Practice Test 28 - ACT Math

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

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1. For an angle $\theta$ such that $0 < \theta < \dfrac{\pi}{2}$, it is known that $\sin(\theta) = \dfrac{3}{5}$. What is the value of $\cos(\theta) + \tan(\theta)$?
2. Two lines intersect at point $O$. One of the angles formed is $65^\circ$. What is the measure of angle $x$ if $x$ is the vertical angle to the $65^\circ$ angle?
3. A plant is 6 inches tall when it is purchased and grows at a constant rate of 1.5 inches per week. Let $x$ be the number of weeks since purchase and let $y$ be the plant's height (in inches). Which equation best models the relationship?
4. For the function $f(x) = \begin{cases} x^2 + 1 & \text{if } x < 0 \\ 3x - 4 & \text{if } 0 \leq x < 3 \\ 2x + 5 & \text{if } x \geq 3 \end{cases}$, what is f(-1)?
5. You are simplifying the expression $(2-9i)-(11+3i)$ and need the result in standard form $a+bi$. What is the simplified value?
6. Simplify: $\dfrac{5^6}{5^2}$
7. What is the complex conjugate of $6 + i$?
8. A linear function describes a phone plan cost: $y=\dfrac{1}{2}x+8$, where $x$ is data used (GB) and $y$ is dollars. What is the y-intercept of the line $y=\dfrac{1}{2}x+8$?
9. If a model car has a scale of 1:20 and the model is 15 cm long, how long is the actual car?
10. A calculus student uses log rules to rewrite $\ln(\sqrt{e^{10}})$. What is its value?
11. A polygon has $7$ sides. What is the sum of its interior angles, in degrees?
12. In a carnival game, rolling an even number wins $4.00 and rolling odd loses $2.00. What is the expected value of a single roll?
13. What is the range of $x$ if $|2x + 1| < 7$?
14. What is the y-intercept of the line $y = 4x - 5$?
15. A student is converting between logarithmic and exponential forms. Which equation is equivalent to $\log_3(81)=4$?
16. Solve: $5 - 2x \leq 1$
17. Which of the following is equivalent to $(2x - 3)^3$?
18. What is A + B for matrices $A = \begin{pmatrix} 1 & -2 \\ 0 & 3 \end{pmatrix}$ and $B = \begin{pmatrix} 3 & 1 \\ -1 & 2 \end{pmatrix}$?
19. What is the determinant of matrix $\begin{pmatrix} 3 & 0 \\ 2 & 5 \end{pmatrix}$?
20. What is the surface area of a rectangular prism with dimensions 4 units, 3 units, and 2 units?

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