ACT Math Practice Test 1 (60 Question Full Test OR Review Question Solution)

ACT Math Practice Test 1 (60 Question Full Test OR Download PDF): Students can either download free printable ACT Math practice test question answers or participate in the full-length online test with 60 minutes time limit. You can also prepare your math skill by reviewing the questions with solution.

Test Name	ACT Test Prep
Category	Free ACT Practice Test
Knowledge tested in Math	algebra, geometry, and trigonometry
Type of Question	Sample Multiple Choice
What should I do?	either join the free full-length test or review question and solution
Total Question (MCQ)	60
Total time duration	60 minute (1 hour)
Answers Available	YES
Solution / Explanation	YES
Printable PDF	YES

ACT Math Practice Test Online Quiz

(60 Question – 1 hr. Full Test)
To Stat the Quiz – Click on “Start Quiz Button” as shown below

ACT Math Practice Test 1 (Review & Solution)

For each problem, choose the correct answer. You are allowed to use a calculator on this test for any problems you choose. Unless the problem states otherwise, you should assume that figures are not drawn to scale. For this test, all geometric figures lie in a plane, the word line refers to a straight line, and the word average refers to the arithmetic mean.

1. The expression a[b – (c – d)] is equivalent to

• A). ab – ac – ad
• B). ab + ac – ad
• C). ab – c – d
• D). ab – ac + ad
• E). ab – c + d

Q2. To date, a student has four test scores of 81, 87, 91, and 86. What must he receive on his fifth test to achieve an average of 88 for the five tests?

• A). 65
• B). 75
• C). 85
• D). 90
• E). 95

Q3. What two distinct integers should be placed in the blank spaces so that the difference between the four integers is the same? 23, ____, ____, 62

• A). 36, 49
• B). 27, 43
• C). 33, 39
• D). 29, 49
• E). 26, 39

Q4. Sasha ran 2 \frac13  miles on Monday,  3 \frac34  miles on Tuesday, and 5 \frac23 miles on Wednesday. How many miles in total did she run in those three days?

• A). 10 \frac13
• B). 10 \frac49
• C).  11 \frac59
• D). 11 \frac34
• E). 12 \frac19

Q5. What is the value of the expression h (h + 1)² for h = 3?

• A). 14
• B). 32
• C). 48
• D). 97
• E). 144

Q6. Company X sells 80 markers for $49.60, and Company Y sells 125 of the same markers for $72.50. Which company offers a better price per marker, and how much less is its price?

• A). Company X, 4 cents
• B). Company X, 2 cents
• C). Company Y, 4 cents
• D). Company Y, 58 cents
• E).The costs are the same

Q7. A rectangular lot is entirely enclosed by a fence. If the lot measures 225 feet long and 165 feet wide, what is the length, in yards, of the fence?

• A). 260
• B). 360
• C). 960
• D). 1160
• E). 1260

Q8. A ladder is 16 feet long and reaches 10 feet up a wall. Approximately how many feet from the bottom of the wall is the base of the ladder?

• A). 5.5
• B). 8.5
• C). 9
• D). 10.9
• E). 12.5

Q9. If 7x – 12 = 11x + 24, then x =

• A).  –1
• B). –3
• C). –5
• D). –6
• E). –9

Q10. Mr Johnson teaches fifth grade at Littleton Elementary School and earns $21,850 for teaching a 190-day school year. He is going on a five-day vacation, and his substitute will be paid $90 per day. How much money will Littleton Elementary School save while Mr Johnson is away?

• A). $125
• B). $155
• C). $325
• D).$1125
• E). $2125

Q11. If x is a real number so that x³ = 125, then 2(x² + x) = ?

• A). 15
• B). 30
• C). 60
• D). 120
• E). 160

Q12. If a marble is chosen at random from a bag that contains 16 blue marbles, 12 red marbles, 6 green marbles, and 10 white marbles, what is the probability that the marble chosen will NOT be blue?

• A). 7/11
• B). 9/11
• C). 16/11
• D). 1/11
• E). 17/11

Q13. For all values of x, the quantity (5x + 2)² = 

• A). 10x² + 4
• B). 25x² + 4
• C). 25x² + 10x + 4
• D). 10x² + 10x + 4
• E). 25x² + 20x + 4

Q14. On the number line of all real numbers, what is the midpoint of –12 and 20?

• A). 1
• B). -2
• C). 4
• D). 6
• E). 10

Use the following information to answer questions 15 through 17. The chart shows the current enrollment in classes at St. Middle School.

Q15. What is the average number of students taking a class during period 1?

• A). 22
• B). 23
• C). 27
• D). 26
• E). 28

Q16. During which period do the fewest students take class?

• A). 2
• B). 4
• C). 1
• D). 3
• E). 5

Q17. The school owns 52 chairs, but 6 are broken. For which, period(s) will there not be enough chairs to seat all of the students in classes?

• A). period 1 only
• B). period 4 only
• C). periods 1 and 4
• D). all but period 4
• E). all of the periods

Q18. The formula for the volume V of a sphere with a radius of r is V = 3/4 π r³. If a spherical ball has a radius of 3 (1/4) inch, what is its volume to the nearest cubic inch?

• A). 9
• B). 13
• C). 21
• D). 83
• E). 143

Q19. Celia has five blouses, four pairs of pants, three scarves, and three hats. If every outfit must include one blouse, one pair of pants, one scarf, and one hat, how many different outfits can Celia create?

• A). 15
• B). 30
• C). 90
• D). 180
• E). 360

Q20. Wool socks cost $9.60 for a package of three pairs of socks. If you buy three packages, you receive one free pair of wool socks. What would be the average cost of a pair of socks when you buy three packages?

• A). $2.60
• B). $2.80
• C). $2.88
• D). $3.08
• E). $3.20

Q21. For the system of linear equations shown, which of the following would describe the graph of this system in a standard coordinate plane? 2y = –4x + 7 and 2y = 4x – 7

• A). a single line with a positive slope
• B). a single line with a negative slope
• C). two parallel lines with positive slopes
• D). two parallel lines with negative slopes
• E). two distinct intersecting lines

Q22. Which of the following is a solution to the quadratic equation x² – 24x = 0?

• A). 24
• B). -21
• C). -36
• D). 23
• E). 2

Q23. At Mount Pleasant Ski Resort, 300,000 tons of snow are required to cover 1.5 acres of ski slope. How much snow would be required to cover 6.5 acres?

• A). 1,333,000 tons
• B). 1,300,000 tons
• C). 1,700,000 tons
• D). 1,255,000 tons
• E). 900,000 tons

Q24. In the right triangle Δ ABC shown, tangent B =

• A). b/c
• B). a/b
• C). c/a
• D). a/c
• E). b/a

Q25. A rectangle measures 32 yards by 46 yards. What is the approximate measurement, in feet, of the diagonal of this rectangle?

• A). 16
• B). 68
• C). 168
• D). 268
• E). 368

Q26. For what values of x will the equation (x + a)(x – a) = 0 be true?

• A).  a and x
• B). –a and –x
• C).  x and 0
• D). –a and a
• E). none of the above

Q27. On the number line shown, an object moves from A to B, from B to C, from C to D, and finally from D to E. What is the total distance the object moves?

• A). 12
• B). 18
• C). 36
• D). 47
• E). 58

Q28. What number can you add to the numerator and denominator of \frac{8}{13}  to get 6?

• A). -4
• B).  -12
• C). -14
• D). 4
• E). 13

Q29. For what value of x is the equation log_x 64 = 3?

• A). 1
• B). 2
• C). 4
• D). 8
• E). 16

Q30. In circle C, shown here, a chord 32 inches long is 10 inches from the center of the circle. What is the radius of the circle, to the nearest tenth of an inch?

• A). 18.9
• B). 16.7
• C). 21.9
• D). 19.3
• E). 14.9

Q31. The formula for the length of a spring is given by the equation L= \frac23 F + 0.03 where F is the applied force, in newtons. What is the force, in newtons, if the length of the spring is 0.83 meters? 

• A). 0.5
• B). 1.2
• C). 1.8
• D). 2.2
• E). 0.3

Q32. If y = x + 2, then (x – y)⁵ =

• A). –32
• B). –16
• C). –62
• D). –39
• E). 123

Q33. A mall has the shape and dimensions, in blocks, indicated in the diagram. There is a statue located halfway in between points E and B. What is the location of the statue relative to point C?

• A). 16 blocks west and 4 blocks south
• B). 17 blocks west and 5 blocks south
• C). 14 blocks west and 8 blocks south
• D). 18 blocks west and 5 blocks north
• E). 6 blocks east and 4 blocks north

Q34. A circle C is inscribed in a square as shown. If the area of the square is 256 units square, what is the radius of the circle?

• A). 2 units
• B). 4 units
• C). 8 units
• D). 16 units
• E). 32 units

Q35. In the standard coordinate plane, what is the y-coordinate of the point of intersection of the two lines y = 4x – 6 and y = 2x + 2?

• A). 4
• B). 6
• C). 10
• D). 18
• E). 30

Q36. The ratio of three sides of a triangle is 16:19:28. If the length of the short side of a similar triangle is 20, what is the length of the longest side of the similar triangle?

• A). 29
• B). 31
• C). 32
• D). 33
• E). 35

Q37. Which of the following inequalities describes the solution set for the inequality 25 – 6x ≥ 9?

• A). x ≥ \frac83  
• B).  x ≥ - \frac83  
• C).  x ≤ - \frac83  
• D).  x ≤ \frac83  
• E).  x ≥ \frac23  

Q38. The solution set of \sqrt{x-1} > 7 is the set of all real numbers where

• A). x > 6
• B). x > 9
• C). x > 50
• D). x > 62
• E). x > 72

Q39. In the standard coordinate plane, what is the distance between the points (6,–2) and (–4,8)?

• A). √18
• B). 10√2
• C). 10√6
• D). 10√9
• E). 10√7

Q40. In the figure, points A, B, C, and D are collinear. Angles A, E, F, and D are as marked. What is the measure of angle G?

• A). 50°
• B). 70°
• C). 80°
• D). 90°
• E). 110°

Q41. Light travels at approximately 186,000 miles per second. At that rate, approximately how many miles will it travel in 3 hours?

• A). 1.6 × 10⁵
• B). 1.6 × 10⁸
• C). 2.0 × 10⁸
• D). 2.0 × 10⁹
• E). 2.2 × 10⁹

Q42. The ratio of the diameters of two circles is 6:10. What is the ratio of their areas?

• A). 3:5
• B). 3:25
• C). 6:5
• D). 6:25
• E). 9:25

Q43. Hexagons, as pictured here, have nine diagonals. How many diagonals does the octagon have?

• A). 10
• B). 16
• C). 20
• D). 24
• E). 28

Q44. If 80% of a number is 260, what is 116% of the same number?

• A). 311
• B). 317
• C). 349
• D). 377
• E). 397

Q45. Of the 504 girls in Radcliffe Day School, \frac38  are left-handed and \frac23 of those have brown hair. How many brown-haired, left-handed girls attend Radcliffe Day School?

• A). 94
• B). 126
• C). 136
• D). 156
• E). 166

Q46. As shown here, Xs are arranged in a triangular pattern by adding two Xs to each additional row. If n = number of rows, which of the following properly describes the total number of Xs in the triangular pattern for any value of n?

X
X X X
X X X X X X
X X X X X X X
X X X X X X X X X

• A). n + 2
• B). n – 3
• C). 2n – 1
• D). 2n + 2
• E). n²

Q47. In the right triangle pictured, sin(C) × tan(B) =

• A). a²
• B). a/b
• C). b/a
• D). 1
• E). b²

Q48. Alice is about to cover a patch of her backyard with decorative bricks that measure 2 inches by 6 inches. The area she wishes to cover measures 6 feet by 12 feet. What is the minimum number of bricks she must use to cover such an area?

• A). 720
• B). 864
• C). 995
• D). 1024
• E). 1864

Q49. If the imaginary number i² = –1, then the complex number operation of

\frac{1}{i-1} • \frac{i+1}{i+1} =?

• A). i – 1
• B). i + 1
• C). 1 – i
• D). (i + 1) / 2
• E). (i + 1) / -2

Q50. In the standard coordinate plane, a circle is tangent to the y-axis at 5 and tangent to the x-axis at –5. What is the equation of the circle?

• A). x² + y² = 5
• B). x² + y² = 25
• C). (x + 5)² + (y – 5)² = 25
• D). (x + 5)² + (y + 5)² = 25
• E). (x – 5)² + (y + 5)² = 25

Q51. If the ratio of x:y is 4:5, and the ratio of y:z is 8:9, what is the ratio of x:z?

• A). 8:10
• B). 16:15
• C). 32:45
• D). 36: 40
• E). 55:10

Q52. There are 420 people living in a small town. The 190 men have an average age of 42, and the women have an average age of 37. What is the average age, to the nearest year, of the residents of the town?

• A). 39
• B). 40
• C). 45
• D). 49
• E). 51

Q53. In the graph, the x-axis is intersected by the graph at π/2, 3π/2, 5π/2, 7π/2, and so on. The curve over anyone interval is a repetition of the other intervals. What is the period of the function?

• A). π/2
• B). π
• C). 2π
• D). 3π
• E). 3π/2

Q54. Two triangular prisms are similar. The smaller one has a triangular face with an altitude of 10, and the larger one has a triangular face with an altitude of 15. If the volume of the smaller prism is 4,000, what is the volume of the larger prism?

• A). 9,500
• B). 11,500
• C). 13,500
• D). 16,500
• E). 17,500

Q55. If (x – 3) is a factor of the equation 3×2 – 11x + n, what is the value of n?

• A). –6
• B). 6
• C). 10
• D). 24
• E). 32

Q56. If f(x) = 2x² + 2, then f(x + k) = 

• A). 2x² + 4kx + 2
• B). 2x² + 2k + 2
• C). 2x² + 2k² + 2
• D). 4x² + 2k² + 2
• E). 2x² + 4kx + 2k² + 2

Q57. If sin a =- \frac45 and π < a < \frac{3π}{2} then then cos a = 

• A). -(3/5)
• B). 3/5
• C). 4/5
• D). -4/5
• E). 3/4

Q58.  Which of the following graphs would be the correct graph of the equation y = \frac{3x^2+3x}{x}

Q59. Given the pair of equations A = 6C + 4 and B = –3C – 5, express the value of A in terms of B.

• A). –2B – 6
• B). 2B – 6
• C). –2B + 6
• D). 3B – 1
• E). 2B + 6

Q60. A guitar was marked to be sold in a store for $120 and then marked down 15%. A month later it was marked down an additional 5%. If the same guitar was available online for $100, what percent could be saved by buying it at the store after the second markdown?

• A). 0.31%
• B). 0.4%
• C). 3.1%
• D). 4.0%
• E). 23.1%

ACT Math Practice Test Question Answers [PDF Worksheet]

Document Type	Download Link
Free Editable Doc File
Free Printable PDF File