Practice Test 32 - ACT Math

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

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1. In a right triangle, the hypotenuse is $13$ and the side adjacent to an acute angle $\theta$ is $5$. What is $\cos(\theta)$?​
2. Convert $75\%$ to a decimal.
3. A news website wants to estimate what percent of all adults in a state approve of the governor. To reduce bias, what is the best method to collect data for this purpose?
4. A revenue expression is $x^2+x-12$. Factor: $x^2+x-12$.
5. Which vector represents $4\mathbf{b}$ if $\mathbf{b} = \langle 0, 7 \rangle$?
6. The circumference of a circle is $16\pi$ centimeters. What is the area of the circle, in square centimeters?
7. $\log_9(81)$ equals what?
8. Simplify by combining like terms: $2x^2 + 3x - x^2 + 5x$.
9. A data set of 9 values is $\{2, 3, 3, 4, 4, 4, 5, 6, 20\}$. Which best describes the shape of the distribution?
10. If $f(x) = 7 - x$, what is $f(3)$?
11. A teacher recorded the number of books read by 8 students over the summer: 2, 5, 3, 4, 6, 3, 2, 7. What is the mean of the data set $[2,5,3,4,6,3,2,7]$?
12. To evaluate the effect of a new software tool, a company randomly assigns some employees to use it while others continue with the old system. Is this an experiment or an observational study?
13. A student records that the temperature difference from a target value should stay below 4 degrees. Solve the inequality $|x-3|<4$ and give the solution set in interval notation.
14. A code is made by arranging 4 different digits chosen from 0 through 9, with no repetition. Since the order of digits matters, how many such codes are possible?
15. What is $f(0)$ for the function $f(x) = x + 7$?
16. For an angle $\theta$ such that $0 < \theta < \dfrac{\pi}{2}$, it is known that $\sin(\theta) = \dfrac{3}{5}$. What is the value of $\cos(\theta) + \tan(\theta)$?
17. Based on the piecewise function $f(x)=\begin{cases} -x+4, & x<0\\ 3x+1, & 0\le x<2\\ x^2-1, & x\ge 2 \end{cases}$ what is the value when $x=2$?
18. What is the magnitude of $\mathbf{a} = \langle 9, 12 \rangle$?
19. A regular polygon has interior angles of $135^\circ$ each. How many sides does it have?​
20. Solve: $4x + 5 < 13$

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