Practice Test 6 - HSPT Math

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

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1. The integer N is a positive integer with exactly 8 factors. If two of N's factors are 15 and 21, what is the sum of the distinct prime factors of N?
2. A regular hexagon is inscribed in a circle of radius 8. What is the length of the apothem (the distance from the center to the middle of any side)?
3. A right triangle has legs of 9 cm and 12 cm. A semicircle is drawn using the hypotenuse as its diameter. What is the area of the semicircle?
4. A piece of ribbon is $5\frac{1}{3}$ feet long. If $\frac{2}{5}$ of it is cut off, and then $\frac{1}{4}$ of what remains is cut off again, what is the length of the final piece?
5. A survey of 40 homes found an average of 2.5 televisions per home. If 10 of the homes each had 4 televisions, what was the mean number of televisions in the remaining homes?
6. Which digit can be placed in the square to make $8\,\square\,7$ divisible by $9$?
7. What is the length of the space diagonal of a rectangular box that measures $3\text{ cm}$ by $4\text{ cm}$ by $12\text{ cm}$?
8. The ratio of the areas of two similar triangles is $9:16$. If the perimeter of the smaller triangle is $24$ cm, what is the perimeter of the larger triangle?
9. A rectangular swimming pool is 25 feet long, 15 feet wide, and 6 feet deep. If the pool is filled to 80% capacity and water costs $0.003 per cubic foot, what is the cost to fill the pool?
10. A number in the form $10^n - 1$ (where $n$ is a positive integer) is written in decimal notation. If this number has exactly 15 digits that are 9's, what is the value of $n$?
11. The graph of the function f(x) = |x - 3| + 2 is a V-shape. The entire graph is reflected across the y-axis to create a new function g(x). Then, the graph of g(x) is translated 4 units down to create a third function h(x). What are the coordinates of the vertex of h(x)?
12. Which of the following numbers is a multiple of $14$ but not a multiple of $6$?
13. What is the exact volume of a sphere with a radius of 6 centimeters?
14. Set S contains all the positive factors of 240. Set T contains all the multiples of 8 that are less than 100. How many numbers are in both Set S and Set T?
15. What is the slope of the line that passes through the points $(-4,3)$ and $(2,-9)$?
16. A solution contains $40\%$ acid. How many liters of pure water must be added to $3\frac{1}{3}$ liters of this solution to create a mixture that is $25\%$ acid?
17. In triangle DEF, angle F is a right angle. If angle D measures 28°, what is the measure of the remaining angle?
18. The volume of a right circular cone is $100\pi$ cubic inches. Its height is 12 inches. What is the circumference of its base?
19. A number decreased by 15 is equal to 3 times the number increased by 9. What is the number?
20. Which pair of numbers are consecutive multiples of $9$?

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