HiSET Mathematics Practice Test

25 practice questions

Choose an answer, then check it under Show answer.

1. Question 1 of 25Medium

   A right circular cylinder has a radius of 3 centimeters and a height of 10 centimeters. What is the total surface area of the cylinder, rounded to the nearest tenth? (Use pi = 3.14159.)

   1. AA. 188.5 square centimeters
   2. BB. 282.7 square centimeters
   3. CC. 216.8 square centimeters
   4. DD. 245.0 square centimeters
   Show answer to question 1

   Answer: D. 245.0 square centimeters

   Total surface area equals the two circular bases plus the lateral surface: 2(pi)(3^2) + 2(pi)(3)(10) = 18 pi + 60 pi = 78 pi, which is about 245.0 square centimeters. The value 188.5 square centimeters is only the curved lateral surface, so it leaves out both circular bases.

2. Question 2 of 25Hard

   A pump empties water from a holding tank at a constant rate of 45 gallons every 6 minutes. At this rate, how many hours will it take the pump to empty 1,350 gallons of water?

   1. AA. 5 hours
   2. BB. 3 hours
   3. CC. 180 hours
   4. DD. 30 hours
   Show answer to question 2

   Answer: B. 3 hours

   The pump works at a rate of 7.5 gallons per minute, which means pumping 1,350 gallons requires 180 minutes. Dividing 180 minutes by 60 minutes per hour gives 3 hours. The option of 180 hours is incorrect because it treats the number of minutes as hours without completing the time conversion.

3. Question 3 of 25Hard

   A circle with radius 5 inches is drawn inside a square so that the circle touches all four sides of the square. What is the area of the region inside the square but outside the circle? Use 3.14 for pi and round to the nearest tenth.

   1. AA. 21.5 square inches
   2. BB. 78.5 square inches
   3. CC. 68.6 square inches
   4. DD. 25.0 square inches
   Show answer to question 3

   Answer: A. 21.5 square inches

   Because the circle touches all four sides, the square's side is the diameter, 10 inches, so the square area is 100 square inches. The circle area is 3.14 x 25 = 78.5 square inches, and 100 - 78.5 = 21.5 square inches. The value 78.5 is the circle's area alone, not the area outside it.

4. Question 4 of 25Medium

   Simplify the expression -2(3x - 4) + 5(x + 1).

   1. AA. -11x + 13
   2. BB. -x + 9
   3. CC. -x + 13
   4. DD. -x - 3
   Show answer to question 4

   Answer: C. -x + 13

   Distributing -2 gives -6x + 8 and distributing 5 gives 5x + 5; combining like terms gives -x + 13. The option -x - 3 comes from incorrectly treating -2 times -4 as -8 instead of +8.

5. Question 5 of 25Medium

   Elena earns d dollars per day. She worked for 5 days this week and received a $75 performance bonus. She then divided her total weekly earnings equally among 3 separate savings accounts. Which expression represents the amount of money, in dollars, deposited into each savings account?

   1. AA. (5d + 75) / 3
   2. BB. (5d / 3) + 75
   3. CC. 5d + (75 / 3)
   4. DD. (d + 75) / 3
   Show answer to question 5

   Answer: A. (5d + 75) / 3

   Elena's base pay for 5 days is 5d, so her total weekly earnings including the bonus are 5d + 75. Dividing the entire total earnings equally among 3 accounts yields (5d + 75) / 3. The expression 5d + (75 / 3) is incorrect because it divides only the bonus by 3 instead of dividing the entire earnings.

6. Question 6 of 25Easy

   A notebook costs $2.75 and a pack of pens costs $4.60. What is the total cost of the notebook and the pack of pens?

   1. AA. $7.35
   2. BB. $7.45
   3. CC. $6.35
   4. DD. $7.25
   Show answer to question 6

   Answer: A. $7.35

   Add the two prices: $2.75 + $4.60 = $7.35. The tempting $6.35 comes from failing to regroup the 13 tenths as 1 one and 3 tenths.

7. Question 7 of 25Medium

   A 25-foot support cable is anchored to the ground and attached to the top of a vertical pole. The cable is anchored 15 feet from the base of the pole on level ground. What is the height, in feet, of the pole?

   1. AA. 10
   2. BB. 29
   3. CC. 20
   4. DD. 40
   Show answer to question 7

   Answer: C. 20

   The cable represents the hypotenuse of a right triangle, while the ground distance and pole height represent the two legs. Using the Pythagorean theorem, 15 squared plus the height squared equals 25 squared, which simplifies to 225 plus the height squared equals 625. Subtracting 225 from 625 gives 400, and the square root of 400 is 20 feet. The value 29 is incorrect because it results from treating 25 as a leg and adding the squares instead of subtracting.

8. Question 8 of 25Medium

   A concrete access ramp is constructed in the shape of a right triangular prism. The triangular end has a base of 9 feet and a height of 4 feet. The length of the ramp along the prism is 15 feet. What is the volume of the ramp in cubic feet?

   1. AA. 270
   2. BB. 180
   3. CC. 540
   4. DD. 135
   Show answer to question 8

   Answer: A. 270

   The volume of a triangular prism equals the area of the triangular base multiplied by the length of the prism. The area of the triangular base is one-half times 9 times 4, which is 18 square feet, and multiplying 18 by the length of 15 feet yields 270 cubic feet. The option 540 cubic feet is incorrect because it omits the factor of one-half required for the area of a triangle.

9. Question 9 of 25Easy

   A recipe calls for 5/8 pound of pecans. Marcus wants to make only 2/3 of the recipe. What fraction of a pound of pecans does Marcus need?

   1. AA. 15/16
   2. BB. 7/24
   3. CC. 5/12
   4. DD. 10/11
   Show answer to question 9

   Answer: C. 5/12

   Multiplying the numerators gives 10 and multiplying the denominators gives 24, which simplifies to 5/12 by dividing both by 2. The value 15/16 is incorrect and results from cross-multiplying the numerators and denominators instead of multiplying straight across.

10. Question 10 of 25Hard

    A running club has 12 members with a mean age of 28 years. Two new members join the club, and one of them is 4 years older than the other. With both new members included, the mean age of all 14 members is 29 years. What is the age, in years, of the older new member?

    1. AA. 37
    2. BB. 35
    3. CC. 33
    4. DD. 39
    Show answer to question 10

    Answer: A. 37

    The original total age is 12 times 28, or 336 years, and the new total age is 14 times 29, or 406 years. The sum of the ages of the two new members is 406 - 336 = 70 years. Setting the younger member's age as x gives the equation x + (x + 4) = 70, leading to x = 33 for the younger member and 37 for the older member. The value 35 is incorrect because it represents the average age of the two new members rather than the age of the older member.

11. Question 11 of 25Hard

    A painter mixes 2 1/2 gallons of white paint with 1 3/4 gallons of blue paint. After using 5/8 gallon of the mixture, how much mixture remains?

    1. AA. 4 3/8 gallons
    2. BB. 4 7/8 gallons
    3. CC. 3 3/8 gallons
    4. DD. 3 5/8 gallons
    Show answer to question 11

    Answer: D. 3 5/8 gallons

    The total mixture is 2 4/8 + 1 6/8 = 4 2/8 gallons. Subtracting 5/8 gallon requires borrowing one whole, giving 3 10/8 - 5/8 = 3 5/8 gallons. The tempting 4 3/8 gallons comes from subtracting the smaller fractional part from the larger instead of borrowing.

12. Question 12 of 25Easy

    What is the value of 3^4?

    1. AA. 64
    2. BB. 81
    3. CC. 12
    4. DD. 27
    Show answer to question 12

    Answer: B. 81

    An exponent tells how many times to use the base as a factor, so 3^4 = 3 x 3 x 3 x 3 = 81. Multiplying the base by the exponent, 3 x 4 = 12, gives a product but not a power.

13. Question 13 of 25Hard

    What is the value of the expression (x^2 - 4(x - y)) / (2x + y) when x = -2 and y = 6?

    1. AA. -14
    2. BB. 14
    3. CC. 18
    4. DD. -6
    Show answer to question 13

    Answer: C. 18

    Substituting the given values into the numerator yields (-2)^2 - 4(-2 - 6) = 4 - 4(-8) = 4 + 32 = 36, and the denominator simplifies to 2(-2) + 6 = -4 + 6 = 2. Dividing 36 by 2 gives 18. The value 14 is obtained if (-2)^2 is mistakenly evaluated as -4 instead of positive 4.

14. Question 14 of 25Medium

    Marcus took four math tests this semester and earned scores of 76, 84, 87, and 89. He wants to have an overall mean score of exactly 86 after he takes the fifth test. What score must Marcus earn on his fifth test?

    1. AA. 90
    2. BB. 84
    3. CC. 94
    4. DD. 86
    Show answer to question 14

    Answer: C. 94

    To achieve a mean of 86 on five tests, the sum of all five test scores must equal 5 times 86, which is 430. The sum of the first four tests is 76 + 84 + 87 + 89 = 336. Subtracting 336 from 430 leaves 94 points required on the fifth test. The option of 84 is incorrect because it represents the mean of the first four tests rather than the required score on the fifth test.

15. Question 15 of 25Medium

    A committee of 2 students is to be randomly chosen from a school club that has 6 juniors and 4 seniors. What is the probability that both chosen students will be juniors?

    1. AA. 3/10
    2. BB. 9/25
    3. CC. 4/15
    4. DD. 1/3
    Show answer to question 15

    Answer: D. 1/3

    Choosing two students without replacement creates dependent events. The probability of selecting a junior first is 6/10, and the probability of selecting another junior second is 5/9; multiplying these gives 30/90, which simplifies to 1/3. The fraction 9/25 incorrectly assumes the first student is replaced before the second is selected, while 4/15 represents the probability of choosing one junior and then one senior.

16. Question 16 of 25Easy

    A circular swimming pool has a diameter of 18 feet. Using 3.14 for pi, what is the circumference of the swimming pool, in feet?

    1. AA. 56.52
    2. BB. 28.26
    3. CC. 113.04
    4. DD. 254.34
    Show answer to question 16

    Answer: A. 56.52

    Circumference is found using the formula C = pi * d. Multiplying 3.14 by the diameter of 18 feet gives 56.52 feet. The value 113.04 feet is incorrect because it mistakenly treats 18 feet as the radius rather than the diameter.

17. Question 17 of 25Hard

    A random sample of 400 registered voters finds that 54% support a proposal. The margin of error is 5 percentage points at the 95% confidence level. Which conclusion is best supported by this information?

    1. AA. Support among all voters is exactly 54%.
    2. BB. The data do not show a clear majority.
    3. CC. Exactly 95% of all voters support the proposal.
    4. DD. A majority of all voters support the proposal.
    Show answer to question 17

    Answer: B. The data do not show a clear majority.

    The margin of error gives an interval from 49% to 59%, which includes 50%, so the data do not establish a clear majority. The tempting conclusion that a majority supports the proposal ignores the margin of error and treats 54% as exact.

18. Question 18 of 25Hard

    Which of the following numbers satisfies the inequality -1.75 < x < -1 3/8?

    1. AA. -1 1/4
    2. BB. -1 2/3
    3. CC. -1.35
    4. DD. -1.8
    Show answer to question 18

    Answer: B. -1 2/3

    Writing the boundary values as decimals gives -1.75 and -1.375. The value -1 2/3 is approximately -1.67, which lies strictly between -1.75 and -1.375 on the number line. The option -1.35 is incorrect because -1.35 is greater than -1.375, so it exceeds the upper bound of the inequality.

19. Question 19 of 25Medium

    A veterinarian notes that a dog weighs 66 pounds. Given that 1 kilogram is approximately equal to 2.2 pounds, what is the weight of the dog in grams?

    1. AA. 3,000 grams
    2. BB. 30 grams
    3. CC. 145,200 grams
    4. DD. 30,000 grams
    Show answer to question 19

    Answer: D. 30,000 grams

    Dividing 66 pounds by 2.2 pounds per kilogram yields 30 kilograms, and multiplying 30 kilograms by 1,000 grams per kilogram gives 30,000 grams. The value of 145,200 grams results from incorrectly multiplying by 2.2 instead of dividing.

20. Question 20 of 25Medium

    Which expression is equivalent to (18x^6 y^(-2)) / (3x^(-2) y^4) for all non-zero values of x and y?

    1. AA. 6x^4 y^2
    2. BB. (6x^4) / y^6
    3. CC. (6x^8) / y^2
    4. DD. (6x^8) / y^6
    Show answer to question 20

    Answer: D. (6x^8) / y^6

    Dividing the coefficients gives 18 / 3 = 6, subtracting the exponents for x gives 6 - (-2) = 8, and subtracting the exponents for y gives -2 - 4 = -6, which places y^6 in the denominator to yield (6x^8) / y^6. The distractor (6x^4) / y^6 results from incorrectly computing 6 - 2 rather than accounting for the negative exponent in the denominator.

21. Question 21 of 25Medium

    A concrete patio is shaped like a trapezoid. The two parallel sides have lengths of 16 feet and 24 feet. The perpendicular distance between these parallel sides is 11 feet. What is the area of the patio in square feet?

    1. AA. 264
    2. BB. 176
    3. CC. 220
    4. DD. 440
    Show answer to question 21

    Answer: C. 220

    The area of a trapezoid is calculated by multiplying half the sum of the parallel bases by the perpendicular height: 0.5 * (16 + 24) * 11 = 220 square feet. The value 440 square feet occurs when one forgets to multiply by one-half after adding the two bases.

22. Question 22 of 25Easy

    Which of the following is the solution to the inequality 4x - 7 <= 6x + 5?

    1. AA. x >= 6
    2. BB. x <= 6
    3. CC. x <= -6
    4. DD. x >= -6
    Show answer to question 22

    Answer: D. x >= -6

    Subtracting 6x from both sides yields -2x - 7 <= 5, and adding 7 gives -2x <= 12. Dividing both sides by -2 requires flipping the direction of the inequality sign, producing x >= -6. The result x <= -6 occurs if one forgets to reverse the inequality sign when dividing by a negative number.

23. Question 23 of 25Easy

    What is the solution (x, y) to the system of equations below? x + 2y = 11 y = 2x - 2

    1. AA. (4, 3)
    2. BB. (3, 4)
    3. CC. (5, 3)
    4. DD. (1, 5)
    Show answer to question 23

    Answer: B. (3, 4)

    Substituting the expression 2x - 2 for y into the first equation gives x + 2(2x - 2) = 11, which simplifies to 5x - 4 = 11 and yields x = 3. Substituting x = 3 back into y = 2x - 2 results in y = 4, giving the ordered pair (3, 4). The option (4, 3) is incorrect because it reverses the values of x and y.

24. Question 24 of 25Easy

    A weather station recorded the daily high temperatures for a city over a 7-day period: Monday: 68°F Tuesday: 72°F Wednesday: 75°F Thursday: 71°F Friday: 69°F Saturday: 80°F Sunday: 74°F What was the median daily high temperature for this 7-day period?

    1. AA. 75°F
    2. BB. 72°F
    3. CC. 73°F
    4. DD. 71°F
    Show answer to question 24

    Answer: B. 72°F

    To find the median, the temperatures must first be ordered from least to greatest: 68, 69, 71, 72, 74, 75, and 80. The median is the middle value of this ordered list, which is 72°F. The value 71°F is incorrect because it is the middle value in chronological order (Thursday) rather than in numerical order.

25. Question 25 of 25Medium

    A person 5 feet tall casts a shadow 3 feet long at the same time that a flagpole casts a shadow 21 feet long. How tall is the flagpole?

    1. AA. 35 feet
    2. BB. 29 feet
    3. CC. 12.6 feet
    4. DD. 15 feet
    Show answer to question 25

    Answer: A. 35 feet

    Because the triangles are similar, height divided by shadow length is constant, so 5/3 = h/21 and h = 35 feet. Multiplying 21 by 3/5 gives 12.6 feet, which reverses the ratio and makes the tall flagpole shorter than its shadow relative to the person.

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