SAT 8
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PART I / ABOUT THE SAT MATH LEVEL 2 TEST |
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DIAGNOSTIC TEST QUESTIONS |
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1. c−1 ( |
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+ |
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a |
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b |
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(A)2 c
a + b
(B) c
ab
a + b
(C)
abc
(D) −c a + b abc
1
(E)
abc
2.(x + y + 3)(x + y − 3) =
(A)x2 + y2 − 32
(B)(x + y)2 + 6(x + y) + 9
(C)(x + y)2 + 6(x + y)
(D)(x + y)2 − 9
(E)x2 + 2xy + y2 + 32
3.If 2x = 5, 5x =
(A)2
(B)2.32
(C)11.61
(D)41.97
(E)25
4. If 7x = 6.24, then what is the value of x?
(A)38.94
(B)5.56
(C)30.94
(D)2.36
(E)6.49
5.If E and F are different points in a plane, then the set of all points in this plane the sum of whose distances from E and F is constant is
(A)a square
(B)a circle
(C)a parabola
(D)a hyperbola
(E)an ellipse
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CHAPTER 3 / DIAGNOSTIC TEST |
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6. Assuming cos and sec are defined, cos (4θ) sec (4θ) = |
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(A)4
(B)−1
(C)1
(D)0
(E)cot 4θ
7.What is the equation of a line that contains the point (−5, 2) and is parallel to the y-axis and perpendicular to the x-axis?
(A)y = − 2 x
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(B) |
y = −5 |
(C) |
y = x + 2 |
(D) |
x = −5 |
(E) |
y = 2 |
8. What is the distance in space between the points A(−2, 1, 3) and B(3, 4, −1)?
(A) 5 2
(B) 3 2
(C) 34
(D) 41
(E) 10
9. sin π =
2
(A)sin 4π
(B)sin 3 π 2
(C)cos 2π
(D)sin − π
2
(E)cos π
10.If 1 and − 4 are both roots of a given polynomial, then which of the following must be a factor of the polynomial?
(A)x + 1
(B)x2 − 3x − 4
(C)x2 + 3x − 4
(D)x − 4
(E)x2 − 1
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11.Figure 1 shows one cycle of the graph of y = sin 2x for 0 ≤ x < π. What are the coordinates of the point where the maximum value of the function occurs on this interval?
(A) |
π |
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, π |
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π
(B)4 , 1
(C)π , π2
π
(D)2 , 1
π
(E)3 , 2
12.In Figure 2, r sin θ =
(A)x
(B)y
(C)r
y
(D) r ry
(E)
x
13. If f (x) = 4x − 1 and |
f (g(6)) = − |
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then g(x) could |
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equal which of the following?
(A)1 x
(B)x2
x
(C)
6
(D) − x 18
2
(E)
x
PART I / ABOUT THE SAT MATH LEVEL 2 TEST
USE THIS SPACE AS SCRATCH PAPER
y
x
Figure 1
(x,y)
r y
θ
x
Figure 2
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CHAPTER 3 / DIAGNOSTIC TEST |
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14. At a distance of 50 feet from a flagpole, the angle |
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from the ground to the top of the flagpole is 42°. |
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Assuming the flagpole is perpendicular to the |
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ground, what is its height? |
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(A) |
75 ft |
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(B) |
56 ft |
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(C) |
37 ft |
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(D) |
33 ft |
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(E) |
45 ft |
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15. If f (x) = x − 4 and g(x) = x3 + 1, then g(f (12)) =
(A)9
(B)16 2 + 1
(C)5 69
(D)2 2
(E)8 2 + 1
16. What |
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the domain of the function defined by |
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f (x) = 3 4x2 − 1? |
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(A) |
− |
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≤ x ≤ |
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(B) |
− |
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≤ x or x ≥ |
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(C) |
x ≥ |
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(D)x ≥ 0
(E)All real numbers
17.The half-life of a radioactive substance is 9 years. If 40 grams of the substance exist initially, how much will remain after 23.5 years?
(A)0.077 grams
(B)244.30 grams
(C)6.11 grams
(D)2.49 grams
(E)6.55 grams
18.Which of the following could be a quadratic equation with integral coefficients having roots 3 + i and 3 − i?
(A)x2 + 9x − 10 = 0
(B)x2 − 6x + 10 = 0
(C)x2 − 9x + 8 = 0
(D)x2 − 9 = 0
(E)x2 + 9x − 8 = 0
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PART I / ABOUT THE SAT MATH LEVEL 2 TEST |
19. If f (x) = |
x |
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− 25 |
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, what value does the function |
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x − 5 |
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approach as x approaches 5? |
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(A)5
(B)10
(C)0
(D)11
(E)Undefined
20. Figure 3 shows the graph of y = f (x). Which of the following could be the graph of y = f (x) ?
(A)
Figure 3
(B)
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CHAPTER 3 / DIAGNOSTIC TEST |
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(C)
(D)
(E)
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PART I / ABOUT THE SAT MATH LEVEL 2 TEST |
21. What is the equation, in standard form, of the hyper- |
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bola having foci at (0, 4) and (6, 4) and vertices (1, 4) |
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and (5, 4)? |
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(A) |
(x − 3)2 |
− |
(y − 4)2 |
= 1 |
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49
(B)(x − 3)2 − (y − 4)2 = 1
54
(C) |
(x − 3)2 |
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(y − 4)2 |
= 1 |
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4 |
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(D) |
(y − 4)2 |
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(x − 3)2 |
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(x − 3)2 |
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(y − 4)2 |
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(E) |
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22.In how many ways can the letters of the word NUMBER be arranged using all of the letters?
(A)16
(B)24
(C)120
(D)720
(E)5,040
23.The second term of a geometric sequence is 6 and the
5th term is 81. What is the common ratio of the 4
sequence?
(A)
(B)
(C)
2
(D)
3
6
(E) 3
4
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CHAPTER 3 / DIAGNOSTIC TEST |
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24. If x2 − 5x + 1 = (x − a)2 + c, then what is the value |
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of c? |
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(A)− 29 4
(B)− 21 4
(C)− 5 2
(D)− 25 4
(E)1
25.Solve 3x − 5 x − 2 = 0
(A){19 , 4}1
(B) ⎩9
(C){4}
(D), 4
9
(E){−4}
26.If 162 − x = 88 − x, then x =
(A)16
(B)−16
(C)−3
(D)32
(E)8 1
27. If f (x) = 4x + 1 and g(x) = x2 − 3x + 1, then ( f + g)(−2) =
(A)8
(B)−7
(C)−8
(D)4
(E)3
28.(2x − 1)5 =
(A)32x5 + 80x4 + 80x3 + 40x2 + 10x + 1
(B)32x5 − 80x4 + 80x3 − 40x2 + 10x − 1
(C)(2x − 1)(8x3 − 12x2 + 6x − 1)
(D)32x5 − 1
(E)x5 − 5x4 + 10x3 − 10x2 + 5x − 1
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PART I / ABOUT THE SAT MATH LEVEL 2 TEST |
29. How many different chords can be drawn from 8 dis- |
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tinct points on a circle? |
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(A) |
48 |
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(B) |
7 |
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(C) |
8 |
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(D) |
16 |
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(E) |
28 |
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30. The diagonals of a rhombus measure 24 and 18 inches. |
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What is the measure of the larger angle of the |
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rhombus? |
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(A) |
73.7° |
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(B) |
53.1° |
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(C) |
145° |
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(D) |
120° |
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(E) |
106.3° |
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31. The first three terms of an arithmetic sequence are |
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3n, 6n − 2, and 8n + 1 where n is any real number. |
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What is the value of the fourth term of the sequence? |
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(A) |
41 |
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(B) |
56 |
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(C) |
54 |
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(D) |
58 |
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(E) |
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32. Which of the following is NOT a factor of x4 − 3x3 − 11x2 + 3x + 10?
(A)x + 1
(B)x − 1
(C)x + 2
(D)x − 2
(E)x − 5
33. f (x) = ax2 + bx + c for all real numbers x. If f (0) = −1, f (1) = 3, and f (2) = 5, then what is f (x)?
(A)2x2 + 2x − 1
(B)−x2 + 5x − 1
(C)x2 + 3x − 1
(D)x2 + 4x − 1
(E)−2x2 + 6x − 1
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CHAPTER 3 |
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DIAGNOSTIC TEST |
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34. If ( a |
b ) |
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= 10b2 and a and b are nonzero real |
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numbers, then which of the following could equal a? |
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(A)10
(B)0.1
(C)10
(D)4 10
(E)−10
35.In a class of 25 students, 80% are passing the class with a grade of C or better. If two students are randomly selected from the class, what is the probability that neither student is passing with a grade of C or better?
(A)0.03
(B)0.20
(C)0.08
(D)0.63
(E)0.64
36.If, for all real numbers x, f (4x − 8) = 2x − 2, then f (x) could equal which of the following?
(A) |
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x |
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4 |
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(B) |
4x − 4 |
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(C) |
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x + 2 |
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(D) |
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x − 2 |
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(E) |
2x − 4 |
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37. If f (x) = 2x3 + 6, then what is f −1(−10)?
(A) |
1.26 |
(B) |
−2 |
(C) |
−7.08 |
(D) |
−2.52 |
(E) |
2.83 |
38. What are the intercepts of the circle given by the equation (x + 3)2 + (y − 3)2 = 9?
(A) |
(−3, 3) |
(B) |
(0, 3) |
(C) |
(0, ± 3), (± 3, 0) |
(D) |
(0, 3), (−3, 0) |
(E) |
(0, −3), (3, 0) |
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