Practice Test 44 - ACT Math

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

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1. Two lines intersect, forming vertical angles. One of the angles at the intersection is labeled $x$, and the vertical angle opposite it is labeled $65^\circ$. What is the value of $x$?
2. In quadrilateral ABCD, the measures of angles A, B, and C are (2x)°, (3x)°, and (2x + 10)° respectively. The measure of angle D is 70°. What is the measure of angle C?
3. What is the measure of each interior angle in a regular quadrilateral?
4. A force vector is $\mathbf{v}=\langle 4, -9\rangle$. What is $3\mathbf{v}$?
5. A printing company charges according to $y = 0.12x + 15$, where $x$ is the number of pages printed and $y$ is the total cost in dollars. What is the meaning of the $15$ in this model?
6. For an acute angle $\theta$ in a right triangle, it is given that $\tan \theta = \frac{3}{4}$. What is the value of $\sin \theta$?
7. Based on the piecewise function $f(x)=\begin{cases} 2-x, & x<-4\\ (x+4)(x-1), & -4\le x<1\\ 3, & x\ge 1 \end{cases}$ what is the value when $x=-4$?
8. A rectangular garden has an area represented by $x^2+7x+12$ square feet, where $x$ is the width added in a redesign. Factor: $x^2+7x+12$.
9. John has $150. If he spends $45 on a new shirt, how much money does he have left?
10. What is the scale factor from a triangle with sides 3, 4, 5 to a similar triangle with sides 6, 8, 10?
11. In the diagram, angle $x$ and angle $y$ are vertical angles. If angle $x$ measures $45^\circ$, what is the measure of angle $y$?
12. What is the mode of the data set [3, 6, 9, 6, 15, 6, 10]?
13. What is the slope of the line through points (-3, -2) and (1, 6)?
14. If $f(x)=\dfrac{2x-1}{3}$, what is $f(x-4)$? Substitute $(x-4)$ for every $x$: $f(x-4)=\dfrac{2(x-4)-1}{3}$.
15. Which equals $\sin\left(\frac{\pi}{6}\right)$?
16. In the diagram, angle $A$ and angle $B$ are complementary. If angle $A$ is $55^\circ$, what is the measure of angle $B$?
17. A bookstore stacks books with the relationship $7x + 3 = 52$. Solve for $x$. Give your answer in simplest form.
18. Which congruence criterion applies to triangles MNO and PQR if $MN = PQ$, $\text{angle } N = \text{angle } Q$, and $NO = QR$?
19. In triangle MNO, angle M measures 45° and angle N measures 45°. What is the measure of angle O?
20. In an AC circuit calculation, a technician multiplies two complex impedances. What is $(3 + 4i)(2 - 5i)$? Use FOIL and apply $i^2 = -1$ to write the result in standard form $a + bi$.

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