Summer Math Packet Students Entering 12th Grade

SUMMER MATH SAT PACKET For students entering 12 th grade

Student Name:

(Adapted from www.stratfordk12.org )

a) 0

1. The use of a calculator is permitted.

2. All numbers used are real numbers.

3. Figures that accompany problems in this test are intended to provide information useful in solving the problems.

They are drawn as accurately as possible EXCEPT when it is stated in a specific problem that the figure is not

drawn to scale. All figures lie in a plane unless otherwise indicated.

4. Unless otherwise specified, the domain of any function f is assumed to be the set of all real numbers x for which

f(x) is a real number.

F

b

W

A = tw A= yrr2 C =2.7rr A= 2-

1 bh

ff ph

V = twh

The number of degrees of arc in a circle is 360.

The sum of the measures in degrees of the angles of a triangle is 180.

Q C a) C a)

h

V = zr2h (.2 a 2 + b2

2x 60° x

30° r

x -Na Special Right Triangles

SAT Reference Information

2011 12 th Grade Summer Packet

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Directions: Solve each problem and circle which is the best of the choices given.

1. Which of the following numbers is between —1

and —1

? 5 4

(A) .014

(B) .015

(C) 0.19

(D) 0.21

(E) 0.26

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

(A) 10

(B) 11

(C) 100

(D) 101

(E) 1,001

3. If m x • m 7 = m28

and (m 5) = m

15, what is the value of x + y ?

(A) 7

(B) 12

(C) 14

(D) 24

(E) 31

2011 12'h Grade Summer Packet 5

HOME SALES

160,000

150,000

140,000

130,000

120,000

110,000

100,000 1985

1986 1987 1988 1989 1990

4. According to the graph above, which of the following is closest to the decrease

per year in the number of homes sold between 1987 and 1990?

(A) 7,000

(B) 11,500

(C) 14,000

(D) 17,500

(E) 42,000

5. 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

6. If 2 x - 10 = 20, then x - 5 =

(A) 5

(B) 10

(C) 15

(D) 20

(E) 30 2011 12 th Grade Summer Packet

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7. If t represents an odd integer, which of the following expressions represents an even

integer?

(A) t + 2

(B) 2 t — 1

(C) 3 t — 2

(D) 3 t + 2

(E) 5 t + 1

C 9

8. For the triangles above, the perimeter of 1ABC equals the perimeter of £DEF. If

ABC is equilateral, what is the length of AB ?

(A) 4

(B) 5

(C) 7

(D) 9

(E) 15

9. 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

2011 121h Grade Summer Packet

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SALES OF JEANS IN 2001

10. 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

. 1

4 i 11. On a blueprint, — inch represents 16 feet. If a driveway is 40 feet long,

what is its length, in inches, on the map?

3 (D) 2 1

(A) —3

—5

4 (B)

(C) — (E) 10

8 8 2

t 2 0

-2 0 2 4 g(t)

1

12. The table above gives values of the linear function of t. Which of the following defines g ?

(A) g (t) = —1t + 1

2

(B) g (t) = --1

t + 1 2

g for selected values

(C) g (t) = - t + 1

(D) g (t) = - t + 2


(E) g (t) = -2 t + 2

8

13. How many positive three — digit integers have the hundreds digit equal to 3 and the

units digit (ones digit) equal to 4?

(A) 10

(B) 19

(C) 20

(D) 190

(E) 200

3 14. If y 5x , 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.

15. For which of the following values of m will the value of 3m - 1 be greater than 10 ?

(A) 4

(B) 3

(C) 2

(D) 1

(E) 0

16. If a x k = a for all values of a, what is the value of k ?

(A) -a

(B) - 1

(C) 0

(D) 1

(E) a

2011 12th Grade Summer Packet 9

Note: Figure not drawn to scale.

17. In the figure above, / I I m. If x = 80 and y = 70, what is the value

of z ?

(A) 30

(B) 60

(C) 75

(D) 90

(E) 150

18. In the triangles above, what is the average (arithmetic mean) of u, v, w, x, and y ?

(A) 21

(B) 45

(C) 50

(D) 52

(E) 54

2011 12th Grade Summer Packet

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x3 x 2 x

19. If x, X 2 , and x ' lie on a number line in the order shown above, which of the following could be the value of x ?

(A) -2

(B) — 1— 2

(C)3

4

(D) 1

(E)3 — 2

20. In the figure above, line / passes through the origin. What is the value of —k

? h

(A) 3 (B) 2 (C) —(D) --3

2 2 (E) -3


11

m -31=5

k+71=15

21. 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

g(n) = n2 + n

h(n) = n2 — n

22. g (5)— h(4) =

(A) 0

(B) 8

(C) 10

(D) 18

(E) 32

23. A store charges $28 for a certain type of sweater. This price is 40 percent more than the amount it costs the store to buy one of these sweaters. At an end — of — season sale, store employees can purchase any remaining sweaters at 30 percent off the store's cost. How much would it cost an employee to purchase a sweater of this type at this sale?

(A) $8.40

(B) $14.00

(C) $19.60

(D) $20.00

(E) $25.20

2011 12th Grade Summer Packet

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Set X = { 30, 31, 32, 33 }

Set Y = { 32, 33, 34, 35, 36 }

24. 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

25. If x = k (k - 2), then x + 1 =

(A) k 2 - k

(B) k 2 - 3 k

(C) k 2 - 2 k + 1

(D) k 2 + 2 k + 1

(E) k 2 -1

x

26. In the figure above, the perimeter of the triangle is 4 + 2,12 . What is the value of x ?

(A) 2 (B) 4 (C) (D) 2h (E) 2 +NE


13

HISTORY TESTS RESULTS

Score Number of Students

100 1 95 2 90 4 85 1 80 3 75 2 70 2 65 0 60

27. The scores on Tuesday's history test for 16 students are shown in the table above. Sam, who was the only student absent on Tuesday, will take the test next week. If Sam receives a score of 95 on the test, what will be the median score for the test?

(A) 90

(B) 87.5

(C) 85

(D) 82.5

(E) 80

2, 6, 14, 30, . .

28. 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 2011 12th Grade Summer Packet 14

29. If a (x + y) = 45 and ax = 15, what is the value of ay?

(A) 3

(B) 5

(C) 15

(D) 25

(E) 30

30. The three-dimensional figure represented above consists of rectangular and triangular faces. Each rectangular face has area r and each triangular face has area t. What is the total surface area of the figure, in terms of r and t ?

(A) 2 r + t

(B) 3 r + 2 t

(C) 4 r + 3 t

(D) 6 r t

(E) r 3 t 2

31. If n is a positive integer and n +1 = —1

, then n = 2" 2

(A) 1

(B) 2

(C) 3

(D) 4

(E) 5


y.

C ( 2, 5 )

B (k, t)

0 ( 2, - 1 )

32. Point B is the midpoint of AC in the figure above. What is the value of t ?

(A) 1

(B) 1.5

(C) 2

(D) 2.5

(E) 3

33. What is the radius of a circle that has a circumference of 7C ?

(B) 2

(C) 1

(D) 2

(E) 4

34. If y is directly proportional to x 2 and y = —1

2 when x = —

1, what is the

8

positive value of x when y = -9— ? 2

(A)

(B)

(C)

3 4 3 2 9 4

(D) 3

(E) 9 2011 12'h Grade Summer Packet

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35. 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

36. In the figure above, y + z =

(A) 180 (B) 195

(C) 215

(D) 230 (E) 245

The sum of three consecutive odd integers is 111.

37. If n represents the least of the three integers, which of the following equations

represents the statement above ?

(A) 3 n = 111

(B) 3 n + 2 = 111

(C) 3 n + 4 = 111

(D) 3 n + 6 = 111

(E) 3 n + 9 = 111

38. If 6,700 = 100 ( 6k + 7 ) , then k =

(A) —1

(B) 1 (C) 10 (D) 100 (E) 1,000 10


Note: Figure not drawn to scale.

39. In the figure above, if x = 70 and y = 40 and the dotted lines bisect the angles with measures x° and y° , what is the value of z ?

(A) 30 (B) 40 (C) 45 (D) 50 (E) 55

40. A piece of fruit is to be chosen at random from a basket of fruit. The probability that

2 the piece of fruit chosen will be an apple is — . Which of the following could NOT

5

be the number of pieces of fruit in the basket?

(A) 20

(B) 35

(C) 52

(D) 70

(E) 80

41. A square and an equilateral triangle have equal perimeters. If the square has sides of

length 3 , what is the length of one side of the triangle?

(A) 2

(B) 3

(C) 4

(D) 5

(E) 6


42. If x = -1 and k > 0 , which of the following has the greatest value?

(A) 2kx

(B) 4kx2

(C) 6kx 3

(D) 8k,r4

(E) 101a5

43. Josephine's daily exercise routine consists of swimming, cycling, and running, in that order. She runs faster than she swims and cycles faster than she runs. If she does not rest between the activities, which of the following could be the graph of the distance she covers during the entire time of her exercise routine?

(A)

e

n a

D

(B)

e

a

D

(C)

a

S

D

Time Time Time

Time Time

(D)

(E)

e

n

n a a

S

D


44. If 2 — xl < 3, which of the following is a possible value of x ?

(A) 4

(B) 5

(C) 6

(D) 7

(E) 8

45. If all interior angles of the polygon above are congruent, then x =

(A) 60 (B) 65 (C) 72 (D) 80 (E) 84

46. If x + 3 is an integer, then x must be 2

(A) a negative integer

(B) a positive integer

(C) a multiple of 3

(D) an even integer

(E) an odd integer

47. 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 —I

2

(B) —1 1 —7 (C) — (D) (E) 1

4 8


48. If xy = 7 and x - y = 5 , then X 2 y - xy 2 =

(A) 2

(B) 12

(C) 24

(D) 35

(E) 70

49. 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

x 1 2 3 4

Y 3 7 11 15

50. 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


Summer Math Packet Students Entering 12th Grade

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