Practice Test 25 - ACT Math

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

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1. A line is drawn on a coordinate plane through the two points shown: $(0, -2)$ and $(3, 4)$. What is the slope of the line shown?
2. The ratio of cats to dogs at an animal shelter is $2:5$. If there are 21 animals total (only cats and dogs), how many cats are there?
3. If $4x + 8 = 2x + 14$, what is $x$?
4. In similar triangles $\triangle ABC \sim \triangle DEF$, the correspondence is $A\leftrightarrow D$, $B\leftrightarrow E$, $C\leftrightarrow F$. If $AB=8$, $DE=12$, and $BC=10$, what is $EF$?
5. A matrix is scaled to represent three identical copies of a system. If $A=\begin{bmatrix}1 & -3\\ 4 & 0\end{bmatrix}$, what is $3A$?
6. What is the determinant of $\begin{bmatrix}-4 & 1 \\ 2 & -3\end{bmatrix}$?
7. What is the absolute value of $5 + 12i$?
8. A polynomial $f(x)=x^3-x$ models a changing quantity. Which statement best describes the end behavior of $f(x)$?
9. A student has 6 different photos and wants to choose 4 of them to put in an album, where the order of the photos in the album does not matter. How many different sets of 4 photos are possible?
10. What is the absolute value of $-8$?
11. A ball's height is modeled by $h(t)=t^2-5t+6$. To find when it hits the ground, solve $t^2-5t+6=0$.
12. What is the absolute value of $-12$?
13. What is the range of $x$ if $|x - 4| > 3$?
14. What is $-2\mathbf{w}$ if $\mathbf{w} = \langle -3, 5 \rangle$?
15. Which congruence criterion applies to triangles ABC and DEF if $AB = DE$, $\text{angle } B = \text{angle } E$, and $BC = EF$?
16. A concert ticket costs $30. If you buy 3 tickets, what is the total cost?
17. A car rental company charges a flat fee of $30 plus $0.25 per mile driven. What is the meaning of the slope in the equation that models this scenario?
18. The equation $H = 180 - 10d$ models the height of a candle in centimeters, where $H$ is the height and $d$ is the number of days it has been burning. What is the height after 12 days?
19. Convert $0.6$ to a percent.
20. Which represents a rational number? $\sqrt{5}$, $0.333\ldots$, $\pi$, $e$

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