ACT Math — Practice Test 1

Pre-algebra

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1. Compute. 2/3 + 1/4

2. Compute. 0.6 × 0.25

3. A recipe uses flour and sugar in a ratio of 5 : 2. If 20 cups of flour are used, how many cups of sugar are needed?

4. A car travels 150 miles in 3 hours. At the same rate, how many miles will it travel in 5 hours?

5. What is 35% of 80?

6. A sweater is on sale for 20% off its original price of $45. What is the sale price?

7. The numbers of books five students read are 4, 7, 9, 5, 10. What is the mean?

8. A bag contains 3 red, 4 blue, and 5 green marbles. If one marble is chosen at random, what is the probability that it is blue?

9. Solve. 4x − 7 = 17

10. Solve. 3(x + 2) = 21

11. Evaluate. |−9| + |4|

12. What is the next term in the arithmetic sequence 4, 9, 14, 19, … ?

13. A restaurant offers 4 appetizers, 6 entrées, and 3 desserts. How many different 3-course meals (one of each) are possible?

14. Which list is in order from LEAST to GREATEST? −2.5, −5/2, −2.05, −2.55

Elementary Algebra

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15. Simplify. 3(2x − 5) − 4(x − 1)

16. Simplify. (5x^2 + 3x − 4) + (2x^2 − 7x + 6)

17. Multiply. (x + 5)(x − 2)

18. Factor completely. x^2 + 8x + 15

19. Factor completely. 4x^2 − 25

20. Factor out the GCF. 6x^3 − 9x^2

21. Solve by factoring. x^2 − 5x + 6 = 0

22. Solve by factoring. x^2 − x − 12 = 0

23. Solve. 5x − 3 > 12

24. What is the solution to the system? y = x + 2 and y = 2x − 1

Intermediate Algebra

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25. Use the quadratic formula to solve. x^2 − 6x + 4 = 0

26. Use the quadratic formula to find the discriminant of 2x^2 + 5x − 3 = 0.

27. Simplify. (x^2 − 9) / (x + 3)

28. Simplify. √50 + √18

29. Solve. |2x − 5| = 7

30. An arithmetic sequence has first term 4 and common difference 6. What is the 10th term?

31. Solve the system. 2x + y = 7 and x − y = 2

32. Simplify. (3 + 2i) + (4 − 5i)

33. Simplify. (2x^3)(4x^2)

Coordinate Geometry

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34. What is the slope of the line through the points (2, 3) and (8, 15)?

35. What is the distance between the points (1, 2) and (4, 6)?

36. What is the midpoint of the segment with endpoints (−2, 4) and (6, 10)?

37. What is the equation of the line that passes through (2, −1) with slope 3?

38. What is the equation of a circle with center (3, −2) and radius 4?

39. Which line is PERPENDICULAR to y = (1/2)x + 4?

40. The graph of which equation is a parabola opening DOWNWARD?

41. The point (3, 5) is reflected across the x-axis. What are the coordinates of the image?

42. The equation of a circle is (x − 1)^2 + (y + 4)^2 = 25. What is the radius of the circle?

Plane Geometry

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43. A rectangle has length 12 cm and width 5 cm. What is its area?

44. A trapezoid has parallel bases of length 8 in and 14 in and a height of 6 in. What is its area?

45. A regular hexagon has a side length of 7 cm. What is its perimeter?

46. A rectangular prism has dimensions 4 × 5 × 6. What is its volume?

47. A right circular cylinder has radius 3 in and height 10 in. What is its volume? (Use V = πr^2h.)

48. What is the surface area of a cube with edge length 4?

49. Two parallel lines are cut by a transversal. One of the angles is 110°. What is the measure of the corresponding angle?

50. Two parallel lines are cut by a transversal. One interior angle on the same side of the transversal is 65°. What is the measure of the other co-interior (same-side interior) angle?

51. What is the sum of the interior angles of a regular pentagon?

52. Triangles ABC and DEF are similar. The sides of ABC are 3, 4, and 5. If the side of DEF that corresponds to the side of length 3 is 9, what is the perimeter of DEF?

53. Two triangles have congruent corresponding angles and one pair of corresponding sides in a 1 : 2 ratio. The triangles are:

54. In a 30-60-90 triangle, the side opposite the 30° angle has length 5. What is the length of the side opposite the 60° angle?

55. The legs of a right triangle measure 6 and 8. What is the length of the hypotenuse?

56. A circle has a radius of 6. What is the area of a sector with a central angle of 60°? (Express in terms of π.)

Trigonometry

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57. In a right triangle, the side opposite angle A has length 5 and the hypotenuse has length 13. What is sin A?

58. What is the value of sin 30°?

59. If sin θ = 3/5 and θ is an acute angle, what is cos θ? (Use sin^2 θ + cos^2 θ = 1.)

60. What is the period of the function y = sin(x)?

Pre-algebra

Elementary Algebra

Intermediate Algebra

Coordinate Geometry

Plane Geometry

Trigonometry

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