Practice Test 8 - ACT Math

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

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1. A bacteria culture starts with 50 bacteria and doubles every hour. Let $x$ be the number of hours and $y$ be the number of bacteria. Which equation best models this relationship?
2. Which of the following expressions is equivalent to $4(a + 2b) - 2(a - 3b)$?
3. For the piecewise function $f(x)=\begin{cases} 3x+2, & x<2\\ 8-x, & 2\le x<6\\ (x-6)^2, & x\ge 6 \end{cases}$ what is $f(5)$?
4. Convert 0.45 to a percent.
5. What is $\tan(30^\circ)$? Give your answer in simplest form.
6. What is $(8 - 5i) + (3 + 2i)$?
7. A circle has radius $6$. What is the circumference of the circle?
8. A quantity decreases from $90$ to $72$. What is the percent decrease from the original value?
9. In the right triangle, if the opposite side is 8 and the hypotenuse is 17, what is $\sin(\theta)$?
10. A line shows a constant rate of change in a game score. The line passes through points $(-3,-1)$ and $(1,7)$. What is the slope of the line through points $(-3,-1)$ and $(1,7)$?
11. A student wants to estimate the average price of a textbook at her college bookstore. She records the prices of the first 30 textbooks she sees on the "New Arrivals" shelf. That shelf mostly contains expensive new editions. Which characteristic makes this sample biased?
12. A map uses the scale $1\text{ inch} : 4\text{ miles}$. Two towns are $3.5$ inches apart on the map. How many miles apart are the towns in real life?
13. A student tracks the temperature (in °C) of a cooling liquid, which changes linearly with time. The line passes through points $(0,18)$ and $(4,6)$. What is the y-intercept of the line through these points?​​
14. Two triangles have the following marked information: $\angle A \cong \angle D$, $\angle B \cong \angle E$, and a non-included side $AC=13$ equals $DF=13$. Which congruence criterion applies?
15. Which of the following represents $f(x+3)$ if $f(x) = x^2 - 3x$? Give your answer in simplest form.
16. A model uses the product $(x+3i)(2-4i)$, where $x$ is a real number. What is the real part of $(x+3i)(2-4i)$ after using FOIL and applying $i^2=-1$?
17. A local bakery sells muffins in boxes of 6 and donuts in boxes of 12. If a customer buys the same number of muffins as donuts, what is the smallest total number of baked goods (muffins plus donuts) the customer could have purchased?
18. A phone plan's total cost is modeled by $y = 45 + 0.08x$, where $x$ is the number of text messages sent in a month and $y$ is the total monthly cost in dollars. Which variable represents the number of text messages?
19. Simplify: $2x - (4x - 6)$
20. Two lines intersect at point $O$. One of the angles is labeled $120^\circ$. The angle adjacent to it on the same straight line is labeled $x$. \ 120° / \ / -----O----- / x \ / \What is the measure of angle $x$?

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