Practice Test 22 - ACT Math

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

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1. What angle $\theta$ (in degrees) has $\sin(\theta)=\frac{\sqrt{2}}{2}$, where $0^\circ \le \theta \le 90^\circ$?​​
2. A matrix $A$ is used to encode a 2-variable system. If $A=\begin{bmatrix}0 & -3\\ 2 & 1\end{bmatrix},$ what is $-2A$?
3. A runner's distance from the starting line increases at a constant rate. The relationship is modeled by $y = 0.25x$, where $x$ is time in seconds and $y$ is distance in meters. What is the meaning of the slope in this context?
4. Let $A=\begin{bmatrix}-2 & 1\\ 3 & -1\end{bmatrix}$ and $B=\begin{bmatrix}5 & 0\\ -4 & 2\end{bmatrix}.$ Which of the following is the product $AB$?
5. Tickets to a high school play cost $12 for adults and $8 for children. On opening night, 150 tickets were sold and total revenue was $1,440. How many more children's tickets were sold than adult tickets?
6. A car rental price is modeled by a line with slope $-2$ that passes through the point $(3,5)$. Which equation represents this line?
7. A worker earns $15.00 per hour for the first 40 hours worked in a week. For any hours worked over 40, the worker earns $22.50 per hour. If the worker works 46 hours in one week, what is the total amount earned?
8. At 3:00 PM, a flagpole casts a 24-foot shadow and a 6.0-foot-tall man casts a 4.0-foot shadow. What is the height, in feet, of the flagpole?
9. A polynomial is given by $a(x) = 9 - 5x + x^3$. What is the degree of $a(x)$?
10. A rectangular prism has length 8 units, width 5 units, and height 3 units. What is the volume of the rectangular prism?
11. Which of the following is the product $AB$ if $A = \begin{bmatrix} 0 & 2 \\ 3 & 1 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & -1 \\ 4 & 0 \end{bmatrix}$?
12. Triangles $\triangle ABC$ and $\triangle DEF$ are shown. $\angle A \cong \angle D$ and $\angle B \cong \angle E$ are marked. Also, the side $BC$ is marked congruent to $EF$ (one tick), but it is not the included side between the marked angles. Which congruence criterion applies?
13. If $\mathbf{v} = \langle 5, 12 \rangle$, what is $-\mathbf{v}$?
14. Lines $r$ and $s$ are parallel, cut by transversal $t$. If angle $1$ is $75^\text{o}$, what is the measure of angle $4$, the alternate exterior angle?
15. A county wants to estimate the percentage of households with reliable internet. They have a complete address list and use a random number generator to select 600 addresses to mail a survey. Some households may not respond, creating nonresponse bias. Which sampling method is being used?
16. What is $-2\mathbf{v}$ if $\mathbf{v}=\langle 9, -4\rangle$?
17. Events A and B are mutually exclusive. $P(A) = 0.5$ and $P(B) = 0.3$. What is $P(A \text{ or } B)$?
18. Solve the system: $\begin{cases} x + y = 8\\ 3x - y = 4 \end{cases}$ What is the solution $(x, y)$?
19. Let $P(t) = 400(3)^{\frac{t}{2}}$. What is the value of $P(6)$?
20. A regular polygon has an interior angle sum of $1{,}080^\circ$. How many sides does the polygon have?

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