Practice Test 1 - HSPT Math

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

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1. A number $N$ is equal to $0.2\overline{7}$. What is $N \div \frac{5}{6}$?
2. Points $A$, $B$, and $C$ form a right triangle where the right angle is at $B$. If $A(1, 5)$, $B(1, 2)$, and $C(x, 2)$, and $BC = 4$, what is a possible value of $x$?
3. What is the radius of the smallest circle that can contain a rectangle measuring $6\text{ cm}$ by $8\text{ cm}$?
4. A square has a diagonal of length 18 inches. What is the length of each side of the square?
5. In a chemistry lab, three solutions must be mixed in the ratio $3:7:5$ by volume. However, the available containers can only measure in increments of $25$ mL. What is the smallest total volume of mixture that can be prepared using this ratio with the measuring constraint?
6. A square pyramid has a square base with side length 12 units. The slant height of each triangular face is 10 units. What is the height of the pyramid?
7. A construction crew needs to fill a foundation that requires $18\frac{5}{6}$ cubic yards of concrete. They have already poured $7\frac{2}{3}$ cubic yards and plan to pour the remaining amount in 3 equal loads. If each truck can carry a maximum of $4\frac{1}{4}$ cubic yards, how many trucks will be needed for the remaining concrete?
8. A rectangular garden measures 15 meters by 20 meters. Maria wants to build a straight path from one corner to the diagonally opposite corner. If building materials cost $8 per meter, how much will the materials for the path cost?
9. Two similar polygons have perimeters in the ratio 3:5. The sum of their areas is 544 square centimeters. What is the area of the larger polygon?
10. What is the exact circumference, in terms of $\pi$, of a circle whose diameter is 18 cm?
11. Solve the inequality $-4(2y-3)\le 8-6y.$
12. A rectangular garden has a length that is 4 feet less than twice its width. If the perimeter of the garden is 88 feet, what is its area in square feet?
13. What is the solution to the equation $10 - [3x - (2x - 1)] = 4(x + 2)$?
14. A storage box in the shape of a rectangular prism has a volume of 24 cubic feet. Its length is 4 feet and its width is 3 feet. A painter needs to paint the exterior of the box, including the lid. If one can of paint covers 18 square feet, how many cans of paint are needed?
15. A technology club has 40 members. 25 members are skilled in programming, and 15 members are skilled in hardware design. 10 members are skilled in both. If a member who is skilled in hardware design is chosen at random, what is the probability that this member is also skilled in programming?
16. A solid metal cube with a side length of 4 inches is placed inside a larger, empty cubical box with a side length of 5 inches. How much empty space is in the box, in cubic inches?
17. If a number is first multiplied by $\frac{5}{6}$ and then 1.25 is subtracted from the product, the result is $2 \frac{1}{2}$. What is the original number?
18. In $0.00457$, the digit $7$ is in which place?
19. The equation $4(3x - 2) - 6(2x - 1) = -2$ is an example of:
20. A hiker travels $4\text{ km}$ due north and then $7\text{ km}$ due east. How many kilometers is she from her starting point, to the nearest tenth?

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