SAT 8

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PRACTICE TEST 2

235

PRACTICE TEST 2

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 2

237

PRACTICE TEST 2

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

238

PRACTICE TEST 2 QUESTIONS

1.If x5 = 84, x =

(A)0.13

(B)5.28

(C)13.45

(D)819.20

(E)6,208.37

2.If f (x) = e2x and g(x) = x−2, then f (g(4)) =

(A)0.07

(B)2,981

(C)1.13

(D)1.27

(E)7.89

3.

If

m

=

1

, then

n

=

3m − n

5

m

(A)

−2

(B)

−

1

2

(C)

1

2

(D)

2

(E)

3

5

4.

For all x ≠ 0,

1

+

2

+

3

=

x

x2

x3

(A)

6

x3

(B)

6

x6

(x2 + x + 1)

(C)

x3

(D)(x2 + 2x + 3) x3

(x2 + 5)

(E)

x3

5. What is the reciprocal of 6 + i?

(A) 1 6

6 − i

(B)

35

6 + i

(C)

36

(D)6 − i

37

6 − i

(E)

36

PART III / EIGHT PRACTICE TESTS

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PRACTICE TEST 2		239
6. In factored form, x3 − 2x2 + 2x − 4 =		USE THIS SPACE AS SCRATCH PAPER
(A)	(x − 2)(x + 2)2
(B) (x − 2)(x + 2)(x + 1)
(C) (x − 2)2(x + 2)
(D)	(x − 2)3
(E)	(x − 2)(x2 + 2)

7. 3 20x2 y7 3 50x4 y2 =

11

(A)20 3 (50 3 )x6y9

1

(B) 703 x2y3

814

(C)10x 3 y 3

(D)10x2y3

814

(E)1,000x 3 y 3

	8. If	x + 2	≥ 0 , then which of the following describes x?
		x − 5

(A)x ≥ −2

(B)−2 ≤ x < 5

(C)x ≤ −2 or x > 5

(D)x > 5

(E)x ≤ −2 or x ≥ 5

9.Which of the following expressions represents the statement “N varies jointly with the square of x and with y”?

(A)N = kx2y

(B) N = k

yx

(C)N = ky x

(D)N = kx2y2

	(E) N =	k
		x2 y

10.What is the vertex of the parabola given by f (x) = x2 − 6x + 5?

(A)(−3, 4)

(B)(3, −4)

(C)(3, 4)

(D)(3, −3)

(E)(4, −4)

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240

11.In Figure 1, cot θ = 1.33. sin θ =

(A)0.01

(B)0.63

(C)0.60

(D)0.75

(E)0.80

12.What are the zeroes of f (x) = 8x3 − 2x2 − 3x?

			1	3
	(A)	−		,
			2
				4
			3	1
	(B)	−			,
			4
				2
			1	1						3
	(C)	−		,				,
			2
				2						4
			3						1
	(D)	−			,0,
			4					2
			1						3
	(E)	−		,0,
			2					4

13. The probability that it will snow tomorrow is 2 and, 3

independently, the probability that it will also snow

the day after tomorrow is 1 . What is the probability 5

that it will snow tomorrow but not the day after tomorrow?

2

(A)

15

2

(B)

5

3

(C)

4

8

(D)

15

22

(E)

15

14.An operation is defined on any three real numbers by a ▫ b ▫ c = a(c − b). If 2 ▫ 1 ▫ x = 10, then x =

(A)−6

(B)−4

(C)5

(D)6

(E)4

PART III / EIGHT PRACTICE TESTS

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θ

8

Figure 1

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PRACTICE TEST 2

2

15.If (x − 1)3 = 25, then x =

(A)8.5

(B)15,625

(C)124

(D)125

(E)126

16. If cos 2θ =	3	, then	1	=
	4		cos2θ − sin2 θ

(A) −1 3

(B)

4

4

(C)

3

(D)4

(E)1

17.What does the angle − 5π equal in degree measure?

12

(A) −75°

(B) −15°

(C) −150°

(D) 37.5°

(E) −52.5°

		f (x) =	4x2	− 9
	18. If				, what value does the function
			2x	+ 3
						3
	approach as x approaches −						?
				2

(A)0.02

(B)0

(C)−4.33

(D)−6

(E)−9

19.If i is a zero of the polynomial p(x), then which of the following must be a factor of p(x)?

(A)−i

(B)x2

(C)x2 + 1

(D)x2 − 1

(E)x2 − 2ix + 1

241

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242

20.For all x ≠ 2, f (x) = (x − 2)(2 − x)−1. Which of the following must be a true statement?

I.f (1) = f (−1)

II.f (4) = f (0)

		1			= f (−2)
	III.	f
			2
		(A)			I only
		(B)			III only
		(C)			I and II only
		(D)			II and III only
		(E)			I, II, and III

21. If f (x) = 5x − 1 and g( f (−3)) = 18, then g(x) could be which of the following?

(A)x + 2

(B)−x + 2

(C)−2x − 12

(D)x + 14 4

(E)x + 4

22. Which of the following is a y-intercept of the hyperbola y2 − x2 = 1?

916

(A)(0, −3)

(B)(0, 4)

(C)(3, 0)

(D)(0, 81)

(E)(0, 9)

23.What is the length of segment DE in Figure 2?

(A)3.46

(B)4.47

(C)6

(D)6.16

(E)11

PART III / EIGHT PRACTICE TESTS

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z

E (0,2,5)

y

D (3,0,0)

x

Figure 2

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PRACTICE TEST 2					243
24. A car is purchased for $24,500. If it decreases in					USE THIS SPACE AS SCRATCH PAPER
value at a rate of 7% per year, how much will it be
worth in 5 years?
(A)	$15,851
(B)	$15,925
(C)	$17,044
(D)	$22,785
(E)	$32,787
25. f (x) = 4x for all real values of x. If p > 1 and q > 1,
then f −1( p) f −1(q) =
(A)	4 p + q
(B)	log4 p log4 q
(C)	log4 pq
(D)	log4 p + log4 q
(E)	logp 4 logq 4
26. If logb 6 = 36, then b =
(A)	0.17
(B)	0.50
(C)	1.05
(D)	1.50
(E)	2
27. tan (arcos 0.75) =
(A)	0.66
(B)	0.75
(C)	0.80
(D)	0.88
(E)	41.4
28. Five-sixths of the students in class are passing with
a grade of C− or better. Three-fourths of the students
in the same class are passing with a grade of B− or
better. What fraction of the class is not passing with
a grade of B− or better but is passing with a grade of
C− or better?
(A)	5
	8
(B)	1
	12
(C)	1
	6
(D)	1
	4
(E)	1
	15

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