ACT Practice (questions change often)
Questions 1–20 (Easy)
1. What is the value of 6+4×36 + 4 \times 36+4×3?
A. 18
B. 24
C. 30
D. 36
E. 42
2. Solve for xxx: 3x+5=203x + 5 = 203x+5=20
A. 3
B. 4
C. 5
D. 6
E. 7
3. What is 12+34\frac{1}{2} + \frac{3}{4}21+43?
A. 34\frac{3}{4}43
B. 54\frac{5}{4}45
C. 74\frac{7}{4}47
D. 14\frac{1}{4}41
E. 94\frac{9}{4}49
4. What is the area of a rectangle with length 8 and width 5?
A. 13
B. 26
C. 40
D. 64
E. 80
5. If x=3x = 3x=3, what is 2x2−x2x^2 - x2x2−x?
A. 9
B. 12
C. 15
D. 18
E. 21
6. What is the value of 49\sqrt{49}49?
A. 6
B. 7
C. 8
D. 9
E. 14
7. A shirt costs $30 and is discounted by 10%. What is the sale price?
A. $25
B. $26
C. $27
D. $28
E. $29
8. Which number is divisible by both 3 and 5?
A. 10
B. 12
C. 15
D. 18
E. 20
9. What is the average of 6, 8, and 10?
A. 6
B. 7
C. 8
D. 9
E. 10
10. What is the slope of the line through (1, 2) and (3, 6)?
A. 1
B. 2
C. 3
D. 4
E. 5
11. If 4y=364y = 364y=36, what is yyy?
A. 6
B. 7
C. 8
D. 9
E. 12
12. What is the perimeter of a square with side length 7?
A. 21
B. 28
C. 35
D. 42
E. 49
13. What is ∣−9∣| -9 |∣−9∣?
A. –9
B. –3
C. 0
D. 3
E. 9
14. How many degrees are in a right angle?
A. 45
B. 60
C. 90
D. 180
E. 360
15. Solve: x−7=12x - 7 = 12x−7=12
A. 3
B. 5
C. 12
D. 17
E. 19
16. What is the value of 525^252?
A. 10
B. 15
C. 20
D. 25
E. 50
17. Which fraction is equivalent to 23\frac{2}{3}32?
A. 49\frac{4}{9}94
B. 36\frac{3}{6}63
C. 69\frac{6}{9}96
D. 26\frac{2}{6}62
E. 912\frac{9}{12}129
18. If x+y=12x + y = 12x+y=12 and x=5x = 5x=5, what is yyy?
A. 5
B. 6
C. 7
D. 8
E. 12
19. What is the area of a circle with radius 4?
A. 8π8\pi8π
B. 12π12\pi12π
C. 16π16\pi16π
D. 20π20\pi20π
E. 32π32\pi32π
20. What is the solution to 2x=142x = 142x=14?
A. 5
B. 6
C. 7
D. 8
E. 9
Questions 21–40 (Medium)
21. Solve: 2(x−4)=x+62(x - 4) = x + 62(x−4)=x+6
A. 2
B. 4
C. 6
D. 8
E. 10
22. If f(x)=3x−2f(x) = 3x - 2f(x)=3x−2, what is f(5)f(5)f(5)?
A. 11
B. 12
C. 13
D. 14
E. 15
23. The sum of the interior angles of a hexagon is:
A. 540°
B. 720°
C. 900°
D. 1080°
E. 1260°
24. Expand: (x+3)(x−4)(x + 3)(x - 4)(x+3)(x−4)
A. x2−x−12x^2 - x - 12x2−x−12
B. x2+x−12x^2 + x - 12x2+x−12
C. x2−7x+12x^2 - 7x + 12x2−7x+12
D. x2+7x−12x^2 + 7x - 12x2+7x−12
E. x2−12x^2 - 12x2−12
25. If 5a=3b5a = 3b5a=3b and a=6a = 6a=6, what is bbb?
A. 5
B. 8
C. 10
D. 12
E. 15
26. What is the probability of rolling a number greater than 4 on a standard die?
A. 16\frac{1}{6}61
B. 13\frac{1}{3}31
C. 12\frac{1}{2}21
D. 23\frac{2}{3}32
E. 56\frac{5}{6}65
27. Solve: x2−9=0x^2 - 9 = 0x2−9=0
A. 3
B. –3
C. 0
D. –3 and 3
E. No solution
28. If sinθ=12\sin \theta = \frac{1}{2}sinθ=21, where 0∘≤θ≤90∘0^\circ \le \theta \le 90^\circ0∘≤θ≤90∘, what is θ\thetaθ?
A. 15°
B. 30°
C. 45°
D. 60°
E. 90°
29. The ratio of cats to dogs is 2:3. If there are 25 animals total, how many are cats?
A. 8
B. 10
C. 12
D. 15
E. 18
30. A triangle has base 10 and height 6. What is its area?
A. 30
B. 40
C. 50
D. 60
E. 70
31. What is 4!4!4!?
A. 12
B. 16
C. 20
D. 24
E. 48
32. Solve: x5+4=10\frac{x}{5} + 4 = 105x+4=10
A. 20
B. 25
C. 30
D. 35
E. 40
33. What is the midpoint of (–4, 6) and (2, 10)?
A. (–1, 8)
B. (–2, 8)
C. (–1, 10)
D. (1, 8)
E. (2, 8)
34. Which equation has a slope of 2 and y-intercept –1?
A. y=2x−1y = 2x - 1y=2x−1
B. y=−2x+1y = -2x + 1y=−2x+1
C. y=x+2y = x + 2y=x+2
D. y=2x+1y = 2x + 1y=2x+1
E. y=x−1y = x - 1y=x−1
35. Simplify: 18x26x\frac{18x^2}{6x}6x18x2
A. 3x3x3x
B. 6x6x6x
C. 12x12x12x
D. 18x18x18x
E. 36x36x36x
36. If 3x=813^x = 813x=81, what is xxx?
A. 2
B. 3
C. 4
D. 5
E. 6
37. A right triangle has legs 9 and 12. What is the hypotenuse?
A. 13
B. 14
C. 15
D. 18
E. 21
38. What is the range of y=x2y = x^2y=x2?
A. All real numbers
B. y≤0y \le 0y≤0
C. y≥0y \ge 0y≥0
D. y≥1y \ge 1y≥1
E. y≤1y \le 1y≤1
39. How many real solutions does x2+1=0x^2 + 1 = 0x2+1=0 have?
A. 0
B. 1
C. 2
D. 3
E. Infinitely many
40. What is log10(100)\log_{10}(100)log10(100)?
A. 1
B. 2
C. 3
D. 4
E. 10
Questions 41–60 (Hard)
41. If x:y=5:8x:y = 5:8x:y=5:8 and x+y=65x + y = 65x+y=65, what is xxx?
A. 20
B. 25
C. 30
D. 35
E. 40
42. What is the equation of a circle centered at (–3, 2) with radius 4?
A. x2+y2=16x^2 + y^2 = 16x2+y2=16
B. (x+3)2+(y−2)2=16(x + 3)^2 + (y - 2)^2 = 16(x+3)2+(y−2)2=16
C. (x−3)2+(y+2)2=16(x - 3)^2 + (y + 2)^2 = 16(x−3)2+(y+2)2=16
D. (x+4)2+(y−3)2=16(x + 4)^2 + (y - 3)^2 = 16(x+4)2+(y−3)2=16
E. (x−4)2+(y+3)2=16(x - 4)^2 + (y + 3)^2 = 16(x−4)2+(y+3)2=16
43. Solve: ∣x−5∣=3|x - 5| = 3∣x−5∣=3
A. 2 only
B. 8 only
C. 5 only
D. 2 and 8
E. –2 and 8
44. What is the 12th term of an arithmetic sequence starting at 4 with common difference 3?
A. 34
B. 37
C. 40
D. 43
E. 46
45. What is the sum of the first 15 positive integers?
A. 105
B. 110
C. 120
D. 130
E. 225
46. If tanθ=3\tan \theta = \sqrt{3}tanθ=3 and 0∘<θ<90∘0^\circ < \theta < 90^\circ0∘<θ<90∘, what is θ\thetaθ?
A. 30°
B. 45°
C. 60°
D. 75°
E. 90°
47. The volume of a cube is 343. What is the length of one edge?
A. 6
B. 7
C. 8
D. 9
E. 10
48. If x3=64x^3 = 64x3=64, what is xxx?
A. 2
B. 3
C. 4
D. 8
E. 16
49. How many ways can 5 different books be arranged on a shelf?
A. 60
B. 100
C. 120
D. 240
E. 720
50. Solve the system:
2x+y=112x + y = 112x+y=11
x−y=1x - y = 1x−y=1
A. (3, 5)
B. (4, 3)
C. (5, 1)
D. (6, –1)
E. (7, –3)
51. A quantity doubles every time xxx increases by 1. This is:
A. Linear growth
B. Quadratic growth
C. Exponential growth
D. Logarithmic growth
E. Constant growth
52. What is the diagonal of a square with side length 10?
A. 10210\sqrt{2}102
B. 202020
C. 505050
D. 100100100
E. 200200200
53. If 3x=612\frac{3}{x} = \frac{6}{12}x3=126, what is xxx?
A. 3
B. 4
C. 6
D. 12
E. 24
54. What is the domain of y=x−2y = \sqrt{x - 2}y=x−2?
A. x≤2x \le 2x≤2
B. x<2x < 2x<2
C. x≥2x \ge 2x≥2
D. All real numbers
E. x≠2x \neq 2x=2
55. If two angles of a triangle are 38° and 72°, what is the third angle?
A. 60°
B. 70°
C. 80°
D. 90°
E. 110°
56. Simplify: (2x3)2(2x^3)^2(2x3)2
A. 4x54x^54x5
B. 4x64x^64x6
C. 8x68x^68x6
D. 16x616x^616x6
E. 16x916x^916x9
57. What is the probability of selecting a red card from a standard deck?
A. 152\frac{1}{52}521
B. 126\frac{1}{26}261
C. 113\frac{1}{13}131
D. 14\frac{1}{4}41
E. 12\frac{1}{2}21
58. What is the product of the roots of x2−5x+6=0x^2 - 5x + 6 = 0x2−5x+6=0?
A. 2
B. 3
C. 5
D. 6
E. 11
59. If cosθ=−1\cos \theta = -1cosθ=−1, which angle satisfies this?
A. 0°
B. 90°
C. 180°
D. 270°
E. 360°
60. A phone loses 20% of its value each year. This represents:
A. Linear decay
B. Quadratic decay
C. Exponential decay
D. Logarithmic decay
E. Constant decrease