Digital SAT — Practice Test 1: 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 both modules at 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 4x + 9 = 33, what is the value of x? (A) 4 (B) 6 (C) 8 (D) 24
2. A line passes through (0, −2) with slope 3. What is its equation? (A) y = 3x − 2 (B) y = −2x + 3 (C) y = 3x + 2 (D) y = 2x − 3
3. What is 30% of 250? (A) 60 (B) 75 (C) 80 (D) 90
4. If f(x) = 2x² − 1, what is f(3)? (A) 11 (B) 17 (C) 18 (D) 35
5. The mean of 5, 9, 13, and x is 10. What is x? (A) 8 (B) 11 (C) 13 (D) 15
6. Solve: 5(x − 3) = 2x + 6. (A) 3 (B) 5 (C) 7 (D) 9
7. A triangle has base 12 and height 5. What is its area? (A) 17 (B) 30 (C) 34 (D) 60
8. Simplify (x⁴)(x³). (A) x¹ (B) x⁷ (C) x¹² (D) x¹²
9. If 2/5 of a number is 18, what is the number? (A) 36 (B) 40 (C) 45 (D) 90
10. A car travels 240 miles in 4 hours. What is its average speed (mph)? (A) 50 (B) 55 (C) 60 (D) 64
11. The solutions to x² − 7x + 12 = 0 are: (A) 2 and 6 (B) 3 and 4 (C) −3 and −4 (D) 1 and 12
12. A right triangle has legs 6 and 8. What is the hypotenuse? (A) 10 (B) 12 (C) 14 (D) 48
13. If a shirt is marked down 20% from $45, what is the sale price? (A) $25 (B) $36 (C) $38 (D) $40
14. The line y = mx + 4 passes through (2, 10). What is m? (A) 2 (B) 3 (C) 5 (D) 7
15. What is the value of 3² + 4 × 2? (A) 14 (B) 17 (C) 20 (D) 26
16. A circle has radius 4. What is its area? (Use πr²) (A) 8π (B) 12π (C) 16π (D) 64π
17. If x : y = 2 : 3 and y = 12, what is x? (A) 6 (B) 8 (C) 9 (D) 18
18. The expression (x + 5)(x − 3) equals: (A) x² + 2x − 15 (B) x² − 2x − 15 (C) x² + 8x − 15 (D) x² + 2x + 15
19. A bag has 4 green and 6 yellow marbles. P(green) = ? (A) 2/5 (B) 3/5 (C) 4/6 (D) 1/4
20. Two angles are supplementary; one is 125°. The other is: (A) 45° (B) 55° (C) 65° (D) 75°
21. If 2^x = 32, what is x? (A) 4 (B) 5 (C) 6 (D) 16
22. A worker earns $16/hour plus a $40 bonus. Which equation gives pay p for h hours? (A) p = 40h + 16 (B) p = 16h + 40 (C) p = 56h (D) p = 16 + 40h

Module 2 (22 questions · 35 minutes)

23. If 3(x + 2) − 4 = 2x + 7, what is x? (A) 3 (B) 5 (C) 7 (D) 9
24. The vertex of y = (x − 3)² − 5 is at: (A) (3, −5) (B) (−3, 5) (C) (3, 5) (D) (5, −3)
25. A population of 800 grows 5% per year. After 1 year, the population is: (A) 805 (B) 840 (C) 880 (D) 1200
26. If g(x) = x² − 4x, for what positive x is g(x) = 0? (A) 2 (B) 4 (C) 6 (D) 8
27. A map scale is 1 cm = 15 km. A distance of 6 cm represents: (A) 60 km (B) 75 km (C) 90 km (D) 21 km
28. The median of 4, 6, 9, 11, 13, 20 is: (A) 9 (B) 10 (C) 11 (D) 11.5
29. If √x = 7, what is x? (A) 14 (B) 28 (C) 49 (D) 343
30. A cylinder has radius 3 and height 10. Its volume (πr²h) is: (A) 30π (B) 60π (C) 90π (D) 300π
31. Solve the system: y = x + 1 and 2x + y = 7. What is x? (A) 2 (B) 3 (C) 4 (D) 5
32. The price of a stock rose from $80 to $100. The percent increase is: (A) 20% (B) 25% (C) 30% (D) 80%
33. If f(x) = 5x − 2 and f(x) = 13, what is x? (A) 2 (B) 3 (C) 4 (D) 5
34. A rectangle's length is twice its width. If the perimeter is 36, the width is: (A) 6 (B) 8 (C) 9 (D) 12
35. The discriminant of x² + 6x + 9 = 0 is: (A) 0 (B) 6 (C) 9 (D) 36
36. In a right triangle, sin(θ) = 3/5. What is cos(θ)? (A) 3/4 (B) 4/5 (C) 5/3 (D) 5/4
37. A recipe needs 3 cups flour per 12 cookies. For 20 cookies, how many cups? (A) 4 (B) 5 (C) 6 (D) 7
38. If x² = 2x + 8, the positive solution is: (A) 2 (B) 4 (C) 6 (D) 8
39. A regular pentagon's interior angles sum to: (A) 360° (B) 540° (C) 720° (D) 900°
40. Data set: 2, 4, 4, 4, 6, 10. The mode is: (A) 4 (B) 5 (C) 6 (D) 10
41. The line through (1, 4) and (3, 10) has slope: (A) 2 (B) 3 (C) 4 (D) 6
42. If 40% of a class of 30 students play sports, how many do NOT? (A) 12 (B) 15 (C) 18 (D) 20
43. Simplify: (2x³)². (A) 2x⁶ (B) 4x⁵ (C) 4x⁶ (D) 4x⁹
44. A 13-foot ladder leans so its base is 5 feet from the wall. How high up the wall does it reach? (A) 11 ft (B) 12 ft (C) 13 ft (D) 17 ft