Practice Test 38 - ACT Math

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

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1. A researcher is interested in the study habits of high school students. They select a random sample of schools and survey all students in those schools. Which sampling method is being used?
2. Order the following from least to greatest: $-\frac{1}{4}$, $0.5$, $0$, $\frac{1}{3}$.
3. In $\triangle ABC$ and $\triangle DEF$, $\angle A\cong\angle D$, $\angle B\cong\angle E$, and the side between them is equal: $AB=DE=7$. Which congruence criterion applies (SSS, SAS, ASA, AAS)?
4. Triangles $\triangle ABC$ and $\triangle DEF$ are shown. Angles $\angle A$ and $\angle D$ are marked congruent (one arc), and angles $\angle C$ and $\angle F$ are marked congruent (two arcs). No side lengths are needed. Which statement is true?
5. A circle has area $64\pi$. What is the radius of the circle?
6. How many ways can you arrange 3 red balls and 2 blue balls in a row?
7. The equation $E = 50t + 1000$ models the energy consumption of a factory, where $E$ is the energy used in kilowatt-hours and $t$ is the number of hours of operation. What is the meaning of the y-intercept in this context?
8. What is $11^0$?
9. If $f(x) = -x^2 + 3x + 4$, what is $f(1)$?
10. What is 60% of 75?
11. A bar graph shows the number of tickets sold for four movies on opening night. Values are integers. Based on the graph, what is the measurement (tickets sold) for Movie B?
12. What is $\log_{e}(e^2)$?
13. Find the radius of a circle with an area of $81\pi$.
14. Two triangles are shown: $\triangle ABC$ has $AB=8$, $BC=6$, and $AC=10$. $\triangle DEF$ has $DE=12$, $EF=9$, and $DF=15$. No angles are marked. Are the triangles similar? If so, why?
15. A 15-foot ladder is leaning against a vertical wall. The base of the ladder is 9 feet away from the base of the wall on level ground. How high up the wall, in feet, does the ladder reach?
16. A hiker walks with displacement vector $\mathbf{v}=\langle -3,\,5\rangle$ and then $\mathbf{w}=\langle 4,\,-2\rangle$. What is $\mathbf{v}+\mathbf{w}$?
17. What is $(x + 2)(x + 3)$?
18. A school has 10 students and needs to choose 4 of them to attend a workshop. Since only the set of students matters, order does not matter. How many ways can 4 students be chosen from 10?
19. What is $\mathbf{v} \cdot \mathbf{w}$ if $\mathbf{v} = \langle 0, 9 \rangle$ and $\mathbf{w} = \langle 4, -3 \rangle$?
20. A classroom has $28$ students. The teacher forms groups with $4$ students in each group. How many groups can be formed?

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