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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.

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Step 2: Check your answers with the following video.

Questions 1 - 60

- 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?
- Which of the following expressions is equivalent to
−4x
^{3}− 12x^{3}+ 9x^{2}? - When x = 2, 10 + 3(12 ÷ (3x)) = ?
- ⎪6 − 4⎪ − ⎪3 − 8⎪ = ?
- The expression (4c − 3d)(3c + d) is equivalent to:
- 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?
- The number of fish, f, in Skipper’s Pond at the
beginning of each year can be modeled by the equation
f(x) = 3(2
^{x}), 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 ? - 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. ?
- In the figure shown below, E and G lie on
- Katerina runs 15 miles in 2 1/2 hours. What is the average number of minutes it takes her to run 1 mile?
- 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?
- 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 ?

- 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?
- 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?
- What is 3% of 4.14 × 10
^{4}? - What value of x satisfies the equation −3(4x − 5) = 2(1 − 5x) ?
- In right triangle nABC shown below, the given lengths are in millimeters. What is sin A ?
- (27/64)
^{-2/3 = ?} - 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?
- 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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