Practice Test 13 - ACT Math

20 questions. Answer them in any order, then submit to see your score and every explanation.

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1. What is the value of $x$ if $5x + 3 = 2x + 12$?
2. What is the sum of all real solutions to the rational equation $\dfrac{x^2 - x}{x - 3} = \dfrac{6}{x - 3}$?
3. How many ways can 4 students be lined up for a group photo?
4. What is $f(-1)$ if $f(x) = 4x + 3$?
5. A cylinder has radius 4 units and height 10 units. What is the volume of the cylinder?
6. A sports drink is mixed in a ratio of water to concentrate of $7:1$. If you have 6 cups of concentrate, how many cups of water do you need?
7. Order the following numbers from greatest to least: $-\frac{3}{5}$, $0.8$, $-0.9$, $\frac{1}{4}$.
8. What is kA if $k = 3$ and $A = \begin{bmatrix} 2 & -1 \\ 0 & 4 \end{bmatrix}$?
9. In a right triangle, an acute angle $\theta$ has opposite side length $7$ and hypotenuse length $25$. What is $\sin(\theta)$?​
10. In a tournament, there are 5 single matches. How many ways can the matches be arranged if no match can be repeated?
11. Angles $A$ and $B$ are complementary. If $m\angle A = 28^\circ$, what is $m\angle B$?
12. A teacher has 6 different stickers and will hand out all 6 to students, one after another, in a specific sequence. Because the sequence of stickers given out matters, how many different sequences are possible?
13. A function is defined by $f(x)=7x+2$. What is the value of $f(2x)$?
14. A circle has area $49\pi$. What is the radius of the circle?
15. A rectangular garden has a length that is 3 feet longer than its width. If the perimeter of the garden is 54 feet, what is the area of the garden, in square feet?
16. A box contains 30 chocolates. If 10 chocolates are eaten, how many are left?
17. Solve: $2(x-4)\ge 6$.
18. A restaurant offers 5 different sandwiches, 3 different sides, and 2 different drinks. A customer chooses exactly one sandwich, one side, and one drink. What is the number of outcomes for this meal choice?
19. The area of a circle is $81\pi$ square units. What is the radius of the circle?
20. A sensor is considered accurate if its reading $x$ is within 3 units of 8. What is the range of $x$ if $|x-8|\le 3$? Give your answer as a compound inequality.

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