Practice Test 34 - ACT Math

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

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1. A finance model uses natural logs. What is $\ln(e^5)$?
2. In simplifying an expression, a student multiplies two complex numbers. What is $(-4+3i)(-2-7i)$? Use FOIL and apply $i^2=-1$.
3. What is $\sin(0^\circ)$?
4. Triangles $\triangle GHI$ and $\triangle JKL$ are similar by AA with correspondence $G\leftrightarrow J$, $H\leftrightarrow K$, $I\leftrightarrow L$. If $GH=12$, $JK=8$, and $HI=15$, what is the length of the corresponding side $KL$?
5. What is the solution $(x, y)$ to the system $x + y = 9$ and $x - y = 1$?
6. Which expression is equivalent to $4x(2 + 3)$?
7. Solve: $-3(x-2)<9$.
8. Let $A=\begin{bmatrix}2 & -1\\ 3 & 0\end{bmatrix}$ and $B=\begin{bmatrix}-4 & 5\\ 1 & -2\end{bmatrix}.$ What is $A+B$ for matrices $A$ and $B$?​
9. Two triangles have side lengths $\triangle ABC$: $AB=6$, $BC=10$, $AC=12$ and $\triangle DEF$: $DE=3$, $EF=5$, $DF=6$. Are the triangles similar? If so, why?
10. What is the absolute value of $9i$?
11. Triangle ABC is an isosceles triangle with angles A and B equal. If angle C measures 40°, what is the measure of angle A?
12. What is the absolute value of $7 - 24i$?
13. A polynomial expression appears in a worksheet as $-(x-4)^2 + 3x$. Which polynomial is equivalent to this expression in standard form?
14. In triangles $\triangle ABC$ and $\triangle DEF$, $\triangle ABC$ has sides $AB = 4$, $BC = 3$, $CA = 5$. $\triangle DEF$ has sides $DE = 8$, $EF = 6$, $FD = 10$. Are these triangles similar?
15. A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles (10 total). One marble is selected at random. What is $P(\text{red or green})$? (Assume the events are mutually exclusive.)
16. A right circular cylinder has a volume of $72\pi$ cubic inches and a height of 8 inches. What is the radius, in inches, of the cylinder's base?
17. What is the median of [15, 9, 7, 5, 13]?
18. What is the magnitude of vector $\mathbf{v}$ if $\mathbf{v} = \langle 8, 15 \rangle$?
19. Factor: $x^2 - 9$
20. A delivery fee is linear in distance. The line has slope $m=-3$ and y-intercept $b=12$. Which equation has slope $-3$ and y-intercept $12$?

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