ACT Practice Test 2021/2022 Math Solutions


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Step by step solutions for ACT Math 2021/2022, Questions 1 to 60.

Step 1: Print out the Practice Test Questions 2021/2022 (pdf) and attempt the test.
(Try to do a timed test if possible.)
Step 2: Check your answers with the following video.

Questions 1 - 60

  1. The numbers 1 through 15 were each written on individual pieces of paper, 1 number per piece. Then the 15 pieces of paper were put in a jar. One piece of paper will be drawn from the jar at random. What is the probability of drawing a piece of paper with a number less than 9 written on it?
  2. Which of the following expressions is equivalent to −4x3 − 12x3 + 9x2?
  3. When x = 2, 10 + 3(12 ÷ (3x)) = ?
  4. ⎪6 − 4⎪ − ⎪3 − 8⎪ = ?
  5. The expression (4c − 3d)(3c + d) is equivalent to:
  6. Of the 180 students in a college course, 1/4 of the students earned an A for the course, 1/3 of the students earned a B for the course, and the rest of the students earned a C for the course. How many of the students earned a C for the course?
  7. The number of fish, f, in Skipper’s Pond at the beginning of each year can be modeled by the equation f(x) = 3(2x), where x represents the number of years after the beginning of the year 2000. For example, x = 0 represents the beginning of the year 2000, x = 1 represents the beginning of the year 2001, and so forth. According to the model, how many fish were in Skipper’s Pond at the beginning of the year 2006 ?
  8. Manish drove from Chicago to Baton Rouge. At 8:00 a.m., he was 510 km from Baton Rouge. At 1:00 p.m., he was 105 km from Baton Rouge. Which of the following values is closest to Manish’s average speed, in kilometers per hour, from 8:00 a.m. to 1:00 p.m. ?
  9. In the figure shown below, E and G lie on
  10. Katerina runs 15 miles in 2 1/2 hours. What is the average number of minutes it takes her to run 1 mile?
  11. A bag contains 8 red marbles, 9 yellow marbles, and 7 green marbles. How many additional red marbles must be added to the 24 marbles already in the bag so that the probability of randomly drawing a red marble is 3/5?
  12. In the standard (x,y) coordinate plane, the point (2,1) is the midpoint of CD. Point C has coordinates (6,8). What are the coordinates of point D ?



  1. At his job, the first 40 hours of each week that Thomas works is regular time, and any additional time that he works is overtime. Thomas gets paid $15 per hour during regular time. During overtime Thomas gets paid 1.5 times as much as he gets paid during regular time. Thomas works 46 hours in 1 week and gets $117 in deductions taken out of his pay for this week. After the deductions are taken out, how much of Thomas’s pay for this week remains?
  2. At Sweet Stuff Fresh Produce the price of a bag of grapes depends on the total number of bags purchased at 1 time, as shown in the table below. In 2 trips to Sweet Stuff this week, Janelle purchased 3 bags of grapes on Monday and 4 bags of grapes on Wednesday. How much money would Janelle have saved if she had instead purchased 7 bags of grapes in 1 trip on Monday?
  3. What is 3% of 4.14 × 104 ?
  4. What value of x satisfies the equation −3(4x − 5) = 2(1 − 5x) ?
  5. In right triangle nABC shown below, the given lengths are in millimeters. What is sin A ?
  6. (27/64)-2/3 = ?
  7. Loto begins at his back door and walks 8 yards east, 6 yards north, 12 yards east, and 5 yards north to the barn door. About how many yards less would he walk if he could walk directly from the back door to the barn door?
  8. For a given set of data, the standard score, z, corresponding to the raw score, x, is given by z = , where μ is the mean of the set and σ is the standard deviation. If, for a set of scores, μ = 78 and σ = 6, which of the following is the raw score, x, corresponding to z = 2 ?

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