Practice Test 12 - ACT Math

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

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1. What is the value of $x$ in the proportion $\frac{11}{x}=\frac{22}{18}$? (If $\frac{a}{b}=\frac{c}{d}$, then $ad=bc$.)
2. Order the following numbers from least to greatest: $\frac{3}{5}$, $0.6$, $-1$, $\frac{1}{2}$.
3. A thermostat uses a rule $f(x)$ to convert an input setting $x$ to an output level. For the piecewise function $f(x)=\begin{cases}5-x & \text{if } x<2\\ 2x-1 & \text{if } 2\le x<8\\ x+3 & \text{if } x\ge 8\end{cases}$ what is $f(2)$?
4. Which inequality is equivalent to $-2x + 3 > 9$?
5. What is $f(1)$ for the polynomial $f(x) = 4x^2 - 2x + 1$?
6. A lab report states $\log_2(32)=x$. What is the value of $x$?
7. Convert 0.25 to a percent.
8. A measurement is written as $\sqrt{0.09}$. What is the approximate value of $\sqrt{0.09}$?
9. Given $f(x)=x^2-9$, which statement is true? Use substitution: $f(x+1)=(x+1)^2-9$ and compare to $f(x)+1$.
10. To expand an expression in a formula, compute: What is $(x+4)(x+1)$?
11. Which ratio is equivalent to $6:11$?
12. A movie lasts 120 minutes. How many hours is the movie?
13. How many permutations of 6 distinct items taken 3 at a time are there? (That is, how many ordered arrangements of length 3 can be formed from 6 different items?)
14. Given $\triangle RST$ with sides $RS = 7$, $ST = 24$, $RT = 25$, and $\triangle XYZ$ with sides $XY = 14$, $YZ = 48$, and $XZ = 50$. What is the scale factor from $\triangle RST$ to $\triangle XYZ$?
15. A city council wants to estimate support for a new bus route. A volunteer stands outside the downtown transit station from 5–6 PM on weekdays and asks the first 200 riders who pass by to answer a short poll. Many residents who don't use transit at that time are not included. Which sampling method is being used?
16. In $\triangle ABC$: $\angle A = 50°$, $\angle B = 60°$, $\angle C = 70°$. What is the correct ordering of side lengths from least to greatest?
17. A boat's velocity is $v=\langle -2,1\rangle$ (in m/s). Which vector represents the opposite direction with the same speed?
18. What is $2^{-3}$?
19. A function is defined by $f(x)=2-x$. What is the value of $f(1-x)$?
20. What is $f(-2)$ if $f(x) = 5x - 2$?

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