Practice the setup as well as the calculation. These 30 original problems include worked solutions and explanations of all four choices, so you can identify the reasoning behind each mistake.
Keep scratch paper nearby. Check the units, domain restrictions and requested quantity before you submit an answer.
Showing 30 of 30 questions
Answer B. Subtract the fixed fee before dividing by the hourly rate: (29 − 8) ÷ 3 = 7 hours. Substitution gives 8 + 3(7) = 29.
Answer B. The mixture has 7 equal parts, each containing 21 ÷ 7 = 3 liters. Blue occupies 2 parts, or 6 liters.
Answer C. The discount leaves 80 × 0.75 = 60 dollars. Tax is 0.10 × 60 = 6 dollars, so the final price is 66 dollars.
Answer A. Subtract 5 to obtain −2x > 6. Dividing by −2 reverses the inequality, giving x < −3.
Answer B. If all 18 tickets were student tickets, revenue would be 144 dollars. Each adult ticket adds 4 dollars, so (184 − 144) ÷ 4 = 10 adult tickets.
Answer D. Substitute −2 everywhere: 2(−2)² − 3(−2) + 1 = 8 + 6 + 1 = 15.
Answer A. Slope is change in y divided by change in x: (−5 − 7)/(4 − (−2)) = −12/6 = −2.
Answer B. A power raised to a power multiplies exponents, so the numerator is x⁶. Division subtracts exponents: x⁶/x⁴ = x².
Answer C. Factor the expression as (x − 2)(x − 3). A product is zero when one factor is zero, so x = 2 or x = 3.
Answer D. This is a difference of squares: (3y)² − 4² = (3y − 4)(3y + 4). The cross terms cancel.
Answer D. The squared term is at least zero, so its negative is at most zero. The maximum occurs at x = 3, where h = 16.
Answer A. The path removes 1 m from each end of both dimensions. The planting rectangle is (12 − 2) by (8 − 2), or 10 × 6 = 60 m².
Answer C. The length scale factor is 15/6 = 2.5. Area scales by its square: 2.5² = 6.25.
Answer C. Cylinder volume is πr²h = π(3²)(10) = 90π cm³.
Answer B. The ladder is the hypotenuse: h² + 5² = 13². Thus h² = 144 and h = 12 feet.
Answer B. The arc is 60/360 = 1/6 of the circumference. The circumference is 2π(6) = 12π, so the arc length is 2π cm.
Answer A. Sine is opposite divided by hypotenuse, so sin θ = 8/17. The other leg is 15, but it is not needed.
Answer C. The total is 20(70) + 30(80) = 3,800 points among 50 students. The combined mean is 3,800/50 = 76.
Answer B. The six ordered values are 4, 7, 7, 10, 12, 30. The median is the average of the third and fourth values: (7 + 10)/2 = 8.5.
Answer A. The first red has probability 3/5. After it is removed, 2 of 4 tiles are red. Multiply: (3/5)(2/4) = 3/10.
Answer C. Convert the rate to 2,400 mL/min, then divide by 60 to get 40 mL/s. In 25 seconds it delivers 40 × 25 = 1,000 mL.
Answer C. An absolute value equals 7 when its input is 7 or −7. The equations give x = 4 and x = −3, two distinct solutions.
Answer B. Factor x² − 9 = (x − 3)(x + 3). Cancel the nonzero factor x − 3 to obtain x + 3, while retaining the restriction x ≠ 3.
Answer B. Set 15 + 2c = 5 + 4c. Subtract 5 and 2c to obtain 10 = 2c, so c = 5. Each plan then costs 25 dollars.
Answer C. Nine hours contains three doubling intervals. The count is 200 × 2³ = 1,600 cells.
Answer B. The tank loses 18 liters in 3 minutes, or 6 liters per minute. Two more minutes after minute 5 remove 12 liters, leaving 18.
Answer D. The original total is 4 × 12 = 48. The new total is 5 × 14 = 70. The added number is 70 − 48 = 22.
Answer B. Test the inputs. For 2x² + 1 the outputs are 1, 3, and 9. Each competing rule disagrees with at least one listed value.
Answer C. The angle sum gives x + (x + 20) + 50 = 180. Thus 2x = 110 and x = 55. The angles are 55°, 75°, and 50°, so the largest is 75°.
Answer B. There are 12 equally likely outcomes. Three pair an even number (2, 4, or 6) with heads, giving 3/12 = 1/4.
Test Ninjas · Content checked October 23, 2026
Take a first pass of five or six questions without opening the explanations. Write an equation, sketch or unit conversion before choosing an answer. You may use a calculator for arithmetic, but keep the reasoning visible: a calculator cannot decide whether a percent change uses the original amount or a new subtotal.
After checking your work, search for a skill such as slope, probability or quadratic. Use the difficulty filter to adjust the challenge and save questions you answered with uncertainty. When you revisit them, solve from the prompt before looking at the options.
The bank progresses through algebra and functions, geometry, data and applied reasoning, but it is not an official test sequence. Use the timer to observe how long a small set takes. Set official pacing targets only after confirming whether your school gives PreACT, PreACT Secure or PreACT 8/9 and which version is in use.
Translate fixed and variable costs into equations, solve a two-variable system, reverse an inequality when dividing by a negative number, simplify powers and factor a difference of squares. Restrictions such as a nonzero denominator still apply after simplification.
Evaluate a function at a negative input, interpret slope, compare linear pricing plans, find quadratic roots and a vertex maximum, and distinguish exponential growth from repeated addition. Tables connect symbolic rules to observed values.
Use similar figures, area, volume, the Pythagorean theorem, arc length, right-triangle ratios and angle sums. Length scale factors and area scale factors are different; a correct diagram often exposes that distinction.
Compute weighted means, medians, successive percent changes, probabilities with and without replacement, and rate conversions. Decide whether events are independent before multiplying their probabilities.
A discount followed by tax does not usually equal a single subtraction and addition of percentages. Apply each multiplier to the amount at that stage. For example, a 25% discount followed by 10% tax multiplies the original price by 0.75 and then by 1.10.
When all lengths scale by a factor k, area scales by k² and volume by k³. Write the units beside your answer; square units signal that a length factor alone is insufficient.
Drawing without replacement changes the second denominator. Dividing by a negative reverses an inequality. Cancelling a factor does not restore excluded inputs. Underline these conditions before calculating.
A class of 30 students contributes more observations than a class of 20. Recover each group’s total, add the totals, and divide by the combined number of observations.
You can use one while practicing, but show the setup on scratch paper. For the real test, consult ACT’s current calculator policy and your school’s directions; this page does not verify whether a particular device is permitted.
Use the explanation to identify the prerequisite, then study that concept before timing yourself on similar problems. A missed trigonometry or quadratic item may reflect an unfinished course topic rather than careless work.
The math bank has 30 questions. Six also appear in the mixed set; the remaining 24 are additional math practice. Your saved progress is separate on each page.
It reports accuracy on this particular collection. The questions are not calibrated to official score conversions, so a percentage correct here cannot predict a PreACT or ACT scaled score.
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