1. If f(x) = 8x – 9 and g(x) = f(2x) + 5, what is g(3)? (A) (B) (C) (D) (E)
13 34 39 44 52
3. After b games, Maurice's basketball team had scored an average of 60 points per game. Then they played 4 games in which they averaged 84 points per game, which changed their overall average to 72 points per game. What is b? (A) (B) (C) (D) (E)
2 3 4 5 6
2. Lindsey and Jordan each randomly choose one marble from a bag that contains 3 black marbles, 2 green marbles, and 1 red marble. Assuming they do not return the marbles to the bag after they pick, what is the probability that Lindsey picks a green marble and Jordan picks a red one? (A) (B) (C) (D) (E)
1 5 1 6 1 10 1 15 1 30
4. In the figure above, points A, B, C, and D lie on the circle, N is the center of the circle, and AD⊥BC. What fraction of the circle is shaded? (A) 1π (B) 1 −
1 π
1 2π 1 (D) 2 π (E) It cannot be determined from the information given. (C)
PWN the SAT - Math Diagnostic Drill #2 (page #1)
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5. If 6 numbers have an average of –6 , and 4 of the numbers have a sum of 10, then what is the average of the other 2 numbers? (A) (B) (C) (D) (E)
16 2 –23 –26 –46
6. Line m passes through the points (3, 2) and (5, p). If line l is perpendicular to line m, which of the following equations could represent line l? (A) (B) (C) (D) (E)
2 y =− x 3 p−2 p y = x− 1 2 2 y =− x− 8 p2 1 y= x− 5 2 p−4 2 y =− x−3 5− p
8. In rABC, AB = 11 and BC = 15. Which of the following could NOT be the perimeter of rABC? (A) (B) (C) (D) (E)
30 33 40 49.5 51
9. If 6x – 15y = 18 and 2x + 7y = 30, what is x – y? (A) (B) (C) (D) (E)
1.5 6 12 18 48
10. Let cßd be defined as c2 – 10d for all values of c and d. If 11ßm = 81, what is the value of m?
7. What is the volume of the smallest cube that could completely contain a sphere with a radius of r? (A) (B) (C) (D) (E)
(A) (B) (C) (D) (E)
9 6 4 2 1
r3 3r3 4r3 5r3 8r3
PWN the SAT - Math Diagnostic Drill #2 (page #2)
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11. If 4m + n = q, what is 42m + 2n ? (A) (B) (C) (D) (E)
2q 4q q2 2q2 8q2
13. If p2 + q2 = 18, and pq = 9, what is (p – q)2? (A) (B) (C) (D) (E)
0 2 9 27 36
1, 4, 16, 64, ... 14. In the sequence above, each term after the first is determined by multiplying the previous term by 4. Which of the following must be true? I. The nth term in the pattern is equal to 4n II. The nth term in the pattern is equal to 22(n – 1) III. The units digit of the 53rd term is 6 Note: Figure not drawn to scale. 12. In the figure above, AB = x, BC = y, and AB and MN are perpendicular to BC. If BN = 0.2y, what is the area of the shaded region, in terms of x and y? (A) (B) (C) (D) (E)
0.40xy 0.32xy 0.25xy 0.18xy 0.14xy
(A) (B) (C) (D) (E)
15. In the xy-plane, a circle with center (m, n) touches the y-axis at at exactly one point and touches the x-axis at exactly one point. Which of the following must be true? (A) (B) (C) (D) (E)
PWN the SAT - Math Diagnostic Drill #2 (page #3)
I only II only III only II and III only I, II, and III
m+n=0 m=n m–n=0 mn = m2 |m| = |n|
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16. Sharon has 20 water balloons in her bucket and Michelle has 3 in hers. Sharon is tossing water balloons to Michelle, who is trying her best to catch them and put them in her bucket. If every 3rd toss results in a dropped and broken balloon, how many tosses have to occur for the two girls have the same number of balloons? (A) (B) (C) (D) (E)
12 11 10 9 8
18. In the figure above, ABCD is a square, and A, B, C, and D are the centers of four congruent circles which touch each other but do not overlap. If the area of ABCD is 1, what is the perimeter of the shaded region? (A) (B) (C) (D) (E) x
f(x)
g(x)
–2
–7
–9
–1
3
1
0
3
–2
1
2
6
2
–1
–3
3
5
8
17. According to the table above, if f(1) = n, what is g(n–2)? (A) (B) (C) (D) (E)
–9 –2 0 1 6
PWN the SAT - Math Diagnostic Drill #2 (page #4)
3π 4π 6π 7π 9π
19. The length of one leg of a right triangle is increased by 15%, and the length of the other leg is decreased by 20%. The new triangle's area is what percent of the original triangle's area? (A) (B) (C) (D) (E)
46% 92% 95% 96% 105%
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20. The lowest score on the most recent chemistry exam in Professor Wren's class was a 39, and the highest score was a 75. Which inequality could be used to determine whether a particular score, s, could have come from Professor Wren's class? (A) (B) (C) (D) (E)
|s – 39| ≤ 75 |s – 20| ≤ 57 |s – 18| ≤ 55 |s – 60| ≤ 17 |s – 57| ≤ 18
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PWN the SAT - Math Diagnostic Drill #2 (page #5)
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