Practice Test 3 - ACT Math

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

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1. A data set consists of 5 distinct positive integers. If the median of the data set is 8 and the arithmetic mean is 10, what is the greatest possible value of the largest integer in the data set?
2. A coach tracked the number of push-ups completed by 8 athletes: 18, 22, 20, 24, 19, 21, 23, 20. What is the median of $\{18,22,20,24,19,21,23,20\}$?
3. A computation produces the complex number $-7+9i$, and you need its conjugate to eliminate the imaginary part in a product. What is the complex conjugate of $-7+9i$?
4. A car's value decreases from $15,000 to $12,000. What is the percent decrease?
5. A regular polygon has each interior angle equal to $135^\circ$. How many sides does this polygon have?
6. A ferry service charges $15 per passenger plus a flat fee of $100 per trip. Which equation represents the total cost $T$ for $p$ passengers?
7. Which expression is equivalent to $(x + 2)(x - 2)$?
8. A student has 6 different photos and wants to arrange exactly 3 of them in a row in a frame. Since the order in the frame matters, how many possible arrangements are there?
9. The data set $\{2, 3, 3, 4, 4, 4, 5, 20\}$ has one unusually large value. Which best describes the shape of the distribution?
10. What is the length of arc AB with central angle 120° in a circle with radius 6?
11. A temperature controller requires the error from $10^\circ$ to be at most $3^\circ$. If the actual temperature is $x$, which values of $x$ satisfy $|x-10|\le 3$?
12. A scatterplot shows four points: (10, 3), (12, 5), (14, 4), and (16, 6). The x-axis is x (units) and y-axis is y (units). Which point on the graph represents the condition $y=5$?
13. Which equals $\cos\left(\frac{\pi}{3}\right)$?
14. A jar contains 2 green marbles, 3 red marbles, and 5 blue marbles. One marble is chosen at random. What is $P(\text{green or red})$? (Assume these events are mutually exclusive.) Give your answer in simplest form.
15. Given the function $f(x) = 2x^2 - 3x + 5$, what is the value of $f(-3)$?
16. A circle has a radius of 4. What is the length of an arc with a central angle of 180°?
17. The data set is $\{2, 4, 6, 8\}$. If the value 10 is added to the data set, what is the new median?
18. A line on a coordinate plane crosses the y-axis at $3$ and decreases 1 unit for every 2 units it moves to the right. Which equation matches this description?
19. What is $f(0)$ for the function $f(x) = 9x - 7$?
20. A landscaper buys 9 bags of mulch at $4.75 per bag and a pair of gloves for $6. Which expression represents the total cost in dollars?

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