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374

45. B Let w = the width, l = the length, and h = the height of the prism. Using the three given areas:

wh = 10.

wl = 30.

lh = 12.

Use substitution to solve for the variables and determine w = 5, l = 6, and h = 2.

The volume is, therefore, 6 × 5 × 2 = 60 units3.

46. A If sec θ = 3, then cos θ = 13 . Picture a right triangle in quadrant I to determine that the value of

sin θ = 2 32 .

Recall the double angle formula for sine:

sin 2θ = 2 sin θ cos θ.

 

2

2

 

1

 

 

4 2

 

sin 2θ = 2

 

 

 

 

 

 

=

 

≈ 0.63.

3

 

 

 

9

 

 

3

 

 

PART III / EIGHT PRACTICE TESTS

47. E The circle given by the equation (x + 4)2 + (y − 4)2 = 2 is centered at (−4, 4) and has a radius of

2 . Because the radius is less than 4 units long, there are no x and y intercepts.

48.E If each score is increased by 5 percentage

points, the mean also increases by 5. The new mean would, therefore, be 85 + 5 = 90%.

49.C

g 14 = tan arcsin 14 ≈ 0.258. f (0.258) = sin(arctan 0.258) = 0.25.

50. B Recall that the absolute value of a complex number is given by: a + bi = a2 + b2 .

6 − 3i = 62 + (−3)2 = 45 = 3 5

PRACTICE TEST 7

375

DIAGNOSE YOUR STRENGTHS AND WEAKNESSES

Check the number of each question answered correctly and “X” the number of each question answered incorrectly.

Algebra

1

2

3

7

14

32

43

44

 

Total Number Correct

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

8 questions

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Solid Geometry

20

45

Total Number Correct

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2 questions

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Coordinate Geometry

4

12

17

26

33

34

47

 

Total Number Correct

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

7 questions

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Trigonometry

5

16

24

29

30

35

46

49

 

Total Number Correct

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

8 questions

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Functions

6

8

15

18

22

23

27

37

38

39

41

42

Total Number Correct

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

12 questions

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Data Analysis,

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Statistics, and

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Probability

21

28

36

48

Total Number Correct

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4 questions

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Numbers and

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Operations

9

10

11

13

19

25

31

40

50

Total Number Correct

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

9 questions

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Number of correct answers − 14 (Number of incorrect answers) = Your raw score

___________________________ − 14 (_____________________________) = ________________

376

PART III / EIGHT PRACTICE TESTS

Compare your raw score with the approximate SAT Subject Test score below:

 

 

SAT Subject Test

 

Raw Score

Approximate Score

 

 

 

Excellent

43–50

770–800

 

 

 

Very Good

33–43

670–770

 

 

 

Good

27–33

620–670

 

 

 

Above Average

21–27

570–620

 

 

 

Average

11–21

500–570

 

 

 

Below Average

< 11

< 500

 

 

 

PRACTICE TEST 8

377

PRACTICE TEST 8

Treat this practice test as the actual test and complete it in one 60-minute sitting. Use the following answer sheet to fill in your multiple-choice answers. Once you have completed the practice test:

1.Check your answers using the Answer Key.

2.Review the Answers and Solutions.

3.Fill in the “Diagnose Your Strengths and Weaknesses” sheet and determine areas that require further preparation.

This page intentionally left blank

PRACTICE TEST 8

379

PRACTICE TEST 8

MATH LEVEL 2

ANSWER SHEET

Tear out this answer sheet and use it to complete the practice test. Determine the BEST answer for each question. Then, fill in the appropriate oval using a No. 2 pencil.

1.

A

B

C

D

E

21.

A

B

C

D

E

41.

A

B

C

D

E

2.

A

B

C

D

E

22.

A

B

C

D

E

42.

A

B

C

D

E

3.

A

B

C

D

E

23.

A

B

C

D

E

43.

A

B

C

D

E

4.

A

B

C

D

E

24.

A

B

C

D

E

44.

A

B

C

D

E

5.

A

B

C

D

E

25.

A

B

C

D

E

45.

A

B

C

D

E

6.

A

B

C

D

E

26.

A

B

C

D

E

46.

A

B

C

D

E

7.

A

B

C

D

E

27.

A

B

C

D

E

47.

A

B

C

D

E

8.

A

B

C

D

E

28.

A

B

C

D

E

48.

A

B

C

D

E

9.

A

B

C

D

E

29.

A

B

C

D

E

49.

A

B

C

D

E

10.

A

B

C

D

E

30.

A

B

C

D

E

50.

A

B

C

D

E

11.

A

B

C

D

E

31.

A

B

C

D

E

 

 

 

 

 

 

12.

A

B

C

D

E

32.

A

B

C

D

E

 

 

 

 

 

 

13.

A

B

C

D

E

33.

A

B

C

D

E

 

 

 

 

 

 

14.

A

B

C

D

E

34.

A

B

C

D

E

 

 

 

 

 

 

15.

A

B

C

D

E

35.

A

B

C

D

E

 

 

 

 

 

 

16.

A

B

C

D

E

36.

A

B

C

D

E

 

 

 

 

 

 

17.

A

B

C

D

E

37.

A

B

C

D

E

 

 

 

 

 

 

18.

A

B

C

D

E

38.

A

B

C

D

E

 

 

 

 

 

 

19.

A

B

C

D

E

39.

A

B

C

D

E

 

 

 

 

 

 

20.

A

B

C

D

E

40.

A

B

C

D

E

 

 

 

 

 

 

This page intentionally left blank

PRACTICE TEST 8

381

PRACTICE TEST 8

Time: 60 minutes

Directions: Select the BEST answer for each of the 50 multiple-choice questions. If the exact solution is not one of the five choices, select the answer that is the best approximation. Then, fill in the appropriate oval on the answer sheet.

Notes:

1.A calculator will be needed to answer some of the questions on the test. Scientific, programmable, and graphing calculators are permitted. It is up to you to determine when and when not to use your calculator.

2.Angles on the Level 2 test are measured in degrees and radians. You need to decide whether your calculator should be set to degree mode or radian mode for a particular question.

3.Figures are drawn as accurately as possible and are intended to help solve some of the test problems. If a figure is not drawn to scale, this will be stated in the problem. All figures lie in a plane unless the problem indicates otherwise.

4.Unless otherwise stated, the domain of a function f is assumed to be the set of real numbers x for which the value of the function, f (x), is a real number.

5.Reference information that may be useful in answering some of the test questions can be found below.

Reference Information

Right circular cone with radius r and height h:

Volume =

1

πr2h

3

 

 

 

 

 

 

 

 

Right circular cone with circumference of base c

 

 

 

 

 

1

 

and slant height :

Lateral Area =

c

2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sphere with radius r:

Volume =

4

 

πr3

 

 

3

 

 

 

 

 

 

 

 

 

 

 

Surface Area = 4πr2

 

 

 

 

 

 

 

 

Pyramid with base area B and height h:

Volume =

1

 

 

Bh

 

 

3

 

 

 

 

 

 

 

 

 

 

382

PRACTICE TEST 8 QUESTIONS

1.If i = −1, then (6 − i)(6 + i) =

(A)35

(B)36 − i

(C)37

(D)35 + 12i

(E)36

2.If f (x) = x2 − 8x, then 2f (2x) =

(A)2x2 − 16x

(B)4x2 − 16x

(C)8x2 − 16x

(D)8x2 − 32x

(E)4x2 − 32x

3.If a function f is an odd function and (x, y) is a point on its graph, then which of the following will also be a point on its graph?

(A)(y, x)

(B)(−x, −y)

(C)(−y, −x)

(D)(x, −y)

(E)(−x, y)

4.What real values of a and b satisfy the equation a + b + 14i = 4 + (3a − b)i?

(A)a = 5, b = 1

(B)a = 9 , b = 1

22

(C)a = 5, b = −1

(D)a = 3, b = 1

(E)a = 9 , b = − 1

22

5.Standing 25 feet away from a tree, the angle of elevation of the top of the tree is 26°. Assuming the tree grows perpendicular to the ground, what is its height?

(A)12.2 ft

(B)16.2 ft

(C)19.1 ft

(D)21.2 ft

(E)29.5 ft

PART III / EIGHT PRACTICE TESTS

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GO ON TO THE NEXT PAGE

PRACTICE TEST 8

 

 

 

6. If

sin θ = −

9

 

and π < θ <

3π

, then cos θ =

 

 

 

41

2

 

(A)

−

40

 

 

 

 

 

 

 

 

 

 

 

41

 

 

 

 

 

 

 

 

(B)

−

9

 

 

 

 

 

 

 

 

 

 

 

 

 

40

 

 

 

 

 

 

 

 

(C)

−

32

 

 

 

 

 

 

 

 

 

 

 

 

 

41

 

 

 

 

 

 

 

 

9

(D)

40

40

(E)

41

7.Which of the following is an equation of the line with x-intercept of 5 and y-intercept of −1?

(A)1 x − y = −1

5

(B)1 x + y = 1

5

(C)x − 5y = 5

(D)x + 5y = −5

(E)x − 5y = −5

8.The product of the roots of a quadratic equation is −5 and their sum is −4. Which of the following could be the quadratic equation?

(A)x2 − 4x + 5 = 0

(B)x2 − 4x − 5 = 0

(C)x2 + 4x − 5 = 0

(D)x2 + 5x − 4 = 0

(E)x2 − 5x − 4 = 0

 

f (n) = 9− n , then

 

−

1

=

9. If

f

 

 

 

 

 

 

 

4

 

(A)9− 14

(B)3

(C)3

(D)1

9

(E)9

10.If log4 x + 3 log4 x = 9, then x =

(A)1.86

(B)2.25

(C)9

(D)22.6

(E)256

383

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