Practice Test 20 - ACT Math

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

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1. What are the solutions to the quadratic equation $x^2 - 4x + 4 = 0$?
2. What is $5^{-2}$?
3. Two lines intersect at point $O$, forming vertical angles. One of the angles is labeled $x$, and the vertical angle opposite it is labeled $65^\circ$. What is the measure of angle $x$?
4. In the coordinate plane, a circle is given by $(x+1)^2+(y-4)^2=36$. What is the radius of the circle?
5. Which values of $x$ satisfy $5-x\ge 2$?
6. A bag contains 3 red balls and 9 blue balls. One ball is drawn at random. What is the probability of drawing a red ball? Give your answer in simplest form.
7. Lines $m$ and $n$ are parallel and cut by a transversal. The angle labeled $x$ is an interior angle at the top intersection on the right of the transversal. The angle labeled $60^\circ$ is the interior angle at the bottom intersection on the right of the transversal. m ⇒ ⇒ ⇒ / x / / n ⇒ ⇒ ⇒ / 60° If lines $m$ and $n$ are parallel, what is the measure of angle $x$?
8. What is the approximate value of $\sqrt{3}$?
9. For the function $f(x) = \begin{cases} x^2 + 2x & \text{if } x < 1 \\ 2x - 5 & \text{if } x \geq 1 \end{cases}$, what is $f(1)$?
10. A store offers a 30% discount on a $120 jacket. What is the sale price?
11. In $\triangle XYZ$ and $\triangle ABC$, $\triangle XYZ$ has angles $X = 90^\text{o}$, $Y = 45^\text{o}$, and $\triangle ABC$ has angles $A = 90^\text{o}$, $B = 45^\text{o}$. Are the triangles similar?
12. A fair six-sided die is rolled once. What is the probability of rolling an even number or a number greater than 4? (Assume outcomes are mutually exclusive only when appropriate.)
13. Find the circumference of a circle with radius 14.
14. What is $f(0)$ for the function $f(x) = 3x - 2$?
15. A bar graph shows the number of minutes of screen time on four days. How many days had screen time greater than 85 minutes?
16. A displacement is represented by $\mathbf{v}=\langle 2,\,-7\rangle$. What is $-2\mathbf{v}$?
17. In $\triangle ABC$, the side lengths are $AB=6$, $AC=8$, and $BC=10$. In $\triangle DEF$, the side lengths are $DE=9$, $DF=12$, and $EF=15$. Which triangles are similar?
18. Given the function $f(x) = x^2 - 3x + 4$, what is the value of $f(-2)$?
19. Two fair six-sided dice are rolled. What is the probability that the sum is 7?
20. A right triangle has hypotenuse length $17$ and one leg length $15$. What is the length of the other leg? Give your answer in simplest form.

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