Full-length practice covering essential math topics for the ACT.
Topics Included:
Take this exam in our timed interactive simulator to track your performance and get detailed analytics.
Cameron took 4 tests, and his scores were as follows: 100, 60, 80, and 30. Cameron took another test that was scored x. The mean score of the 5 tests he took is 72. What is the value of x?
90
To find the missing score, set up the equation for the mean of 5 tests: 5100+60+80+30+x=72. Multiplying both sides by 5 gives 270+x=360. Subtracting 270 from both sides yields x=90.
In the Venn diagram below, circles S, C, and P represent farms raising sheep, cows, and pigs, respectively. How many of the 47 farms represented in the diagram do not raise cows?
19
To find the number of farms that do not raise cows, sum the values of all the regions completely outside circle C. These are the farms raising only sheep (12), only pigs (5), and both sheep and pigs but not cows (2). 12+5+2=19. Alternatively, total farms in C=13+10+1+4=28. 47−28=19.
Marco designs a spinner wheel that has exactly 4 sections: red, blue, green, and yellow. He wants the spinner wheel to have a 25% chance of landing on each section. He spins the wheel 500 times. The results of the spins are shown in this table.
| Spinner wheel section | Number of times the spinner lands in each section |
|---|---|
| Red | 80 |
| Blue | 165 |
| Green | 130 |
| Yellow | 125 |
Based on the results in this table, one of the following changes would be the best fix. Which one?
He should increase the area of the red section by decreasing the area of the blue section.
Marco expects each section to land 25% of the time, which for 500 spins is 0.25×500=125 times. Red only landed 80 times (too small an area), while blue landed 165 times (too large an area). To fix this, he should increase the red section's area and decrease the blue section's area.
In △ABC, ∠A and ∠C are congruent, and the measure of ∠B is 143.6∘. What is the measure of ∠A?
18.2∘
The sum of angles in a triangle is 180∘. Let the measure of ∠A and ∠C be x. Thus, 2x+143.6∘=180∘. Solving for x: 2x=36.4∘⇒x=18.2∘.
Which of the following expressions is equivalent to x2−x−30?
(x−6)(x+5)
Factoring the quadratic x2−x−30 requires finding two numbers that multiply to −30 and add to −1. Those numbers are −6 and 5. Therefore, the factored form is (x−6)(x+5).
Which of the following matrices is equal to 5[−402−5]?
[−20010−25]
To perform scalar multiplication, multiply every element inside the matrix by 5: 5×−4=−20, 5×2=10, 5×0=0, 5×−5=−25. This gives the matrix [−20010−25].
Lavonne purchased some tickets and snack vouchers for an upcoming event and gave them to the members of her work group. Each member of her work group received the same number of tickets and the same number of snack vouchers. The total number of tickets she gave to her group was 30, and the total number of snack vouchers was 75. Which of the following could be the number of members in Lavonne's work group?
15
The number of members must be a common divisor of both 30 and 75, as the items were divided equally. The greatest common divisor of 30 and 75 is 15. The other options are not factors of both numbers.
The initial speed, in miles per hour, of a certain car that skids to a stop can be estimated by multiplying the length of the skid, in feet, by 35 and then taking the square root of the product. According to this method, what is the estimated initial speed, in miles per hour, of the car when it makes a 108-foot skid?
6105
Calculate 108×35. To simplify, find the prime factorizations: 108=36×3 and 35=5×7. Thus, 108×35=36×3×35=36×105=6105.
If 6y=5x−1, then x=?
56y+1
To solve for x, isolate it on one side: add 1 to both sides to get 6y+1=5x. Divide by 5 to get x=56y+1.
A boat is traveling at a speed of 30 miles per hour. What is the boat's speed in feet per second?
(Note: 1 mile = 5,280 feet)
44
Convert miles per hour to feet per second using dimensional analysis: (30 miles/1 hour)×(5280 feet/1 mile)×(1 hour/3600 seconds)=(30×5280)/3600=44 feet per second.
