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Practice Test 3 - HSPT Math

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

  1. The greatest length of a straight board that can fit through a rectangular doorway 8 ft8\text{ ft} high and 3 ft3\text{ ft} wide is closest to:
  2. What is the value of the expression 314−123212+16 \frac{3 \frac{1}{4} - 1 \frac{2}{3}}{2 \frac{1}{2} + \frac{1}{6}} ?
  3. A quadrilateral has vertices K(-2, 5), L(1, 8), M(7, 2), and N(4, -1). What is the most specific classification for this quadrilateral?
  4. A canister of oil was 78 \frac{7}{8} full. A cook used 13 \frac{1}{3} of the oil in the canister, then added 0.5 liters of oil. If the canister is now 34 \frac{3}{4} full, what is the total capacity of the canister in liters?
  5. What is the simplified value of the expression (45−2)÷(2−45) (\frac{4}{5} - 2) \div (2 - \frac{4}{5}) ?
  6. Solve for kk: 5−k3=2−k.\dfrac{5-k}{3}=2-k.
  7. The mean of four numbers is 1818. If three of the numbers are 12, 20,12,\ 20, and 25,25, what is the fourth number?
  8. If 12n12n is a multiple of 9090, which of the following could be the value of nn?
  9. A rectangular prism has a length of 12 cm, a width of 9 cm, and a height of 8 cm. What is the length of the space diagonal, the longest straight line segment that can be drawn between two vertices of the prism?
  10. Which of the following numbers has a 33 in the tens place and a 55 in the thousands place?
  11. A running track is formed by a rectangle with a semicircle at each end. The rectangle is 100 meters long and 70 meters wide. What is the perimeter of the track?
  12. A machine produces widgets at rates proportional to 3:4:53:4:5 for its three production lines. In an 88-hour shift, the total production is 24002400 widgets. Due to maintenance, the second production line operates at only 75%75\% efficiency for the next 66-hour shift. How many widgets will be produced in this 66-hour shift?
  13. Solve for aa: 7(a−2)+3=2(5a−1).7(a-2)+3=2(5a-1).
  14. A baseball diamond is a square with each side measuring 90 feet. How far does a player run when going from home plate to second base in a straight line?
  15. A rectangular prism has dimensions of 6 cm by 8 cm by 10 cm. If the length is increased by 25% and the width is decreased by 12.5%, what is the new volume?
  16. The numbers 2, 4, 6, 8, and n have a mean of 7. What is the value of n?
  17. At a school, the ratio of freshmen to sophomores to juniors is 6 : 5 : 4. If there are 150 sophomores, how many total students are in these three classes combined?
  18. A ladder leans against a wall, forming a right triangle with the ground. The ladder is 26 feet long and the base of the ladder is 10 feet from the wall. How high up the wall does the ladder reach?
  19. In a right triangle, sin⁡θ=35\sin \theta=\dfrac{3}{5}. What is cos⁡θ\cos \theta?
  20. A bag of mixed nuts contains almonds, cashews, and peanuts in the ratio 7 : 3 : 5 by weight. If the bag holds 3.15 kg of nuts, how many kilograms of cashews are in the bag?

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