# SAT Math 1&2 Subject Tests: Level 2 Practice Test 1

### Test Information

50 questions

60 minutes

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1. If r - s > r + s, then which of the following must be true?

A. r > s
B. s < 0
C. r < 0
D. r < s
E. s > 0

2. If f(x) =|x| + 10, for which of the following values of x does f(x) = f(-x) ?

A. -10 only
B. -10 and 10 only
C. All real x
D. All real x except 10
E. All real x except -10 and 10

3.

A. 0
B. 0.58
C. 1
D. 105
E. 210

4.

Figure 1

In Figure 1, sin ∠BAC =

A.
B.
C.
D.
E.

5. Which of the following is the complete solution set of the system:

A = {(x, y): x2 + y2 = 25} and

B = {(x, y): y = x + 1}?

A. {(5, 5)}
B. {(16, 9)}
C. {(-4, -3)}
D. {(-4, -3), (3, 4)}
E. {(-3, -4), (4, 3)}

6. If jk ≠ 0, then =

A. k2 -
B. j2 -
C. jk - 1
D. j2 - 1
E. k2 - 1

7. All of the following can be formed by the intersection of a cube and a plane EXCEPT

A. a triangle
B. a point
C. a rectangle
D. a line segment
E. a circle

8. If f(x) = and g(x) = + 1, then f(g(2.3)) =

A. 0.1
B. 1.2
C. 1.3
D. 1.8
E. 2.3

9. If x mod y is the remainder when x is divided by y, then (61 mod 7) - (5 mod 5) =

A. 2
B. 3
C. 4
D. 5
E. 6

10. Which of the following must be true?

I. sin(-θ) = -sin θ

II. cos(-θ) = -cos θ

III. tan(-θ) = -tan θ, where tan θ is defined

A. I only
B. II only
C. III only
D. I and III only
E. I, II, and III

11. If for all real numbers x, a function f(x) is defined by f(x) = , then f(15) - f(14) =

A. -2
B. 0
C. 1
D. 2
E. 4

12. If = 25, then x =

A. 1
B. 1.9
C. 2.19
D. 3.62
E. 5

13. If the ratio of sec x to csc x is 1 : 4, then the ratio of tan x to cot x is

A. 1:16
B. 1:04
C. 1:01
D. 4:01
E. 16:01

14.

Figure 2

In Figure 2, rectangle J contains all points (x, y). What is the area of a rectangle that contains all points (2x, y - 1) ?

A. 12
B. 18
C. 24
D. 36
E. 48

15. In right triangle ABC, ∠B measures 90°, ∠C measures 27°, and AB = 9. What is the length of the hypotenuse of -ABC ?

A. 4.1
B. 10.1
C. 17.7
D. 19.8
E. 21.2

16. Which of the following is a zero of f(x) = x2 + 6x - 12 ?

A. -15.16
B. -7.58
C. 0.67
D. 3.16
E. 7.58

17. If sin x = m and 0 < x < 90°, then tan x =

A.
B.
C.
D.
E.

18. If logy 2 = 8, then y =

A. 0.25
B. 1.04
C. 1.09
D. 2.83
E. 3

19. If sinθ = and - θ, then cos(2θ) =

A. -
B. -
C.
D.
E. 1

20. If f(x) = - 1, for all x > 0, then f-1(x)

A. (x + 1)2
B. x2 + 2
C. x2 + 1
D. (x - 1)2
E. (x + 2)2

21. When 4x2 + 6x + L is divided by x + 1, the remainder is 2. Which of the following is the value of L ?

A. 4
B. 6
C. 10
D. 12
E. 15

22. What is the length of the major axis of the ellipse given by the equation = 1 ?

A. 3.2
B. 4.5
C. 8.9
D. 10
E. 20

23. If f(x) = [x], where [x] is the greatest integer less than or equal to x, which of the following is a graph of f - 1 ?

A.

B.

C.

D.

E.

24. Which of the following is equal to the positive value of sec(cos-1(0.3527)) ?

A. 0.01
B. 0.94
C. 1.69
D. 2.84
E. 69.35

25. If f(x) = x2 + 5x + 6, for what value of x will f(x) have its minimum value?

A. -3
B. -
C. -2
D. 0
E.

26. If the 20th term of an arithmetic sequence is 20 and the 50th term is 100, what is the first term of the sequence?

A. -33.33
B. -30.67
C. 1
D. 2
E. 2.67

27. The polar equation r sin θ = 1 defines the graph of

A. a line
B. a circle
C. an ellipse
D. a parabola
E. a hyperbola

28. For which of the following functions f is f -1 a function?

I. f(x) = x2

II. f(x) = x3

III. f(x) = |x|

A. I only
B. II only
C. I and III only
D. II and III only
E. I, II, and III

29. What is ?

A. -2
B. -1
C. 1
D. 2
E. The limit does not exist.

30. If f(x) = , and g(f(x)) = x, then g(x) =

A.
B.
C.
D. 7 ln(2x -)
E.

31. A cube is inscribed in a sphere of radius 6. What is the volume of the cube?

A. 36
B. 36π
C. 216
D. 192
E. 216

32. A right circular cone has height h and radius r. If the cone is cut into two pieces by a plane that passes through the midpoint of the height and is parallel to the base, then the volume of the larger of the two resulting solids is

A.
B.
C.
D.
E.

33. If ex ≠ 1 and = , then x =

A. -1.73
B. -0.55
C. 1
D. 1.1
E. 1.73

34. If the graph of the equation y = 2x2 - 6x + c is tangent to the x-axis, then the value of c is

A. 3
B. 3.5
C. 4
D. 4.5
E. 5

35. If x = i - 1, then x2 + 2x + 2 =

A. 2i + 4
B. 4 + 2i
C. 0
D. i
E. -2

36.

Figure 3

The curve shown in Figure 3 could represent a portion of the graph of which of the following functions?

A. y = ex
B. y = e-x
C. y = 100 - x
D. y = x2 - 3x + 2
E. xy = 3

37. If two coins are removed at random from a purse containing three nickels and eight dimes, what is the probability that both coins will be dimes?

A.
B.
C.
D.
E.

38. A function g(x) is odd if g(-x) = -g(x) for all x and even if g(x) = g(-x) for all x. Which of the following is the graph of a function that is both odd and even?

A.

B.

C.

D.

E.

39. Points A and B lie on the edge of a circle with center O. If the circle has a radius of 5, and if the measure of ∠AOB is 70°, what is the length of chord AB ?

A. 2.9
B. 4.7
C. 5
D. 5.7
E. 9.4

40.

Figure 4

If the graph of y = f(x) is shown in Figure 4, then which of the following could be true?

A. (A)-f(x) = tan
B. (B)-f(x) = cot
C. (C)-f(x) = tan
D. (D)-f(x) = cot
E. (E)-f(x) = tan

41. Vectors v and w have components (-3, 4) and (12, 5), respectively. If z = -(v + w), then z has components

A. (-9, -9)
B. (5, 13)
C. (-5, 13)
D. (9, 9)
E. (, )

42. If f(x) = , then for which of the following values of x does f(x) = 0.33 ?

A. 0.62
B. 0.71
C. 1.36
D. 3.93
E. 4.95

43. The system of equations given by
2x + 3y = 7
10x + cy = 3
has solutions for all values of c EXCEPT

A. -15
B. -3
C. 3
D. 10
E. 15

44. If f(x, y) = for all x, y, f(a, b) = 15, f(b, c) = 20, and f(a, c) = 10, which of the following could be the product of a, b, and c ?

A. 18.26
B. 54.77
C. 284.6
D. 1,800.00
E. 3,000.00

45. If x > 0 and y > 1, then logx2 y =

I. logx y2

II. logx

III. logx

A. I only
B. II only
C. III only
D. I and II only
E. II and III only

46. Carlos is filling a spherical balloon with water. If he increases the volume of the balloon from 4,188.79 cubic centimeters to 14,137.167 cubic centimeters in 12 seconds, then what is the average rate at which he has increased the balloon's surface area?

A. 130.9 square centimeters per second
B. 314.159 square centimeters per second
C. 829.031 square centimeters per second
D. 1,570.796 square centimeters per second
E. 9,948.377 square centimeters per second

47. What is the value of |6 - 3i| ?

A. -3
B. 3
C. 3
D. 9
E. 15

48. The menu of a certain restaurant lists 10 items in column A and 20 items in column B. A family plans to share 5 items from column A and 5 items from column B. If none of the items are found in both columns, then how many different combinations of items could the family choose?

A. 25
B. 200
C. 3,425
D. 3,907,008
E. 5.63 × 1010

49. y varies directly as the square of x. When y = 2.5, x = 0.5. If y = 80, then x could equal

A. -2
B. -8
C. -10
D. -16
E. -64

50. Seven blue marbles and six red marbles are held in a single container. Marbles are randomly selected one at a time and not returned to the container. If the first two marbles selected are blue, what is the probability that at least two red marbles will be chosen in the next three selections?

A.
B.
C.
D.
E.

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