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TABLE of CONTENTS

SAT Practice Book

2009-2010

11

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

1

PROPERTIES of INTEGERS �

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

xxy11

x , 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 �

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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

33x 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 �

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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 w ?

(A) t

(B) v

(C) x

(D) y

(E) z

2

17

2

37

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

1xx?

(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

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 �

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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

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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

99t

(B) 3

33t

(C) t

t

3

99

(D) t

t

3

33

(E) 3

29 t2

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 2 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 �

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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 t2 is in the

set whenever t is in the set. Which of

the following sets has property X ?

(A) 0,1,2 ,12

(B) 0,11

(C) 1,0,11

(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 8x and 31 31 y , which of

the following gives the set of all

possible values of xy?

(A) xy = 4

(B) 240 24xy

(C) 111 111 xy

(D) 241 241 xy

(E) 248 248 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 �

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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

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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2009-2010

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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) 7575n

n%

(B) 752 75n

n%

(C) )( 752100 75n

n%

(D) 75

100

75n

n%

(E) 752

100

75n

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

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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

(B) a

b

c

f b

(C) b

f

a

c

b

f

(D) f

b

c

a

f

b

(E) 1

1

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

2 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

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11

1. If 12

10 b

a 12, 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

1

2

11

n

n,

then n =?

(A) 1

(B) 2

(C) 3

(D) 4

(E) 5

24


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2009-2010

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7. If y is directly proportional to x2 and

8

1

8

1y when

2

1

2

1x what is the positive

value of x when 2

9

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

2 37

39

2x

x, then x = ?

(A) 37

(B) 39

(C) 41

(D) 74

(E) 78

25


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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


SAT Practice Book

2009-

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4

2009-2010

4

17. If tr

tr

t

t =

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

1qr %

(B) r

q

100

11 %

(C)r

q )1(100 1 %

(D) ( q

r100 + 1 ) %

(E) 1

100

1q

r %

27


SAT Practice Book

2009-2010

11

1. If 4

3)25( 32 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

1x =

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-

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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

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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

b

y =

3

2, then

ba

yx

1010

99

10

9= ?

(A) 10

9

(B) 23

20

(C) 27

20

(D) 3

2

(E) 5

3

16. 30


SAT Practice Book

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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

11

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 351335t , what is the value of 3

4t ?

4. If trr1818 , 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

3

12

1

x and 161zy . If z > y

what is the value of x + z?

(A) 5

(B) 7

(C) 11

(D) 13

(E) 15

6. 2233 )( 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

EXPONENTS, SQUARES & SQUARE ROOTS �

SAT Practice Book

2009-

2010

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2009-2010

2

8. If m and k are positive and

mkm 100101210

1 , what is 11m 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 6422cba , then

??cba222

(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

43

6

ba , what is the value of ab?

(A) 6

(B) 12

(C) 18

(D) 24

(E) 36

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

y

xy ?

(A) 5

(B) 8

(C) 10

(D) 12

(E) 20

13.If 93 yx y 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 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

23

4

kx and 23

4

ny n ,

what is 3

2

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 mm and 155 mm y m)( , what is

the value of x + y?

(A) 7

(B) 12

(C) 14

(D) 24

(E) 31

17.If 722222 2222

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 nn ( 101106 must equal

(A) 10

7

(B) n

10

7

(C) n2

10

7

(D) n

10

6

(E) n2

10

6

34


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2009-2010

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20.If x and y are positive integers andyx224 2 , 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

EXPONENTS, SQUARES & SQUARE ROOTS�

SAT Practice Book

2009-2010

11

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 11z

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

6. If a and b are positive integers and

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 22 = 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 11 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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2009-2010

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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

11

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

112

8

112n

(B) 8

112

8

112n

(C) 8

112

8

112n

(D) 8

112

8

112n

(E) 8

112

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 �

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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

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2009-2010

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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 s

(E) sm

s60

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

11

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

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WORD PROBLEMS �

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2009-2010

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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

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2010

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2009-2010

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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

p

(C) pm

py

p

(D) m

pmy )( p

(E) )( pmm

py

p

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 �

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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

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WORD PROBLEMS �

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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

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11

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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2009-2010

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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

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2010

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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?

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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

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11

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

terms of s and a?

(A) a

s

2

(B) 2

as a

(C) 2

as a

(D) as

a2

(E) as

a2

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

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 6422cba , then

??cba222

(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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7. If a and b are positive integers and

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 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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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 y ?

(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

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11

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 z

(B) 2

2 zk z

(C) 3

zk z

(D) 2

zk z

(E) 3

2 )( zk z

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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SAT Practice Book

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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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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 c

(B) 3

c a c

(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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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

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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

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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

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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

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

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

3

3

x

xequal?

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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

2 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

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EQUATIONS �

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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) 15kk 25p

(B) 25kk 15p

(C) 40(kk p)

(D) 0.40(kk p)

(E) (15 k)(25 p)

16. If tx 5 tt 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

xin terms of z ?

(A) z

(B) z + 1

(C) 5 z

(D) 5 z +1

(E) 5 11z

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(6

32 mif What is the value of m?

20. if thenxxx ,24642 2464 x=?

A) -288

B) -2

C) -2

1

D) 2

1

E) 2

21. if 2

1

1

1

2

1

1x, What is the value of x?

A) 2

B) 1

C) 0

D) -1

E) -2

22. if 13)5( 2 15 xxyx what is the

value of y when x=2?

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EQUATIONS �

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23. if ?1010

99,

3

2?

10

9

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

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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. 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

1

8

1y

when 2

1

2

1x what is the positive value of x

when2

9

2

9y ?

(A) 4

3

(B) 2

3

(C) 4

9

(D) 3

(E) 9

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VARIATIONS �

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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�

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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

xxy11

x , 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

112

8

112n

(B) 8

112

8

112n

(C) 8

112

8

112n

(D) 8

112

8

112n

(E) 8

112

8

112n

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6. 2233 )( 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

85

3

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) 5010 51h

(B) 4020 42h

(C) 2030 23h

(D) 1040 14h

(E) 545 54h

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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 8x and 31 31 y , which of

the following gives the set of all

possible values of xy?

(A) xy = 4

(B) 240 24xy

(C) 111 111 xy

(D) 241 241 xy

(E) 248 248 xy

15. If x + y = 30 and x > 8, then which of

the following must be true?

(A) y > 0

(B) y < 22

(C) y = 22

(D) y > 22

(E) x < 30

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16.

On the number line above, which of

the following corresponds to wu w ?

(A) t

(B) v

(C) x

(D) y

(E) z

17. 157

53

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

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

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1. If 32 3x , 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) 22x >7

(E) 99x <9

4. If 8

1

7

11

8

1

7

1

6

1

8

1

7

11

8

1

7

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) 12 1m

(E) 2m

6. . If y

1

6

1

5

1

7

1

6

1

5

1 1

6

1

5

1

7

1

6

1 then y could be

which of the following?

(A) 6

(B) 7

{C) 8

(D) 9

(E) 10

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7. If a+b= 40 and a < 15, which of 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) 11x

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. 33t =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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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

77yx ?

(A) A

(B) B

(C) C

(D) D

(E) E

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

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

m?

(A) 16

3

(B) 3

1

(C) 4

3

(D) 3

(E) 3

16

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16. Marcus can spend no more than $120 on

jeans and shirts for school. He buys 3 pairs of

jeans at $32 each. If x represents the dollar

amount he can spend on shirts, which of 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 < 33x <7 and x< 0, what is one

possible value of x ?

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

5

2

5

2

y

x how many possible values are there for

x ?

(A) One

(B) Two

(C) Three

(D) Four

(E) Five

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LINEAR EQUATIONS �

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1.157

53

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

6

127

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

17

85

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

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

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LINEAR EQUATIONS �

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2009-2010

2

5. If ba

yxthen

ba

yx

1010

99,

3

2

10

9

3

2

b

y

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 �

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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)

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QUADRATIC EQUATIONS �

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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.

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FUNCTIONS �

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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

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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 f(3 ?

(A) 24xxf 4)(

(B) 44)(xf

(C) x

xf44

)(

(D) 34 xxf x4)(

(E) 444xxf )(

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 20+ 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

nn

nn

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

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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

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?

(Disregard the $ sign when gridding your

answer.)

4. 2)(

)( 2

2xxt

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)(

6xxf ,

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 r

(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

b

bab 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 z 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

y

y

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

1

2

1x – 5

(E) y = 2

1

2

1x + 5

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

origin and is perpendicu1ar to the line

kyx ky4 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

3

4

(B) 4

5

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

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

33yx ?

(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

=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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