Practice Test 4 - ACT Math

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

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1. Lines $m$ and $n$ are parallel. If angle $3$ is $150^\circ$, what is the measure of the alternate exterior angle $4$?
2. A student simplifies $\log_7(49)$. What is the value of $\log_7(49)$?
3. Two fair coins are flipped. What is the probability of getting exactly one head?
4. A $2 \times 2$ matrix represents a linear transformation. What is the determinant of $\begin{bmatrix} 2 & -5 \\ 1 & 3 \end{bmatrix}$?
5. A photograph is enlarged with a scale factor of 2. If the original width is 6 inches, what is the width of the enlarged photograph?
6. What is the range of the data set [15, 22, 8, 17, 10]?
7. A bar graph shows the number of students who chose each club. Based on the graph, how many students chose the Music club?
8. The ratio of red marbles to blue marbles in a bag is $3:5$. If there are $40$ blue marbles, how many red marbles are in the bag?
9. A shipping company uses a piecewise pricing rule for a package based on its weight $x$ (in pounds). The cost function is $f(x)=\begin{cases} 2x+5 & \text{if } x<3 \\ 11 & \text{if } 3\le x<7 \\ 3x-4 & \text{if } x\ge 7 \end{cases}$ What is $f(3)$ for the piecewise function defined below?
10. For $\triangle KLM$ and $\triangle OPQ$, $\triangle KLM$ has sides $KL = 5$, $LM = 12$, $KM = 13$. $\triangle OPQ$ has sides $OP = 10$, $PQ = 24$, $OQ = 26$. What is the scale factor from $\triangle KLM$ to $\triangle OPQ$?
11. Order the following from least to greatest: $1.5$, $-0.75$, $\frac{5}{4}$, $-1$.
12. What is $\mathbf{u} \cdot \mathbf{v}$ if $\mathbf{u} = \langle 5, 6 \rangle$ and $\mathbf{v} = \langle 3, 4 \rangle$?
13. What is the mode of the data set [11, 13, 15, 13, 17, 13]?
14. To simplify an algebraic expression in a model, compute: What is $(x-3)(x+6)$?
15. What is $(2 + 3i) - (4 + i)$?
16. In the diagram, two triangles have matching angle markings: $\angle A$ has one arc and matches $\angle D$, and $\angle B$ has two arcs and matches $\angle E$. Side lengths shown are $AB=6$, $AC=9$, $DE=8$, and $DF=12$. Which triangles are similar? (Angle arcs indicate equal angles.)
17. $\log_2(16)$ is equivalent to which of the following?
18. What is $f(7)$ if $f(x) = \frac{3x - 1}{2}$?
19. A recipe uses a ratio of flour to sugar of $5:2$. If you use 30 cups of flour, how many cups of sugar are needed to keep the ratio the same?
20. Factor: $x^2 - 8x + 15$

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