Practice Test 41 - ACT Math

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

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1. What is the radian measure of an angle of 135°?
2. In a calculation, you need to simplify $\log(4\cdot 25)$ (base 10). Which expression is equivalent?
3. Order the following numbers from least to greatest: $-3$, $\frac{-1}{2}$, $0.75$, $-\frac{3}{4}$.
4. To evaluate a training program, a company assigns some employees to the program while others continue usual work. Their performance is monitored. Is this an experiment or an observational study?
5. A group of 7 people is planning a hiking trip. If 3 people must stay behind to prepare dinner, how many ways can the hiking group be chosen?
6. In triangle DEF, the length of side DE is 7 inches and the length of side EF is 12 inches. Which of the following represents all possible lengths, x, in inches, for the third side DF?
7. In a right triangle, angle $\theta$ has adjacent side length $12$ and hypotenuse length $13$. What is $\cos(\theta)$?​​
8. What is $A + B$ for matrices $A$ and $B$ given by $A=\begin{bmatrix}5 & 0\\ -2 & 1\end{bmatrix},\quad B=\begin{bmatrix}-1 & -3\\ 4 & 2\end{bmatrix}?$
9. A researcher wants opinions about cafeteria food at a large university. She divides students into groups by year (first-year, sophomore, junior, senior) and randomly selects 50 students from each year to survey. This helps ensure each year is represented. Which sampling method is being used?
10. The function $g(x) = -3\cos\\!\left(\dfrac{\pi}{2}x\right) + k$ has a minimum value of 1. What is the maximum value of $g(x)$?
11. 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?
12. How many ways can you arrange 4 people in a car with 4 distinct seats?
13. What is the mean of the data set [4, 8, 10, 12, 6]?
14. What is the measure of each interior angle of a regular hexagon?
15. A store increases the price of an item from $50 to $60. What is the percent increase, based on the original price?
16. In the diagram, $\triangle ABC$ and $\triangle DEF$ have matching angle marks showing $\angle A \cong \angle D$ (one arc) and $\angle B \cong \angle E$ (two arcs). Side lengths shown are $AB=6$, $BC=9$, $DE=8$, and $EF=12$. Which triangles are similar?
17. A polygon has $11$ sides. What is the sum of its interior angles, in degrees?
18. If the system below is true, what is the value of $y$? $\begin{cases} 3x + 4y = 1\\ 6x - 4y = 11 \end{cases}$
19. What is the magnitude of $\mathbf{v}$ if $\mathbf{v}=\langle 6, 8\rangle$? Give your answer in simplest form.
20. What is the magnitude of the vector $\langle 8, 6\rangle$?

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