Practice Test 43 - ACT Math

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

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1. A complex impedance is modeled as $z=(2+3i)+(7-10i)$. What is $z$ in standard form $a+bi$ after combining real and imaginary parts?
2. A line models the amount of water in a tank, changing at a constant rate. The line passes through points $(0,4)$ and $(3,13)$. Which equation represents this linear relationship?
3. A school uses a piecewise function $f(x)$ to assign points based on the number of late days $x$ for an assignment. The policy is $f(x)=\begin{cases} 10-2x & \text{if } x<2 \\ 6 & \text{if } 2\le x<5 \\ - x+9 & \text{if } x\ge 5 \end{cases}$ What is $f(5)$ for the piecewise function defined below?
4. A circle has diameter $10$. What is the area of the circle?​
5. To simplify an algebraic expression involving $i$, evaluate $(6-2i)-(1+7i)$ in standard form.
6. If two dice are rolled, what is the probability that the sum is 7?
7. A taxi fare is modeled by $7x = 56$, where $x$ is the number of miles traveled. What is the solution to the equation?
8. A dice is rolled twice. What is the probability of rolling a 3 and then a 4?
9. Convert $75\%$ to a fraction in simplest form.
10. A drawing is a scale model where 3 inches on the drawing represent 12 feet in real life. How many feet in real life are represented by 8 inches on the drawing?
11. Two triangles, $\triangle GHI$ and $\triangle JKL$, $\triangle GHI$ has angles $G = 60^\text{o}$, $H = 60^\text{o}$, and $\triangle JKL$ has angles $J = 60^\text{o}$, $K = 60^\text{o}$. Are the triangles similar?
12. A bookstore sells notebooks for $4 each. During a sale, a customer buys 6 notebooks and uses a coupon for $5 off the total. What is the total amount paid?
13. Which equals $\cos(30^\circ)$?
14. A class collects canned goods. The total is modeled by $x + 14 = 3x - 2$. What is the solution to the equation?
15. What is the solution set of the inequality $3x + 2 < 11$?
16. In the unit circle, what is $\sin(\frac{\pi}{6})$?
17. What is $f(8)$ for the piecewise function defined below? $f(x)=\begin{cases} 3-x, & x<2\\ (x-2)^2, & 2\le x<6\\ 2x-5, & x\ge 6 \end{cases}$
18. What is the degree of the polynomial $5x^2 - 2x$?
19. What is the absolute value of $-6 + 8i$?
20. A triangle has side lengths $5$, $5$, and $8$. Which describes the triangle? (Choose from: right, isosceles, equilateral, scalene.)

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