SAT 8

254

49. D There are many ways to go about writing an expression for the area of the triangle. You know the

formula for the area of any triangle is A = 12 (base × height). In the given figure, A = 12 ab.

Now, use trigonometric ratios to write a and b in terms of θ.

	sin θ =	a			a = 2 sin θ.
		2
	cos θ =		b		b = 2cos θ.
		2

Substituting these values of a and b into the area equation results in:

A= 12 (2 sin θ)(2 cos θ).

A= 2 sin θ cos θ.

PART III / EIGHT PRACTICE TESTS

50. C Recall that if (x, y) is a point on the graph of f, then (y, x) is a point on the graph of f −1. f −1(6.2) corresponds to the point (x, 6.2) on the graph of f.

Reflect f over the line y = x to get the graph of f −1. The new line segment passes through the origin and has

	a slope of	2		=			1	.
	14					7
	f −1(6.2) =				1	(6.2)			= 0.89.
				7

PRACTICE TEST 2

255

DIAGNOSE YOUR STRENGTHS AND WEAKNESSES

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

Algebra	1	3	4	6	7	8	9	15	24		35		Total Number Correct
10 questions
Solid Geometry	23	33	Total Number Correct
2 questions
Coordinate	22	29	36	37	38	39	Total Number Correct
Geometry
6 questions
Trigonometry	11	16	17	27	41	47	49	Total Number Correct
7 questions
Functions	2	10	12	19	20	21	25	26	30		31		43	44	45			46		50	Total Number Correct
15 questions
Data Analysis,	13	28	42	48	Total Number Correct
Statistics,
and Probability
4 questions
Numbers	5	14	18	32	34	40	Total Number Correct
and Operations
6 questions

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

___________________________ − 14 (_____________________________) = ________________

256	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 3

257

PRACTICE TEST 3

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.

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PRACTICE TEST 3

259

PRACTICE TEST 3

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

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PRACTICE TEST 3

261

PRACTICE TEST 3

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

262

PRACTICE TEST 3 QUESTIONS

1.	If	1 − x	=	4 − 4x	, then	1 − x	=
		x
				x		x

(A)−1

(B)0

1

(C)4

(D)1

(E)4

2.A number k is increased by 10. If the fifth root of that result equals −2, k =

(A)− 42

(B)−22

(C)−11.1

(D)22

(E)32

[(n + 1)!]3 =

3.

(n!)3

(A)n

(B)n + 1

(C)n3

(D)(n + 1)3

n + 1 3

(E) n

4.What is the distance between the points in space J(11, 4, −1) and T(−2, 0, 3)?

(A)10.63

(B)12.37

(C)13.00

(D)14.18

(E)14.49

		x
	5. If sin x = 0.45, then cos				=
			2
	(A)	0.45
	(B)	0.52
	(C)	0.71
	(D)	0.89
	(E)	0.97

6. What is the domain of f (x) = 9 − x2 ?

(A)x ≤ 3

(B)x ≥ −3

(C)−3 ≤ x ≤ 3

(D)x ≥ −3 or x ≥ 3

(E)All real numbers

PART III / EIGHT PRACTICE TESTS

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PRACTICE TEST 3

7.If 7a4 = 28 a2, then which of the following are the possible values of a?

(A)2

(B)−2 or 2

(C)4

(D)−2 or 0 or 2

(E)0

8.If f (x) = 2x + 3 x , then f ( f (8)) =

(A)18

(B)36

(C)38.6

(D)40.2

(E)42

9.How many 4-person committees can be formed from a group of 9?

(A)24

(B)126

(C)1,512

(D)3,024

(E)362,880

10.What is the magnitude of vector v with initial point (3, −5) and terminal point (−2, 7)?

(A)4

(B)5

(C)12

(D)13

(E)25

11. If 2 x − 2x + 1 − 1 = 0 , then what is the value of x?

(A)−2

(B)1

(C)2

(D)4

(E)0

12.If the graph of the equation y = mx + 4 has points in the 4th quadrant, then which of the following must be true for m?

(A)m = 0

(B)m < 0

(C)0 < m < 1

(D)m > 0

(E)m = −4

263

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