Practice Test 5 - HSPT Math

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

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1. Solve for $x$: $3(2x-5)+4 = 2(x+7)-2.$
2. How many positive whole-number factors does $72$ have?
3. A rectangular playground is 12 meters long and 9 meters wide. What is the area of the playground in square meters?
4. Points $A(2, -3)$, $B(6, 1)$, and $C(x, 5)$ are collinear. What is the value of $x$?
5. In the number $4,205,687$, what is the value of the digit $2$?
6. A six-digit number is formed using the digits 1, 2, 3, 4, 5, and 6 exactly once each. If this number is divisible by 4, what is the maximum possible value of the tens digit?
7. Which of the following is not a multiple of $75$?
8. Find the exact volume, in cubic centimeters, of a cylinder with radius 4 cm and height 12 cm.
9. A standard deck of 52 cards is shuffled. What is the probability that a single card drawn at random is a heart?
10. Point $P$ is reflected across the line $y = x$ to give point $P'(5, -2)$. What are the coordinates of the original point $P$?
11. In a class survey, the number of hours students spend online per day has a median of 3 hours. Which statement must be true?
12. A cone has a base radius of 6 inches and a slant height of 10 inches. What is the lateral surface area of the cone?
13. A box contains 10 light bulbs, 3 of which are defective. Two bulbs are selected without replacement. What is the probability both bulbs are good?
14. In right triangle PQR with right angle at Q, if angle P measures 37°, what is the measure of angle R?
15. If the mean of ten numbers is $32$ and one of the numbers, $41,$ is removed, what is the new mean of the remaining nine numbers?
16. The greatest common divisor of two positive integers is 15. Their least common multiple is 300. If one of the integers is 60, what is the other integer?
17. The vertices of triangle $ABC$ are $A(-1, 2)$, $B(3, 5)$, and $C(1, -1)$. If the triangle is translated by the vector $\langle -4, 3 \rangle$, what are the coordinates of the image of vertex $B$?
18. In a class of 25 students, the mean score on a quiz was 80. The median score was 84. If the 5 students with the highest scores each had their scores increased by 4 points, what would be the new mean and median of the class scores?
19. The sum of the digits of a two-digit number is 12. If the digits are reversed, the new number is 18 less than the original number. What is the original number?
20. The sum of three consecutive odd integers is 75. What is the largest of these three integers?

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