Practice Test 7 - ACT Math

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

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1. A class has 10 students. The teacher wants to choose 1 student as class president and 1 different student as vice president. Since the positions are different, order matters. In how many ways can the teacher choose the two students?
2. A student saves $40 in month 1, and $10 more each subsequent month. What is the total amount saved after 6 months?
3. For positive numbers $x$ and $y$, which expression is equivalent to $\log(xy)$ (base 10)?
4. A sweater is discounted $20\%$ from its original price of $65. What is the discounted price?
5. A cylinder has a surface area of 150π square units and a radius of 5 units. What is the height of the cylinder?
6. What is the surface area of a cube with side length 7 units?
7. For the function $f(x) = \begin{cases} x + 2 & \text{if } x \leq -3 \\ 3x - 7 & \text{if } x > -3 \end{cases}$, what is $f(-3)$?
8. A set of 8 integers is: 1, 2, 2, 3, 4, 4, 5, 100. Which best describes the shape of the distribution?
9. A student has taken 3 tests and received scores of 85, 92, and 78. What score must the student earn on the 4th test to have an overall mean score of exactly 85 for the 4 tests?
10. Lines $p$ and $q$ are parallel, and line $r$ is a transversal. If angle $2$ is $110^\circ$, what is the measure of the corresponding angle $4$?
11. A hot air balloon is descending at a rate of 5 meters per minute. If its initial altitude is 200 meters, what equation models the altitude $y$ after $x$ minutes?
12. Given $\triangle GHI \text{ with sides } GH = 5, HI = 12, \text{ and } IG = 13$, and $\triangle JKL \text{ with sides } JK = 10, KL = 24, \text{ and } LJ = 26$. What is the scale factor from $\triangle GHI$ to $\triangle JKL$?
13. For a 2×2 matrix $\begin{bmatrix}a & b\\ c & d\end{bmatrix}$, the determinant is $ad-bc$. What is the determinant of $\begin{bmatrix}2 & 5\\ -1 & 4\end{bmatrix}$?
14. What is the slope of the line through points (-1, 4) and (2, -5)? Give your answer in simplest form.
15. A grocery store wants to know which of two shelf layouts leads to higher sales. For one month, Store 1 uses Layout A and Store 2 uses Layout B, then sales are compared. The stores are in different neighborhoods with different customer bases. Which characteristic makes this comparison potentially biased?
16. Solve the system: $\begin{cases} 4x - y = 9\\ 2x + y = 3 \end{cases}$ Which ordered pair satisfies both equations?
17. Which equation represents a circle with center (3, -4) and radius 5?
18. In a right triangle, the hypotenuse is 15 units and one leg is 9 units. What is the length of the other leg?
19. If angle $A$ and angle $B$ are vertical angles and angle $A$ is $50^\text{o}$, what is the measure of angle $B$?
20. Convert $\log_{2}(16) = d$ to exponential form.

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