Practice Test 27 - ACT Math

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

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1. Let $x$ be a real number. What is $(x+2i)+(3-5i)$ written in standard form $a+bi$?
2. Distribute and simplify: $-2(3a - 5) + 4a$.
3. If an event occurs with a probability of 0.25, what is the probability of the event not occurring?
4. Which equation is equivalent to $\log_5(1) = z$?
5. Which equation is equivalent to $\log_3(9) = y$?
6. Which equation has slope -4 and y-intercept 6?
7. What is the equation of a circle with center (0, 0) and radius 8?
8. Which of the following matches the expansion of $5(2p - 1)$?
9. To simplify a denominator, you compute a product of conjugates. What is $(9+2i)(9-2i)$? Use FOIL and apply $i^2=-1$.
10. Which of the following is equivalent to the expression $\sqrt{-25} + \sqrt{-36} + 2$? (Note: $i = \sqrt{-1}$)
11. A triangle has angles $44^\circ$ and $89^\circ$. What is the measure of the third angle?
12. Simplify: $\sqrt{72}$
13. If $\triangle LMN \thicksim \triangle OPQ$ with $LM = 6$ and $OP = 18$, what is the ratio of $MN$ to $PQ$?
14. Solve: $|x+2|\le 5$ (give your answer in interval notation).
15. Which of the following expressions is equivalent to $3(x - 4) + 2x$?
16. Which polynomial is equivalent to $(x + 2)(x - 2)$?
17. To explore customer satisfaction, a store selects a sample of customers who have left feedback in the past month. Which characteristic makes this sample potentially biased?
18. A point in the complex plane is represented by $8-6i$. What is the absolute value of $(8-6i)$? Use $|a+bi|=\sqrt{a^2+b^2}$ and simplify the radical.
19. A team has 6 players and needs to choose 2 captains (Captain 1 and Captain 2). Since the roles are distinct, order matters. In how many ways can the captains be chosen?
20. Lines $a$ and $b$ are parallel. If angle $9$ measures $105^\circ$, what is the measure of the alternate interior angle $10$?

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