Digital SAT — Practice Test 2: Math

Total questions: 44 · Total marks: 44 · Duration: 70 minutes (two 35-minute modules)

Instructions to candidates

• This section has two modules of 22 questions each. On the real Digital SAT, Module 2's difficulty adapts to your Module 1 performance; this practice test presents a representative mix.
• A calculator is allowed on all Math questions.
• Each question is worth ONE raw mark. There is no penalty for wrong answers — answer every question.
• Choose the single best answer.

Module 1 (22 questions · 35 minutes)

1. If 6x − 5 = 19, what is x? (A) 3 (B) 4 (C) 5 (D) 6
2. What is 40% of 90? (A) 27 (B) 36 (C) 45 (D) 50
3. A line passes through (0, 4) with slope −2. Its equation is: (A) y = −2x + 4 (B) y = 2x + 4 (C) y = −2x − 4 (D) y = 4x − 2
4. If f(x) = 3x + 7, what is f(4)? (A) 12 (B) 17 (C) 19 (D) 21
5. The average of 6, 10, and 14 is: (A) 8 (B) 10 (C) 12 (D) 30
6. Solve: 4x + 3 = 2x + 15. (A) 4 (B) 6 (C) 8 (D) 9
7. A rectangle is 7 by 9. Its area is: (A) 16 (B) 32 (C) 63 (D) 79
8. Simplify x⁵ · x². (A) x³ (B) x⁷ (C) x¹⁰ (D) x²·⁵
9. If 3/4 of a number is 27, the number is: (A) 20 (B) 28 (C) 36 (D) 40
10. A runner covers 12 km in 1.5 hours. Speed (km/h)? (A) 6 (B) 8 (C) 9 (D) 18
11. Factor x² − 6x + 8. (A) (x − 2)(x − 4) (B) (x + 2)(x + 4) (C) (x − 1)(x − 8) (D) (x − 2)(x + 4)
12. A right triangle has legs 9 and 12. Hypotenuse? (A) 13 (B) 15 (C) 18 (D) 21
13. A $60 item is discounted 25%. Sale price? (A) $40 (B) $45 (C) $48 (D) $50
14. The line y = mx − 1 passes through (3, 8). What is m? (A) 2 (B) 3 (C) 4 (D) 5
15. Evaluate 4² − 2 × 5. (A) 6 (B) 10 (C) 16 (D) 26
16. A circle has radius 6. Circumference (2πr)? (A) 6π (B) 12π (C) 36π (D) 18π
17. If a : b = 3 : 4 and a = 9, then b = ? (A) 10 (B) 12 (C) 13 (D) 16
18. Expand (x − 4)(x + 2). (A) x² − 2x − 8 (B) x² + 2x − 8 (C) x² − 6x − 8 (D) x² − 2x + 8
19. A bag has 5 red and 5 blue marbles. P(red)? (A) 1/5 (B) 1/2 (C) 2/5 (D) 1/10
20. Two angles are complementary; one is 28°. The other? (A) 52° (B) 62° (C) 72° (D) 152°
21. If 3^x = 81, what is x? (A) 3 (B) 4 (C) 5 (D) 27
22. A plumber charges $50 plus $25/hour. Equation for cost c over h hours? (A) c = 50h + 25 (B) c = 25h + 50 (C) c = 75h (D) c = 25 + 50h

Module 2 (22 questions · 35 minutes)

23. If 2(x − 4) = x + 1, what is x? (A) 7 (B) 8 (C) 9 (D) 10
24. The vertex of y = (x + 2)² + 1 is: (A) (2, 1) (B) (−2, 1) (C) (−2, −1) (D) (1, −2)
25. A quantity grows 10% on 200. New value? (A) 210 (B) 220 (C) 240 (D) 260
26. If g(x) = x² − 9x, for what positive x is g(x) = 0? (A) 3 (B) 6 (C) 9 (D) 18
27. A scale is 1 inch = 8 miles. 5 inches = ? (A) 32 (B) 40 (C) 45 (D) 48
28. Median of 3, 8, 8, 10, 15, 18? (A) 8 (B) 9 (C) 10 (D) 11
29. If √x = 9, then x = ? (A) 18 (B) 27 (C) 81 (D) 90
30. A cube has edge 4. Its volume? (A) 12 (B) 16 (C) 48 (D) 64
31. Solve: y = 2x − 3 and x + y = 9. What is x? (A) 3 (B) 4 (C) 5 (D) 6
32. A price falls from $120 to $90. Percent decrease? (A) 20% (B) 25% (C) 30% (D) 33%
33. If f(x) = 4x + 1 and f(x) = 21, what is x? (A) 4 (B) 5 (C) 6 (D) 80
34. A rectangle's length is 3 more than its width. If perimeter is 26, width = ? (A) 5 (B) 6 (C) 7 (D) 8
35. The discriminant of x² + 2x + 5 = 0 is: (A) −16 (B) 4 (C) 16 (D) 24
36. In a right triangle, cos(θ) = 8/17. What is the opposite side if hypotenuse is 17? (A) 8 (B) 12 (C) 15 (D) 17
37. A recipe uses 4 eggs for 16 muffins. For 24 muffins, eggs needed? (A) 5 (B) 6 (C) 7 (D) 8
38. Solve x² = 3x + 10 (positive solution). (A) 2 (B) 5 (C) 6 (D) 10
39. Sum of interior angles of a hexagon? (A) 540° (B) 720° (C) 900° (D) 1080°
40. The mode of 5, 7, 7, 9, 9, 9, 12 is: (A) 7 (B) 9 (C) 8 (D) 12
41. The slope of the line through (−1, 2) and (2, 11) is: (A) 2 (B) 3 (C) 4 (D) 9
42. 35% of a class of 40 wear glasses. How many do? (A) 12 (B) 14 (C) 16 (D) 18
43. Simplify (3x²)³. (A) 9x⁶ (B) 27x⁵ (C) 27x⁶ (D) 3x⁶
44. A ladder 17 ft long has its base 8 ft from a wall. How high does it reach? (A) 9 ft (B) 13 ft (C) 15 ft (D) 16 ft