Practice Test 6 - ACT Math

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

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1. Which equals $\tan(45^\circ)$?
2. Solve: $x^2 - x - 12 = 0$
3. What is the leading coefficient of $2x^3 - 3x^2 + 5x - 6$?
4. On a number line, the points $p=-0.6$, $q=-\dfrac{2}{3}$, $r=-\sqrt{\dfrac{1}{4}}$, and $s=-0.65$ are plotted. Which number is smallest?
5. Triangles $\triangle ABC$ and $\triangle DEF$ are shown. $\angle A \cong \angle D$ and $\angle B \cong \angle E$ are marked. Side $AB=10$ and $DE=5$. What is the scale factor from $\triangle ABC$ to $\triangle DEF$?
6. A function is defined by $f(x)=5-2x$. What is $f(6)$?
7. What is $f(-2)$ if $f(x) = x^2 + 3x + 2$?
8. A set of 10 integers is $\{1, 2, 2, 2, 3, 4, 5, 5, 7, 9\}$. What is the median of the data set?
9. A set of 8 values is $\{9, 9, 10, 10, 10, 11, 11, 30\}$. Which best describes the shape of the distribution?
10. What is $\mathbf{v}-\mathbf{w}$ if $\mathbf{v}=\langle -1, 8\rangle$ and $\mathbf{w}=\langle 6, 3\rangle$?
11. What is the determinant of matrix $\begin{bmatrix} 2 & -3 \\ 4 & 1 \end{bmatrix}$?
12. A health department wants to know whether people who bike to work report lower stress. They survey commuters about how they travel and their stress level, without asking anyone to change their commute habits. Some people may misreport their stress. Is this an experiment or an observational study?
13. In the standard (x,y) coordinate plane, the graph of y = f(x) is shifted 3 units right and 2 units down. Which of the following equations represents the new graph?
14. A square pyramid has a square base with side length 6 units and a vertical height of 9 units from the base to the apex. What is the volume of the pyramid in cubic units?​
15. In the standard $(x, y)$ coordinate plane, what is the slope of the line given by the equation $5x + 2y = 10$?
16. A test has $40$ questions, and a student answers $30$ correctly. What percent of the questions did the student answer correctly?
17. What is $6^2$?
18. A video platform sets a recommendation score $f(x)$ based on watch time $x$ (in hours) using the piecewise function. For the function $f(x)=\begin{cases}x+4 & \text{if } x<2\\ 9-2x & \text{if } 2\le x<5\\ x^2-1 & \text{if } x\ge 5\end{cases}$ what is $f(3)$?
19. The area of a circle is $49\pi$ square centimeters. What is the circumference of the circle, in centimeters?
20. What is $f(0)$ for the piecewise function $f(x) = \begin{cases} 2x + 4 & \text{if } x < 1 \\ x^2 - 6 & \text{if } x \geq 1 \end{cases}$?

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