Practice Test 45 - ACT Math

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

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1. A cylinder has radius 4 units and height 10 units. What is the volume?
2. What is the solution set of the inequality $3x - 5 > 4$?
3. A ball is thrown upward from a platform. Its height (in meters) after $x$ seconds is modeled by $y = -5x^2 + 20x + 2$. Which part of the equation represents the initial height of the ball at time $x=0$?
4. What is the y-intercept of the line $y = -5x + 8$?
5. Simplify: $\sqrt{128}$
6. A small store tracked the number of customers per hour over 6 hours: 7, 9, 9, 10, 12, 12. What is the mode of the data set $\{7, 9, 9, 10, 12, 12\}$?​​
7. A student combines two complex-valued signals by addition. What is $(7-3i)+(-2+9i)$ written in standard form $a+bi$?
8. A line represents the balance in a bank account over time. The relationship is given by $y=-4x+12$, where $x$ is weeks and $y$ is dollars. What is the y-intercept of the line $y=-4x+12$?
9. What is $\cos(\frac{\pi}{3})$?
10. How many ways can you choose 2 pencils from 5 of different colors?
11. What is the value of $x$ in the proportion $\dfrac{7}{x}=\dfrac{21}{18}$? (Use cross-multiplication: if $\dfrac{a}{b}=\dfrac{c}{d}$, then $ad=bc$.)
12. Two triangles have these measurements: In $\triangle ABC$, $AB=6$, $AC=8$, and the included angle $\angle A=50^\circ$. In $\triangle DEF$, $DE=9$, $DF=12$, and the included angle $\angle D=50^\circ$. Are the triangles similar? If so, why?
13. Which expression equals $a^{-4}$ (for $a\ne 0$)?
14. What is the mean of the data set [2, 4, 6, 8, 10]?
15. Solve: $-\dfrac{x}{3} \ge 2$.
16. A password consists of 3 letters followed by 2 digits. Letters can be any of the 26 English letters and digits can be any of 0-9. Repetition is allowed. What is the number of possible passwords?
17. What is $f(-3)$ for the piecewise function defined below? $f(x)=\begin{cases} (x-2)^2, & x<-2\\ 4-x, & -2\le x<5\\ 2x+1, & x\ge 5 \end{cases}$
18. If a single card is drawn from a standard deck of 52 cards, what is the probability of drawing a heart?
19. Which equation represents a line with a slope of 0 and a y-intercept of -3?
20. A student is designing a regular polygon tile with $8$ sides for a floor pattern. What is the measure of each interior angle in a regular $8$-gon?

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