Practice Test 26 - ACT Math

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

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1. A student has taken 4 tests and has an average score of 82. What score must the student get on the 5th test to raise the average to exactly 84?
2. To understand commuting patterns, a city surveys every fifth person who uses public transportation. Which sampling method is being used?
3. What is the percent decrease from 250 to 200?
4. What is A + B for matrices $A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}$ and $B = \begin{pmatrix} 4 & 3 \\ 2 & 1 \end{pmatrix}$?
5. What is $\sin(30^\circ)$?​
6. The area of a circle is $49\pi$ square units. What is the radius of the circle?​​​
7. Order the following from least to greatest: $-2$, $-\dfrac{7}{3}$, $-\sqrt{5}$, $-2.2$.
8. How many ways can 2 students be chosen from a class of 10 students to present a project?
9. Solve for $x$: $2(x - 5) = 10$
10. Lines $x$ and $y$ are parallel, and line $z$ is a transversal. If the measure of angle $7$ is $65^\circ$, what is the measure of the corresponding angle $8$?
11. If $f(x)=x^2+4x$, what is the value of $f(2x)$? Substitute $2x$ for every $x$: $f(2x)=(2x)^2+4(2x)$.
12. A company tests a new product by giving it to a selected group of loyal customers and asking for feedback. Which sampling method is being used?
13. A student solves $\log(x)=2$ (base 10). What is the value of $x$?
14. Simplify: $\sqrt{27y^2}$, assuming $y \ge 0$.
15. A delivery driver tracks their route on a map and notes that their position changed from $(2,5)$ to $(8,-1)$ on a coordinate grid. What is the slope of the line through points $(2,5)$ and $(8,-1)$?
16. In a class, the ratio of students wearing sneakers to students not wearing sneakers is $9:7$. If $63$ students are wearing sneakers, how many students are not wearing sneakers?
17. If $4x + 1 = 9$, what is $x$?
18. In the diagram, angle $a$ and angle $b$ are vertical angles. If angle $a$ measures $75^\circ$, what is the measure of angle $b$?
19. A physics student combines logarithms with the same base. If $\log_{3}(9)+\log_{3}(27)$ equals what single value?
20. Solve the system of linear equations: $\begin{cases} 2x + y = 11 \\ x - y = 1 \end{cases}$ What is the solution $ (x, y) $?

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