Practice Test 33 - ACT Math

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

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1. The ratio of red balls to green balls in a box is 2:5. If there are 20 red balls, how many green balls are there?
2. What is the measure of the arc AB with central angle 45° in a circle with radius 7?
3. Lines $m$ and $n$ are parallel (⇒). A transversal $t$ intersects them. At line $m$, the exterior angle on the left side of the transversal is $100^\circ$. m ⇒ ─────────────── 100° \ \ \ t \ \ x n ⇒ ───────────────If lines $m$ and $n$ are parallel, what is the measure of angle $x$?
4. A convex polygon has 7 sides. What is the sum of its interior angles?​​
5. A regular octagon has 8 equal sides. What is the measure of each interior angle in this regular 8-gon?
6. Factor: $x^2 + 6x$.
7. In simplifying a signal equation, you encounter $\ln\!\left(\dfrac{e^7}{e^2}\right)$. What is its value?
8. Two different payment options match at a certain number of items. If $7x + 1 = 5x + 17$, solve for $x$.
9. A principal wants to estimate the average time students spend on homework each night. She sends an optional online survey link through the school newsletter, and only students who choose to respond are counted. Students with strong feelings may be more likely to answer. Which characteristic makes this sample biased?
10. In how many ways can 5 students line up in a row for a photo if two specific students (Ana and Ben) must stand next to each other? Order matters left to right.
11. A car uses 5 gallons of fuel to travel 100 miles. How many miles can it travel on 20 gallons?
12. Factor: $x^2 + 3x - 18$
13. In the right triangle shown, if the adjacent side to angle $\theta$ is 5 and the hypotenuse is 13, what is $\cos(\theta)$?
14. Triangles $\triangle ABC$ and $\triangle DEF$ are shown. The side markings indicate $AB \cong DE$ (one tick) and $BC \cong EF$ (two ticks). Also, $\angle B \cong \angle E$ is marked, and it is the included angle between the tick-marked sides. Which congruence criterion applies?
15. Lines $x$ and $y$ are parallel. If angle $13$ is $145^\circ$, what is the measure of the corresponding angle $14$?
16. What is $\mathbf{v}+\mathbf{w}$ if $\mathbf{v}=\langle -4, -6\rangle$ and $\mathbf{w}=\langle 9, -1\rangle$?
17. The mean age of 5 people in a room is 30 years. When a 6th person enters the room, the mean age becomes 32 years. How old is the 6th person?
18. A complex value is given by $-2-11i$, and you need the conjugate to form a real denominator. What is the complex conjugate of $-2-11i$?
19. What is the sum of the interior angles of an 8-sided polygon (octagon)?
20. Which of the following is the product $AB$ for matrices $A = \begin{pmatrix} 0 & 1 \\ 2 & -1 \end{pmatrix}$ and $B = \begin{pmatrix} 3 & 2 \\ 1 & 0 \end{pmatrix}$?

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