Prepare for the ACT Math section with this practice test and answers. This guide covers pre-algebra, elementary algebra, intermediate algebra, coordinate geometry, plane geometry, and trigonometry.
Q: Barbie answered 2 out of 20 questions on her math test incorrectly. What percent of the questions did Barbie answer correctly?
Answer: Options: 2/20 x 100%, 2/ (20 x 100%), 18/20 x 100%, 18/ (20 x 100%), 2/100% x 20.Answer: 18/20 x 100%. Number of correct questions over number of total questions multiplied by 100.
Q: Set S = {0, x + 2, x + 4, x + 6}. What is the average of Set S?
Answer: Options: 3/4x +3, x+2, x+3, x+4, 3x+12.Answer: ¾ x + 3. Add all the terms in Set S together and divide by 4 to get the average.
Q: A bag contains only red, blue, and green marbles. There are a total of 20 marbles in the bag, and the probability of NOT selecting a blue marble is ¼. How many blue marbles are in the bag?
Answer: Options: 4, 5, 8, 10, 15.Answer: 15. The probability of actually selecting a blue marble is now ¾. ¾ = the amount of blue marbles / 20.Solve for x to equal 15 marbles.
Q: Joanie’s scores for 3 tests are 100, x, and 80. If the median of her scores is higher than the mean of her scores, then which of the following numbers could be x?
Answer: Options: 60, 70, 80, 90, 100Answer: 100.Go through the answers to solve for median and mean of the test scores until the median is greater than the mean.
Q: What is the smallest positive value of x for which cos3x = 0?
Answer: Options: 0, pi/6, pi/3, pi/2, 2pi/3.Answer: pi/6. Find when cosine equals 0. Multiply that answer by 3.
Q: A fish tank has a length of 24 inches, a width of 8 inches, and a height of 10 inches. If the tank contains 1,728 cubic inches of water, what is the depth, in inches, of water in the tank?
Answer: Options: 6, 7, 8, 9, 10.Answer: 9. The length and width of the water is the same as those of the tank. The water’s volume now equals the area of the tank’s base times the water’s depth. 1,728 = (24)(8)(d). d=9.
Q: A car rental company charges $20 per day for a rental car, plus $0.50 for each mile driven. If Kecia kept a car for 3 days and was charged $156.00 dollars, how many miles did she drive?
Answer: Options: 312, 272, 192, 156, 96.Answer: 192. She had the car for 3 days: 3($20)= $60. $156 – $60= $96 is the mileage charges. 96/0.50= 192 miles.
Q: Rain is falling at a rate of 0.25 cm each hour. At this rate, how many hours would it take for c centimeters of rain to fall?
Answer: Options: c/0.25, 0.25/c, 0.25c, 2.5c, c-0.25.Answer: c/0.25. Set up a proportion with the ratio of rainfall in one hour to the ratio of rainfall © per x hours. Solve for x.
Q: If x > y and z > y, which of the following MUST be true?
Answer: Options: x > z, z > x, x^2 > y, z^2 > y^2, x + z > 2y.Answer: x + z > y. X and Z are greater than Y but we do not know how they relate to each other so eliminate the first two choices. Eliminate the next two because if y is a “large” negative number, it will out-do x and z. The last option is left.
Q: In the figure below, a circle is inscribed within a square. If the perimeter of the square is 36 feet, what is the area of the shaded region, in square feet? (Area around the circle.)
Answer: Options: 9-4.5pi, 36-6pi, 36-9pi, 81-20,25pi, 81-36pi.Answer: 81-20.25pi. If the square’s perimeter is 36, then each side is 9 feet. This means the square’s diameter is 9 feet. The area of the square is 9×9= 81 feet^2. The area of the circle is pi(4.5)^2= 20.25pi. Subtract the area of the circle from the area of the square.
Q: The length of the radius of circle A is 3 times as long as the radius of circle B. If the area of circle A is x, what is the area of circle B?
Answer: Options: x/9, x/6, x/3, 3x, 9x.Answer: x/9. Substitute values in for the radii of A and B and make a proportion of A to B.
Q: If the area of triangle ABC is 24 square feet, what is the perimeter of parallelogram BCED, in feet?
Answer: Options: 72 feet, 70 feet, 68 feet, 64 feet, 50+ 2root73 feet.Answer: 64 feet. Using side AC, solve for the base (6) in the area formula, then the hypotenuse using the pythagorean theorem. Since BD is 28, solve for the perimeter.
Q: A ball thrown upward from the ground level is s feet high after t seconds, where s=80t – 16t^2. At which of the following times will the ball be 96 feet above the ground?
Answer: Options: ¼ second, 1 second, 2 seconds, 2.5 seconds, 4 seconds.Answer: 2 seconds. Plus is 96 for s and use the quadratic equation to solve for t.
Q: Working together, a standard printer and a high-speed printer can complete a certain print job in 3 ⅓ hours. If it takes the high-speed printer 5 hours to do the job alone, how many hours would it take the standard printer to do the job alone?
Answer: Options: 1 ⅔, 4 1/6, 6 ⅔, 8 ⅓, 10.Answer: 10. The printers do 1/x of the job every hour. The high-speed printer does 1/5 of the job for 5 hours,, but together they finish the job in 10/3 hours. Each hour they do 3/10 of the job. 1/x + 1/5 = 3/10, solve for x.
Q: The average of a set of 6 integers is 22. When one of these numbers is removed, the average of the set increases to 25. What is this number?
Answer: Options 3, 7, 15, 16, 18.Answer: 7. Re-arrange the mean formula to solve for sum. (Sum = average x number of terms). Find the sum of the 6 integers to be 132. Find the sum of 5 integers to be 125. Subtract 15 from 132 to find 7.
Q: If a fair coin is tossed 4 times, what is the probability of NOT obtaining exactly 3 heads?
Answer: Options: ¼, ½, ⅝, ¾, 15/16.Answer: ¾. Find the total number of possible outcomes to be 16. Which of those contain three heads? (4). If 4 contain 3 heads, then 12 do not. 12/16 = ¾.