Practice Test 19 - ACT Math

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

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1. The scale factor from model A to model B is 3. If the length of model A is 5 cm, what is the length of model B?
2. In $\triangle ABC$, the length of side $a$ is 5, the length of side $b$ is 7, and the measure of $\angle C$ is $60°$. What is the length of side $c$?
3. Solve the system: $3x + 2y = 12$ and $x - y = 1$.
4. The data set is $\{5, 7, 8, 10, 12\}$. If the value 100 is added to the data set, what happens to the median?
5. Lines $a$ and $b$ are parallel, cut by transversal $c$. If angle $9$ is $125^\circ$, what is the measure of angle $7$, the alternate interior angle?
6. What is the result when $2x^2 - 3x + 4$ is subtracted from $5x^2 + 2x - 1$?
7. A circle has area $81\pi$. What is the diameter of the circle?
8. What type of triangle has all angles equal?
9. If 25% of a number is 10, what is the number?
10. A doctor wants to see whether a new reminder app increases medication adherence. Patients in her clinic are randomly assigned to either use the app or not use it, and adherence is checked after 8 weeks. Some patients stop using the app early. Is this an experiment or an observational study?
11. In $\triangle ABC$, the length of side $a$ is 5, the length of side $b$ is 7, and the measure of $\angle C$ is $60°$. What is the length of side $c$?
12. In a right triangle, the side adjacent to angle $\theta$ is $8$ and the hypotenuse is $17$. What is $\cos(\theta)$?
13. The ratio of apples to oranges in a basket is $3:2$. If there are 15 apples, how many oranges are there?
14. In a right triangle, if the opposite side to angle $\theta$ is 5 and the adjacent side is 12, what is $\tan(\theta)$?
15. What is the median of the data set [19, 24, 22, 26, 20]?
16. What is the absolute value of $4 + 3i$?
17. Two lines intersect and form four angles. If one angle is $30^\text{o}$, what is the measure of its adjacent angle?
18. A circle has diameter $12$ units. What is the area of the circle?
19. What is $4\mathbf{v}$ if $\mathbf{v} = \langle 0, 5 \rangle$?
20. Two triangles are shown. In $\triangle ABC$, $AB=6$, $AC=9$, $BC=12$. In $\triangle DEF$, $DE=4$, $DF=6$, $EF=8$. What is the scale factor from $\triangle ABC$ to $\triangle DEF$ (i.e., multiply lengths in $\triangle ABC$ by what number to get corresponding lengths in $\triangle DEF$)?

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