Practice Test 36 - 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 $12.5\%$ of $64$?
2. What is the range of the data set [48, 55, 60, 62, 50]?
3. A worksheet asks you to simplify $\log(2)+\log(50)$ (base 10). Which single logarithm is equivalent?
4. What is the solution $(x, y)$ to the system $x + y = 6$ and $2x - y = 3$?
5. Which expression is equivalent to $\ln(5x)$ for $x>0$?
6. Simplify: $\sqrt{32}$
7. A rectangular prism has length 9 units, width 4 units, and height 2 units. What is the surface area of the rectangular prism?​
8. In the regular pentagon shown, each interior angle is equal. What is the measure of each interior angle of the regular pentagon?
9. A matrix of coefficients is scaled to change units. What is $4A$ if $A=\begin{bmatrix}-1 & 0\\ 2 & -3\end{bmatrix}$?
10. Two angles form a linear pair on a straight line. One angle measures $125^\circ$, and the adjacent angle is labeled $x$. -----------O----------- 125° | x What is the measure of angle $x$?
11. A water tank is being filled at a constant rate. The amount of water is modeled by $y = 7x + 15$, where $x$ is time in minutes and $y$ is the amount of water in liters. According to the model, how many liters of water are in the tank after $x = 9$ minutes?
12. What is the simplified form of $4y - 2(3 - y)$?
13. Which number is greatest? $-5$, $-2$, $0$, $3$.
14. If $A = \begin{bmatrix} 3 & -2 \\ 1 & 0 \end{bmatrix}$, which of the following matrices is equal to $4A$
15. Solve for $x$: $2(x + 6) = 20$.
16. For the complex number $i$, where $i^2 = -1$, what is the simplified form of $\dfrac{3 + i}{1 - i}$?
17. Which number is smallest? $4$, $-4$, $\frac{3}{4}$, $2.5$.
18. In the standard $(x, y)$ coordinate plane, $\vec{u} = \langle 2, -5 \rangle$ and $\vec{v} = \langle -3, 1 \rangle$. What is the magnitude of the vector $\vec{u} + \vec{v}$?
19. A nonprofit wants to estimate how many residents support building a new community center. They plan to knock on doors in one neighborhood because it is close to their office. To get a more representative result for the whole city, what is the best method to collect data?
20. A spinner is divided into 8 equal sections numbered 1 through 8. It is spun once. What is the probability of landing on a number greater than 6?

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