7

1

3. In the figure above, the circle is tangent to

sides 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 rectangle

with BC = 4 and AB = 6. Points P, Q, and R

are different points on a line (not shown) that

is parallel to AD . Points P and Q are

symmetric about line AB and points Q and R

are symmetric about line CD . What is the

length 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 to

completely cover a rectangular region 12L

units long and 19L units wide. How many

rectangles 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 quarter

circle is 1, what is the area of the shaded

region?

(A) 4

1

(B) 2

2

(C) 4

2

(D) 4

(E) 3

2

8. If the areas of two regions are equal and

the sum of the areas of the regions is 5, what

is the average (arithmetic mean) of the areas

of 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 square

centimeters, 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 one

quarter of a circle with center R and radius

6. If the length plus the width of rectangle

ABCR is 8, then the perimeter of the shaded

region is

(A) 8 + 3

(B) 10 + 3

(C) 14 + 3

(D) 1 + 6

(E) 12 + 6

11. In the figure above, ABCDEF is a regular

hexagon, and its center is point O. What is

the value of x?

(A) 80

(B) 60

(C) 40

(D) 30

(E) 20

12. If the five line segments in the figure

above are all congruent, what is the ratio of

the length of AC (not shown) to the length of

BD ?

(A) 2 to 1

(B) 3 to1

(C) 2 to 2

(D) 3 to 2

(E) 3 to 2

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13. The figures above represent three pieces

of cardboard. All angles of the cardboard

pieces are right angles, all short sides have

length 1, and all long sides have length 2.

Which of the following figures could be made

from only the three pieces of cardboard

without over– lapping or cutting them?

(A) None (B) I only (C) II only

(D) III only (E) I and II



rectangular 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 the

midpoint 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) 3

8

=

16. In the figure above, EF divides square

ABCD into two rectangles, and CD bisects

EF. 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 is

72, what is the value of x?

(A) 9

(B) 15ππ

(C) 18

(D) 21

(E) 36

18. In the figure above, a square with sides of

length 6 units is divided into 9 squares. What

is the area of the circle (not shown) that

passes through the points A, B, C, and D,

which are the centers of the four corner

squares?

(A) 6π square units

(B) 8π square units

(C) 9π square units

(D) 10π square units

(E) 18π 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 quadrilateral

P have the same measure, which of the

following 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 is

inside a larger square. What is the area, in

terms of x, of the shaded region?

(A) 2x – 10

(B) 10 – 2x

(C) 25 – 2x

(D) x2 – 25

(E) 25 – x2

2. In the figure above, rectangle ABCD is

made up of seven non-overlapping

rectangles. The two smallest rectangles have

the same area. Each of the other rectangles

has twice the area of the next smaller

rectangle. The area of the shaded rectangle is

what fraction of the area of rectangle ABCD?

(A) 128

1

(B) 64

1

(C) 32

1

(D) 16

1

(E) 7

1




(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 rectangle

with BC = 4 and AB = 6. Points P, Q, and R

are different points on a line (not shown) that

is parallel to AD . Points P and Q are

symmetric about line AB and points Q and R

are symmetric about line CD . What is the

length 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 to

completely cover a rectangular region 12L

units long and 19L units wide. How many

rectangles 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 quarter

circle is 1, what is the area of the shaded

region?

(A) 4

1

(B) 2

2

(C) 4

2

(D) 4

(E) 3

2

8. If the areas of two regions are equal and

the sum of the areas of the regions is 5, what

is the average (arithmetic mean) of the areas

of 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 square

centimeters, 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





region is

(A) 8 + 3

(B) 10 + 3

(C) 14 + 3

(D) 1 + 6

(E) 12 + 6

11. In the figure above, ABCDEF is a regular

hexagon, and its center is point O. What is

the value of x?

(A) 80

(B) 60

(C) 40

(D) 30

(E) 20

12. If the five line segments in the figure

above are all congruent, what is the ratio of

the length of AC (not shown) to the length of

BD ?

(A) 2 to 1

(B) 3 to1

(C) 2 to 2

(D) 3 to 2

(E) 3 to 2

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13. The figures above represent three pieces

of cardboard. All angles of the cardboard

pieces are right angles, all short sides have

length 1, and all long sides have length 2.

Which of the following figures could be made

from only the three pieces of cardboard

without over– lapping or cutting them?

(A) None (B) I only (C) II only

(D) III only (E) I and II



rectangular 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 the

midpoint 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) 3

8

=

16. In the figure above, EF divides square

ABCD into two rectangles, and CD bisects

EF. 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 is

72, what is the value of x?

(A) 9

(B) 15ππ

(C) 18

(D) 21

(E) 36

18. In the figure above, a square with sides of

length 6 units is divided into 9 squares. What

is the area of the circle (not shown) that

passes through the points A, B, C, and D,

which are the centers of the four corner

squares?

(A) 6π square units

(B) 8π square units

(C) 9π square units

(D) 10π square units

(E) 18π 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 quadrilateral

P have the same measure, which of the

following 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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Questions 1-2 refer to the following

figures and information.

The figure on the left is called an ell. The

lengths of some of its sides are given, and all

the angles are right angles. For any positive

integer n, an n-ell is the figure formed by

positioning n ells adjacent to each other as

shown in the 3-ell on the right.

1. What is the perimeter of the 3-ell?

(A) 18

(B) 21

(C) 24

(D) 27

(E) 30

2. The perimeter of an 80-ell is 326 and the

perimeter of a 20-ell is 86. What is the

perimeter of a 100-ell?

(A) 406

(B) 409

(C) 412

(D) 416

(E) 430

3. 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)

(B) 5

(C) 7

(D)

(E) 15

4. The smallest squares in Figure A and

Figure B are all equal in size. If the area of

Figure A is 33 square centimeters, what is

the area, in square centimeters, of Figure B?

(A) 15

(B) 18

(C) 21

(D) 24

(E) 28

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5. In the figure above, ABDE is a square,

ΔBCD is a right triangle, and AB=BC. If a

point 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 3

feet more than its width. If the length of the

garden is 9 feet, what is the area of the

garden 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 nonoverlapping

triangles. Which of the following is true

about 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 figure

above are equilateral. What is the ratio of BD

to 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 feet

more than its width. If the length of the rug

is 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 7π, what is the total

area, to the nearest number, of the unshaded

regions of rectangle ABCD?

(A) 4

(B) 6

(C) 8

(D) 9

(E) 10

11. What is the perimeter of the trapezoid

above?

(A) 52

(B) 72

(C) 75

(D) 80

(E) 87

12. In the figure above, CDE is an equilateral

triangle 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 the

plot, in square meters?

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14. In the figure above, the lengths and

widths of rectangles A, B, C, and D are whole

numbers. The areas of rectangles A, B, and C

are 35, 45, and 36, respectively. What is the

area 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 rectangle

and URST is a square. PU = 5 and UT is a

positive integer. If the area of PQST must be

more than 10 but less than 30, what is one

possible value of UT.

17. In the figure above, EBCD is a square

and 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 lie

on the same line. What is the value of x?

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1. The circle above has center O and

diameter AB. The two semicircles have

diameters OA and OB. If the

circumference of the circle is 36 , what is

the length of the curved path from A to B

through O?

(A) 6

(B) 9

(C) 18

(D) 24

(E) 36




(A) 16

(B) 20

(C) 36

(D) 64

(E) 96

3. Senai customized his bicycle by

exchanging the front wheel for a wheel

that had one half the diameter of the back

wheel. Now when Senai rides the bicycle,

how many revolutions does the front wheel

make for each revolution of the back

wheel?

(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 diameter

of 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 and

RT are quarter circles with centers at

P and S, respectively. If the radius of

each quarter circle is 1, what is the

area 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 the

center 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 circle

whose circumference is 45. If arcs of

length 2 and length b continue to

alternate around the entire circle so that

there are 18 arcs of each length, what is

the degree measure of each of the arcs of

length b?

(A) 4°

(B) 6°

(C) 10°

(D) 16°

(E) 20°





region is

(A) 8 + 3π

(B) 10 + 3π

(C) 14 + 3π

(D) 1 + 6π

(E) 12 + 6π

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9. In the xy–plane above, points Q and S are

the centers of the circles, which are tangent

to 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 are

tangent at point B and AC = 6. If the

circumference of the circle with center A is

twice 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 the

circle with center R is twice the radius of the

circle with center P. What is the radius of the

circle 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 12

inches, 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 a

circle to the circumference of the circle?

(A) 1:2π

(B) 1:π

(C) 1:πr

(D) π:1

(E) 2π:1

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1. What is the radius of a circle whose

circumference is π?

(A)

(B) 1

(C) 2

(D) π

(E) 2π

2. If three different circles are drawn on a

piece of paper, at most how many points can

be common to all three?

(A) None

(B) One

(C) Two

(D) Three

(E) Six

3. The circle above has an area of 25π and is

divided into 8 congruent regions. What is the

perimeter of one of these regions?

(A) 10 - 25π

(B) 10 +

C) 10+

(D) 10+5π

(E) 10+25π

4. In the figure above, O is the center of the

circle and segment AC is tangent to the circle

at point B. If the measure of ∠ABO is x°,

how many possible values

are 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 dashed

line indicating the path of the cut. Which of

the following could be the

other piece of the circle?

(A)

(B)

(C)

(D)

(E)

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6. The circle above has an area of 49π and is

divided into 6 congruent regions. What is the

perimeter of one of these regions?

(A) 14 − 49π

(B) 14+ π

(C) 14+ π

(D) 14 + 7π

(E) 14 + 49π

7. The circumference of the circle with center

O shown above is 2π. What is the area of the

shaded region?

(A)

(B)

(C) 1

(D)

(E)

8. What is the ratio of the diameter d of a

circle to half the circumference of the circle?

(A) 1 : 2π

(B) 1 :π

(C) 2 :π

(D) π : 1

(E) 2π:1

9. Six points are placed on a circle. What is

the greatest number of different lines that

can be drawn so that each line passes

through two of these points?

(A) 12

(B) 15

(C) 25

(D) 30

(E) 36

10. In the figure above, the smaller circles

each have radius 3. They are tangent to the

larger circle at points A and C, and are

tangent to each other at

point B, which is the center of the larger

circle. What is the perimeter of the shaded

region?

(A) 6π

(B) 8π

(C) 9π

(D) 12π

(E) 15

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11. In the figure above, triangle ABC is

inscribed in the circle with center O and

diameter AC. If AB AO, what is the degree

measure 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 the

pizza and the angle at the tip is always

greater than 20°, but less than 30°. What is

one possible value for the number of pieces

into which the pizza is cut?

13. If a circle has circumference 7π, what is

the radius of the circle?

Note: Figure not drawn to scale.

14. The figure above consists of two circles

that have the same center. If the shaded area

is 64 square inches and the smaller circle

has a radius of 6 inches, what is the radius,

in inches, of the larger circle?

15. Naomi makes silver jewelry. For one

style of earrings, she cuts wedges from a

silver disk, as shown in the figure above.

Each wedge makes a 40° angle at the center

of the disk. If the weight of each uncut disk is

a uniformly distributed 2.5 grams, how many

grams does each wedge weigh?

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1. Which of the following has the same

volume as the cylinder shown above with

radius x and height 2x?

(A) A cylinder with radius 2x and height x

(B) A cylinder with radius 2 x and height x

(C) A cube with edge 2x

(D) A cube with edge 2 x

(E) A rectangular solid with dimensions x, 2x,

x

2. Ahmad has containers of two different

sizes. 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 the

capacity, in gallons, of each of the larger

containers?

(A) 4x

(B) 2x

(C) 2

x

(D) 8

x

(E) 16

3. If the rectangular box with no lid shown

above is cut along the vertical edges and

flattened, which of the following figures

best represents the result?

(A)

(B)

(C)

(D)

(E)

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4. How many cubical blocks, each with edges

of length 4 centimeters, are needed to fill a

rectangular box that has inside dimensions

20 centimeters by 24 centimeters by 32

centimeters?

(A) 38

(B) 96

(C) 192

(D) 240

(E) 384

5. The three–dimensional figure above has

two parallel bases and 18 edges. Line

segments are to be drawn connecting vertex

V with each of the other 11 vertices in the

figure. 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 length

2, and A and B are midpoints of two of the

edges. What is the length of AB (not shown)?

(A) 2

(B) 3

(C) 5

(D) 6

(E) 10

7. The three–dimensional figure represented

above consists of rectangular and triangular

faces. Each rectangular face has area r and

each triangular face has area t. What is the

total surface area of the figure, in terms of r

and t?

(A) 2r + t

(B) 3r + 2t

(C) 4r + 3t

(D) 6rt

(E) r3t2

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8. In the cube shown above, points B, C, and

E are midpoints of three of the edges. Which

of the following angles has the least

measure?

(A) <XAY

(B) <XBY

(C) <XCY

(D) <XDY

(E) <XEY

9. The pyramid above has a square base and

four congruent triangular faces. The height

of 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 the

shortest distance from the center of the cube

to the base of the cube?

(A) 1

(B) 2

(C) 4

(D) 2

(E) 22

11. In a windowless, cube-shaped storage

room, the ceiling and 4 walls, including a

door, are completely painted. The floor is not

painted. If the painted area is equal to 80

square meters, what is the volume of the

room, 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 a

cylinder that is 8 inches high and has a base

of radius 3 inches. Of 5 pencils with lengths 6

inches, inches, 9 inches, inches, and

12 inches, how many CANNOT fit entirely

inside the can?

(A) One

(B) Two

(C) Three

(D) Four

(E) Five

13. Of the labeled points on the cube shown

above, which is farthest from point P ?

(A) A

(B) B

(C) C

(D) D

(E) E

14. Which of the rectangular solids shown

above has a volume closest to the volume of a

right circular cylinder with radius 2 and

height 4 ?

(A) A

(B) B

(C) C

(D) D

(E) E

15. The height of a right circular cylinder is 5

and the diameter of its base is 4. What is the

distance from the center of one base to a

point on the circumference of the other base?

(A) 3

(B) 5




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16. Two spheres, one with radius 7 and one

with radius 4, are tangent to each other. If P

is any point on one sphere and Q is any point

on the other sphere, what is the maximum

possible length of PQ ?

(A) 7

(B) 11

(C) 14

(D) 18

(E) 22

17. The interior dimensions of a rectangular

fish tank are 4 feet long, 3 feet wide, and 2

feet high. The water level in the tank is 1

foot high. All of the water in this tank is

poured into an empty second tank. If the

interior dimensions of the second tank are 3

feet long, 2 feet wide, and 4 feet high, what is

the 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 the

figure above. If the circumference of the large

circle is 36 and the radius of the small circle

is half of the radius of the large circle, what

is 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 1

foot high and has a square base. How many

cubic 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 angles

formed by the edges of a cube?

(A) 36

(B) 24

(C) 20

(D) 16

(E) 12

21. A large solid cube is assembled by gluing

together identical unpainted small cubic

blocks. All six faces of the large cube are then

painted red. If exactly 27 of the small cubic

blocks that make up the large cube have no

red paint on them, how many small cubic

blocks make up the large cube?

22. The sphere above has radius 6 inches.

What is the volume, in cubic inches, of the

smallest cube that can contain the entire

sphere?

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Questions 1-2 refer to the following graph:

1. Which of the following regions in Africa

had an elephant population in 1989 that was

approximately of its elephant population in

1979 ?

I. Central

II. 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 elephant

population in

the four regions of Africa decreased by

approximately

what percent?

(A) 10% (B) 30% (C) 50%

(D) 70% (E) 90%

3.

The pictograph above shows the results of a

survey in which 150 people were asked to

indicate which of four hot beverages they

drink. How many more responses did Coffee

receive than Hot cider?

(A) 15 (B) 30 (C) 40

(D) 45 (E) 60

4.

In a survey, 3,400 people responded to the

following question: “How many weeks of

vacation did you take last year?” Their

responses to the question are summarized in

the chart above, where n equals the number

of vacation weeks indicated. How many

respondents took more than 2 weeks of

vacation last year?

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5.

The depth of a lake is the difference between

the altitude at the surface and at the lowest

point of the lake. If the five lakes in the

graph above were listed in order from the

greatest depth to the least depth, which lake

would be third in the list?

(A) Erie (B) Huron (C) Michigan

(D) Ontario (E) Superior

6.

The graph above shows various temperatures

from 10 A.M. to 6 P.M. of a given day. Which

of the following situations best fits the

nformation on the graph?

(A) It rained a little, and then the Sun came

out and warmed things up.

(B) The mild temperature was lowered by a

heavy rain in the morning, and the

temperature dropped lower by evening.

(C) It was more windy in the morning than it

was in the evening, and the temperature was

mild throughout.

(D) The morning was cold, but the Sun later

came out and raised the temperature.

(E) The temperature decreased at a constant

rate from 10 A.M. to 6 P.M.

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7.

Some common nail sizes and their

corresponding lengths are shown in the table

above. If nail sizes from 2d up to 10d increase

by a constant length for each increase of 1d

in 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 monthly

profits between which two consecutive

months?

(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 best

represents the information in the table

above?

10.

The Lyndhurst High School twelfth graders

are represented in the circle graph in Figure

1. Figure 2 is another way to illustrate the

use of computers by these twelfth graders. If

the same 200 twelfth graders are represented

in both figures, what is the total number of

twelfth graders represented by the shaded

circle in Figure 2 ?

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11.

According to the graph above, for which

month 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 to

Farley, passing through Belville, Clinton,

Dryden, and Edgewood on the way. The

graph above shows where she was along the

route during the 6 hours of the trip.

According to the graph, approximately how

long, in hours, did it take Kia to drive from

Dryden 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 in

the scatterplot above, and the line of best fit

for the data is shown. Of the following, which

is 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 locations

around the world. The graph above shows

where its cars were made in 2003. If the

company made 5,000,000 cars in 2003, how

many 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 for

Company A and Company B for the second

half of 2004. What was the largest one-month

decrease in sales for Company B during this

period 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 best

represents the information in the table

above?

17.

The table above shows the number of items

100 customers purchased from a hardware

store over a 4 -hour period. Which of the

following can be determined from the

information in the table?

I. The average (arithmetic mean) number of

items purchased per customer

II. The median number of items purchased

per customer

III. The mode of the number of items

purchased 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 expense

sheet for Carmen’s business trip. If her hotel

expenses were the same each day, what were

her total expenses for Friday, in dollars?


answer.)

19.

Table 1 above shows the number of juniors

and seniors taking Physics and Statistics at

Midland High School. The partially

completed Table 2 above gives the enrollment

for these classes in periods 1 and 2, which

are the only periods Physics and Statistics

are taught. If only juniors and seniors take

these classes, what is the total number of

students who take Physics or Statistics in

period 2?

20.

Graphed above is the amount that a

computer shop charges for a repair job as a

function of the number of hours required to

do the job. Which of the following is most

consistent with the information in the graph?

(A) The shop charges the same amount for

any job of any length.

(B) The shop charges at an hourly rate for

work with no fixed initial amount.

(C) The shop charges a fixed initial amount

plus an hourly rate for work, starting at

the beginning of the first hour.

(D) The shop charges a fixed amount for the

first 2 hours or less of work. The shop

charges at an hourly rate for work beyond

2 hours.

(E) The shop charges at an hourly rate for

work beginning at the start of the first

hour. This rate decreases after 2 hours of

work.

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1.

An amusement park awards tickets that can

be exchanged for prizes to reward high scores

at an arcade game. Some scores and the

corresponding number of prize tickets

awarded are shown in the table above. For

scores from 100 up to 200, the number of

tickets awarded increases by a constant

amount for each

10 -point score increase. How many tickets

would 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 above

gives the prices of these tables and chairs in

three different years. The chart on the right

gives the maximum number of tables and

chairs that can be stocked in each of three

warehouses, X, Y, and Z. Based on the prices

shown, what was the maximum possible

value of the table and chair inventory in

warehouse 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 are

represented in Figure 1 above. Figure 2

above is another way to show which pets

these students have. If the same 500

students are represented in both figures,

what is the total number of students

represented by the shaded circle in Figure 2 ?

4.

The scatterplot above shows, for each of 10

students, the amount of time the student

spent on homework plotted against the

amount of time the student spent on after-

school activities last week. According to the

scatterplot, which of the following statements

is true?

(A) Each of the students spent the same

amount of time on homework as on after-

school activities.

(B) Each of the students spent more time on

homework than on after-school activities.

(C) Each of the students spent less time on

homework than on after-school activities.

(D) Exactly 3 students spent 4 hours on

homework.

(E) Exactly 4 students spent 3 hours on after-

school activities.

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5.

According to the graph above, if there are

6,000 registered voters aged 60 and over in

Washington County, how many registered

voters 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 sold

during the 3rd week of its publication?

7.

The graph above shows the monthly sales for

Company A and Company B for the second

half of 2004. What was the largest one-month

decrease in sales for Company B during this

period 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 hours

worked last week by 12 students of various

ages at after-school jobs. Which of the

following 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 riding

slowly uphill for 1 mile. He rested for 10

minutes and then rode quickly downhill for

the rest of the trip. Which of the following

graphs could correctly represent his trip?

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10.

In a certain game, each person threw a

beanbag at a target until the person missed

the target. The table shows the results for

the 25 people who played the game. For

example, 4 people hit the target on their first

3 throws and missed on their 4th throw.

Based on the information in the table, which

of the following must be true?

I. More than half the people hit the target on

their first throw.

II. For all of the throws attempted, more hit

the 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 1

hours long, each break is to be hour long,

and lunch is to be 1 hour long. If session IV is

to end at 4:30 P.M., at what 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

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12.

The bar graph above shows the number of

tons of beans produced on a large farm for

the years 1985 through 1991. For which of

the following two-year periods was the

average (arithmetic mean) bean production

closest to the bean production in 1985 ?

(A) 1986-1987

(B) 1987-1988

(C) 1988-1989

(D) 1989-1990

(E) 1990-1991

13.

The graph above shows the amount of water

remaining in a tank each time a pail was

used to remove x gallons of water. If 5 gallons

were in the tank originally and 2 gallons

remained after the last pail containing x

gallons was removed, what is the value of x?

14. A store discounts merchandise by 10

percent of the original price at the end of

each week and stops when the merchandise

is priced at 50 percent of the original price.

Which of the following graphs could correctly

represent the price of an article of

merchandise over an eight-week period?

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15.

The table above shows the number of

employees at Company X classified according

to work shift and salary. If a second-shift

employee will be picked at random, what is

the probability that the employee’s salary is

over $30,000?

(A) (B) (C)

(D) (E)

16.

The circle graph above shows how David’s

monthly expenses are divided. If David

spends $450 per month for food, how much

does 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. The

second table shows the average (arithmetic

mean) number of video rentals per premium

member at store B during each of those

years. Based on this information, which of

the following best approximates the total

number of video rentals by premium

members 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 Jackson

family 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 were

born 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 in

inches 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 noon

temperatures for seven cities designated A

through G. If the median noon temperature

of these cities is 40°F, then the noon

temperature for City D could be any of the

following EXCEPT

(A) 29°F

(B) 35°F

(C) 39°F

(D) 40°F

(E) 42°F

2.

The table above, describing the Preston City

workforce, is partially filled in. Based on the

information in the table, how many women

in 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 that

chime as indicated by the check marks in the

table 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 closest

approximation of the cost per donut when

one 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 money

needed 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 is

committed on the Internet. Which of the

following circle graphs most accurately

displays the same data?

(A) (B)

(C) (D)

(E)

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7.

According to the graph above, between which

two 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 did

Ellen’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 timing

12 hamsters in a maze. Each hamster

received at least one practice before being

timed. The scatter-plot above shows the time

each hamster took to complete the maze and

the corresponding number of practices that

each hamster received. Based on the data,

which of the following functions best models

the relationship between t, the number of

seconds to complete the maze, and p, the

number 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 in

scores 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 registration

data for the town of Bridgeton at the time of

a recent election. In the election, 40 percent

of the voting–age population actually voted.

If the turnout for an election is defined

to be the fraction

votersregistered ofnumber

otedactually v number who

What was the turnout for this election?

13.

The table above shows how many students in

a class of 12 preschoolers had 0, 1, 2, or 3

siblings. Later, a new student joined the

class, and the average (arithmetic mean)

number of siblings per student became equal

to the median number of siblings per

student. How many siblings did the new

student have?

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

(D) 3 (E) 4

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14.

According to the graph above, which

salesperson had the greatest increase in the

number 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 the

number of students in that category. Which

of 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 the

following is closest to the decrease per year

in the number of homes sold between 1987

and 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 sold

900 pairs of jeans other than brands J, K, L,

M, and N, how many pairs of jeans did it sell

altogether?

(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 at

Thompson High School are given in the grid

above. It shows the distance, to the nearest

mile, that students at various grade levels

travel to school. According to this grid, which

of the following is true?

(A) There is only one student who travels 2

miles to school.

(B) Half of the students travel less than 4

miles to school.

(C) More 12th graders than 11th graders

travel 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 more

miles to school, half are 9th graders.

19.

According to the table above, car engine oil

with a rating of 5W flows how many times as

fast 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 16

students are shown in the table above. Sam,

who was the only student absent on Tuesday,

will take the test next week. If Sam receives

a score of 95 on the test, what will be the

median score for the test?

(A) 90 (B) 87.5 (C) 85

(D) 82.5 (E) 80

21.

Outdoor Sneaker Company manufactures

only white sneakers and black sneakers, both

of which are available as either high–tops or

low–tops. On the basis of the information in

the table above, how many black sneakers

did Outdoor Sneaker Company manufacture

in July?

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22. Josephine’s daily exercise routine

consists of swimming, cycling, and running,

in that order. She runs faster than she swims

and cycles faster than she runs. If she does

not rest between the activities, which of the

following could be the graph of the distance

she covers during the entire time of her

exercise routine?

(A) (B)

(C) (D)

(E)

23.

The chart above shows the results when

1,000 people were asked, “How old are you?”

The age they gave is represented by x. How

many 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 at

Weston High School from 1992 through 1996.

If the median enrollment for the five years

was 1351, and no two years had the same

enrollment, what is the greatest possible

value for x?

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1. How many positive four-digit integers

have 1 as their first digit and 2 or 5 as their

last 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 marble

2.

A jar contained 10 marbles—some red, some

white, and some blue. The information above

is about 5 marbles that were drawn from the

jar. If x is the total number of blue marbles

drawn, which of the following statements

must 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 letters

above such that the first letter is D and one

of the remaining letters is A. If no letter is

used more than once in an arrangement in

the list and one three-letter arrangement is

randomly selected from the list, what is the

probability that the

arrangement selected will be DCA ?

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

4. If a number is chosen at random from the

set

{-12,-6, 0, 6, 12}, what is the probability that

it is a member of the solution set of both

2x – 3 < 7 and x + 5 > -6 ?

(A) 0 (B) (C) (D) (E)

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5. A box contains 2,900 solid-colored marbles

that are either orange, blue, or green. If 29

percent of the marbles are orange and 29

percent of the marbles are blue, what percent

are green?

(A) 29%

(B) 42%

(C) 52%

(D) 58%

(E) 71%

6.

A snack machine has buttons arranged as

shown above.

If a selection is made by choosing a letter

followed by a one-digit number, what is the

greatest number of different selections that

could be made?

7.

The figure above shows, on the left, the call

buttons for the 12 floors of an apartment

building, and on the right, the 9 buttons

labeled A through I for the 9 apartments on

each floor of the building. How many

different apartments can be called by

pressing one button on the left and one

button on the right?

8. The digits of the positive three-digit

integer n are 7, 8 and 9. How many possible

values are there for n?

(A) Three (B) Four (C) Six

D) Eight (E) Nine

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9.

On the disk shown above, a player spins the

arrow twice. The fraction is formed, where

a is the b number of the sector where the

arrow stops after the first spin and b is the

number of the sector where the arrow stops

after the second spin. On every spin, each of

the numbered sectors has an equal

probability of being the sector on which the

arrow stops. What is the probability that the

fraction is greater than 1?

(A) (B) (C)

(D) (E)

10. A special lottery is to be held to select the

student who will live in the only deluxe room

in a dormitory. There are 100 seniors, 150

juniors, and 200 sophomores who applied.

Each senior’s name is placed in the lottery 3

times; each junior’s name, 2 times; and each

sophomore’s name, 1 time. If a student's

name is chosen at random from the names in

the lottery, what is the probability that a

senior's name will be chosen?

(A) (B) (C)

(D) (E)

11.

There are five houses on each side of a

street, as shown in the figure above. No two

houses next to each other on the same side of

the street and no two houses directly across

from each other on opposite sides of the

street can be painted the same color. If the

houses labeled G are painted gray, how many

of the seven remaining houses cannot be

painted gray?

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

(D) Five (E) Six

12.

In the figure above, a path from point A to

point D is determined by moving upward or

to the right along the grid lines. How many

different paths can be drawn from A to D

that do not include either B or C?

(A) Two (B) Four (C) Six

(D) Eight (E) Sixteen

13.

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2009-2010

4

2009-2010

4

The figure above shows the top view of an

open square box that is divided into 6

compartments with walls of equal height.

Each of the rectangles D, E, and F has twice

the area of each of the equal squares A, B,

and C. When a marble is dropped into the

box at random, it falls into one of the

compartments. What is the probability that

it will fall into compartment F?

(A) (B) (C)

(D) (E)

14.

The tables above show the different colors

and sizes of T-shirts that are available at

Independence High School. How many

different combinations of color and size are

possible?

(A) 7

(B) 12

(C) 15

(D) 25

(E) 64

15. For a class ring, each senior can choose

from 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 6

gray scarves packaged in 24 identical,

unmarked boxes, 1 scarf per box. What is the

least number of boxes that must be selected

in order to be sure that among the boxes

selected 3 or more contain scarves of the

same color?

(A) 3 (B) 6 (C) 7

(D) 8 (E) 9

183

PROBABILITY

SAT Practice Book

2009-2010

1

1. A bag contains only red marbles, blue

marbles, and yellow marbles. The probability

of 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 are

red, what is the probability that a car

selected at random from the assembly line

will be red?

(A) (B) (C)

(D) (E)

3. How many different positive three–digit

integers 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 random

from a basket of fruit. The probability that

the piece of fruit chosen will be an apple is .

Which of the following could NOT be the

number of pieces of fruit in the basket?

(A) 20 (B) 35 (C) 52

(D) 70 (E) 80

184

PROBABILITY

SAT Practice Book

2009-2010

2

2009-2010

5. A restaurant menu lists 8 dinners and 3

desserts. How many different dinner–dessert

combinations are possible from this menu?

(A) 24 (B) 12 (C) 11

(D) 8 (E) 3

6. A clerk accidentally threw a valuable

document into one of 90 trash cans. It is

equally likely that the document is in any of

these 90 trash cans. If exactly 15 of these 90

trash cans are blue, what is the probability

that the document will be in a blue trash

can?

(A) (B) (C)

(D) (E)

7.

The figure above shows the remaining pieces

of a paper chain from which a section has

been removed. The first link of the original

chain was red and the colors of the links

formed the repeating pattern of red (R),

yellow (Y), green (G), white (W), and blue (B)

from left to right. Which of the following

could be the number of links in the section

that was removed?

(A) 60 (B) 61 (C) 62

(D) 63 (E) 64

8.

Above are the four houses on a block of Oak

Road. Each house is painted a different color.

There is a red house, which is next to a blue

house. There is a green house, which is next

to the red house and a yellow house. Which

house could be painted red?

(A) 1 only (B) 2 only (C) 3 only

(D) 2 or 3 (E) 1 or 4

185

PROBABILITY

SAT Practice Book

2009-2010

3

2009-2010

9.

The figure above represents four offices that

will be assigned randomly to four employees,

one employee per office. If Karen and Tina

are two of the four employees, what is the

probability that each will be assigned an

office 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, the

outer left wire A is brought over wire B to the

middle position, forming the order shown in

step 1 , then the outer right wire C is brought

to the new middle position shown in step 2,

and so on, alternately bringing each new left

and each new right wire to the middle. At

what numbered step does the braid first

repeat 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 80

seconds. During each cycle, the light is green

for 40 seconds, amber for 10 seconds, and red

for 30 seconds. At a randomly chosen time,

what is the probability that the light will not

be 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 same

thing as the first

person.

� The fifth person ordered the same

thing as the second

person.

A lunch stand has three choices: hamburger,

hot dog, or salad. Five people from an office

ordered one choice each from the lunch

stand. The statements above are about what

these five people ordered. If n is the number

of 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.

186

PROBABILITY

SAT Practice Book

2009-2010

4

2009-2010

13.

A circle was cut into two pieces, and one of

the pieces is shown above, with the dashed

line indicating the path of the cut. Which of

the following could be the other piece of the

circle?

14.

The figure above shows four apartments in a

building. In this building, each apartment is

occupied by only one person. Alice lives next

to Sam, and Paul lives next to Alice and

Dara. 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 a

team of 3 plumbers to work on a certain job.

The company has 4 experienced plumbers

and 4 trainees. If a team consists of 1

experienced plumber and 2 trainees, how

many different such teams are possible?

187

ANSWERS

SAT Practice Book

2009-2010

1 1 1

01. PROPERTIES OF

INTEGERS I

1 D

2 E

3 C

4 E

5 C

6 A

7 D

8 D

9 E

10 E

02. NUMBER LINES AND

FRACTIONS I

1 B

2 4/9, 0.444

3 D

4 C

5 D

6 D

7 D

8 B

9 D

10 C

11 E

12 E

13 A

14 C

15 E

03. ELEMANTARY

NUMBER THEORY

(DIVISIBILITY) I

1 D

2 D

3 C

4 B

5 C

6 D

7 990

8 C

9 D

10 D

11 C

12 125

13 12

14 B

15 D

16 D

17 10

18 1600

19 C

20 2491

04. SEQUENCE I

1 C

2 D

3 C

4 C

5 E

6 B

7 C

8 C

9 B

10 A

11 202

12 D

13 5

14 B

15. A

16 C

17 D

18 39

19 E

20 D

21. 12.5

22 21

23 6/25

188

ANSWERS

2009-2010

2

05. SETS I

1 C

2 A

3 A

4 33

5 180

6 D

7 B

8 275

9 C

10 A

11 A

12 11

13 E

14 B

15 B

16 E

17 E

18 E

19 A

20 E

06. RATIO, PROPORTION,

PERCENTS I

1 D

2 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


PERCENTS II

1 120

2 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

ANSWERS

2009-2010

3


PERCENTS III

1 3

2 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 5

18 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

190

ANSWERS

2009-2010

4

08. WORD PROBLEMS I

1 D

2 E

3 D

4 C

5 18 mile

6 D

7 C

8 D

9 C

10 B

11 A

12 D

13 7 packages

14 7/15

15 C

16 E

17 E

18 A

19 450

20 128

21 70

22 D

23 C

24 A

25 A

26 B

08. WORD PROBLEMS II

1 n+4

2 B

3 D

4 C

5 B

6 C

7 3 1/3

8 36

9 1 3/7

10 B

11 A

12 E

13 45 mile

14 B

15 E

16 B

17 D

18 32.5

19 B

20 A

21 D

22 B

23 D

24 D

08. WORD PROBLEMS III

1 C

2 100

3 A

4 E

5 C

6 B

7 C

8 D

9 C

10 C

11 7.5

12 22

13 1024

14 A

15 A

16 89

17 A

18 C

19 E

20 115

191

ANSWERS

2009-2010

5

09. FACTORING I

1 B

2 D

3 E

4 B

5 A

6 D

7 B

8 2

9 D

10 A

11 103

12 A

13 A

14 C

15 E

16 15/7

17 A

18 C

10. MEAN, MEDIAN, MODE

I

1 C

2 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 B

2 C

3 B

4 C

5 D

6 2/5

7 C

8 C

9 C

10 B

11 B

12 D

13 A

14 A

15 A

16 B

17 C

18 E

19 3

20 B

21 B

22 15/7

23 E

24 C

25 C

26 C

27 E

28 A

192

ANSWERS

2009-2010

6

12. VARIATIONS I

1 D

2 B

3 D

4 D

5 D

6 8/15

7 E

13. INEQUALITIES I

1 D

2 B

3 E

4 D

5 C

6 B

7 A

8 E

9 13

10 D

11 E

12 C

13 E

14 B

15 B

16 C

17 E

18 B

19 D

20 D

13. INEQUALITIES II

1 A

2 E

3 C

4 E

5 A

6 A

7 D

8 A

9 B

10 D

11 A

12 C

13 E

14 D

15 B

16 A

17 D

18 9.5

19 B

14. LINEAR EQUATIONS I

1 E

2 A

3 A

4 E

5 E

6 3

7 A

15. QUADRATIC

EQUATIONS I

1 D

2 E

3 A

4 B

5 A

6 A

16. FUNCTIONS I

1 E

2 E

3 3

4 E

5 2 or 7

6 D

7 C

8 B

9 28

10 B

11 A

12 C

13 16

14 E

15 B

16 E

17 D

18 E

19 D

20 A

21 3

22 B

23 E

193

ANSWERS

2009-2010

7

16. FUNCTIONS II

1 A

2 B

3 3, -3

4 D

5 C

6 E

7 10

8 D

9 D

10 C

11 D

12 3.5

13 B

14 E

15 D

16 B

17 D

16. FUNCTIONS III

1 D

2 152

3 179

4 C

5 D

6 66

7 B

8 D

9 C

10 C

11 D

12 D

13 E

14 E

15 B

16 D

17. OPERATIONS I

1 1.2

2 A

3 E

4 C

5 11

6 875

7 C

8 A

9 B

10 D

11 B

12 E

13 E

14 D

18. COORDINATE

GEOMETRY I

1 B

2 A

3 A

4 B

5 A

6 E

7 E

8 A

9 D

10 B

11 B

12 D

13 E

14 A

15 C

16 B

17 D

18 B

19 B

20 A

21 E

22 C

194

ANSWERS

2009-2010

8

18. COORDINATE

GEOMETRY II

1 D

2 C

3 C

4 E

5 E

6 E

7 D

8 E

9 D

10 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 C

2 A

3 D

4 C

5 135

6 A

7 A

8 22.5<x<27.5

9 D

10 A

11 A

12 E

13 E

14 B

15 E

16 E

17 40

18 C

19 C

20 A

21 E

22 D

23 A

24 D

25 A

20. TRIANGLES I

1 D

2 B

3 2

4 B

5 B

6 A

7 B

8 9

9 A

10 20 or 50

11 D

12 C

13 C

14 A

15 E

16 E

17 E

18 10.5

19 E

20 A

21 E

195

ANSWERS

2009-2010

9

20. TRIANGLES II

1 E

2 B

3 B

4 3 or 6 or 9 or 12

5 8

6 75

7 D

8 E

9 A

10 C

11 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 C

3 B

4 B

5 B

6 C

7 C

8 A

9 D

10 B

11 C

12 E

13 E

14 A

15 E

16 C

17 B

18 C

19 A

20 A

21 C

21. POLYGONS I

1 E

2 B

3 A

4 D

5 B

6 180

7 B

8 B

9 B

10 B

11 B

12 B

13 C

14 C

15 C

16 B

17 D

18 B

19 D

20 D

196

ANSWERS

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 B

11 D

12 B

13 B

14 28

15 5

16 3

17 192

18 70/3

19 105

22. CIRCLES I

1 B

2 A

3 C

4 C

5 C

6 B

7 A

8 B

9 B

10 B

11 B

12 B

13 A

22. CIRCLES II

1 A

2 B

3 C

4 A

5 B

6 C

7 B

8 B

9 B

10 D

11 D

12 7

13 7/2

14 10

15 5/18

23. SOLID GEOMETRY I

1 E

2 D

3 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 D

19 C

20 B

21 125

22 1728

197

ANSWERS

2009-2010

11

24. STATISTICS, GRAPHS

& TABLES I

1 B

2 C

3 D

4 2380

5 D

6 B

7 C

8 C

9 B

10 180

11 D

12 A

13 C

14 E

15 E

16 B

17 E

18 96

19 39

20 D


& TABLES II

1 D

2 C

3 275

4 D

5 E

6 1300

7 E

8 D

9 B

10 E

11 D

12 A

13 1/3

14 C

15 B

16 C

17 B

18 D

19 C

20 D


& TABLES III

1 E

2 A

3 149

4 B

5 B

6 D

7 D

8 C

9 A

10 E

11 C

12

13 D

14 B

15 E

16 C

17 E

18 C

19 C

20 C

21 2400

22 E

23 D

24 1350

198

ANSWERS

2009-2010

12

25. PROBABILITY I

1 C

2 E

3 D

4 C

5 B

6 54

7 108

8 C

9 A

10 A

11 E

12 B

13 E

14 B

15 D

16 E

25. PROBABILITY I

1 B

2 B

3 C

4 C

5 A

6 C

7 B

8 D

9 E

10 D

11 B

12 E

13 B

14 D

15 24

199

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