Free HiSET Mathematics Practice Questions

Sample Practice Questions

Try these 10 sample questions from the HiSET Mathematics practice bank. Each includes the answer and explanation. Continue with the interactive practice above to review the full question set.

1. 1Which number below is an irrational real number?

   1. A.√25
   2. B.√36
   3. C.√18Correct answer: C
   4. D.√49

   Explanation: OpenStax states: "The square root of a number that is not a perfect square is a decimal that does not stop or repeat." Since 18 is not a perfect square, √18 is irrational; the other roots are integers.

   Reference: Intermediate Algebra 2e, 1.4 Decimals — Identify Rational and Irrational Numbers

2. 2A point at (−2, 4) is translated 3 units right and 2 units down. What are its image coordinates?

   1. A.(1, 2)Correct answer: A
   2. B.(−5, 2)
   3. C.(1, 6)
   4. D.(−5, 6)

   Explanation: OpenStax says: "A translation is a movement that shifts the shape vertically, horizontally, or on the diagonal." Add 3 to the x-coordinate and subtract 2 from the y-coordinate, obtaining (1, 2).

   Reference: Contemporary Mathematics, 10.5 Tessellations — Translation

3. 3A class survey records 12 students who walk to school and 18 who do not. What is the relative frequency of students who walk?

   1. A.12%
   2. B.30%
   3. C.40%Correct answer: C
   4. D.60%

   Explanation: OpenStax states: "The relative frequency is equal to the frequency for an observed value of the data divided by the total number of data values in the sample." Divide 12 by the total of 30, giving 0.4 or 40%.

   Reference: Introductory Statistics 2e, 2.2 Histograms — Relative Frequency

4. 4A taxi fare is modeled by 6 + 3m dollars, where m is miles traveled. What does 3 represent?

   1. A.The starting fare in dollars
   2. B.The fare per mile in dollarsCorrect answer: B
   3. C.The total miles traveled
   4. D.The total fare in dollars

   Explanation: OpenStax states: "The constant that multiplies the variable(s) in a term is called the coefficient." The coefficient 3 multiplies the number of miles, so it is the cost per mile.

   Reference: Prealgebra 2e, 2.2 Expressions — Identify Terms, Coefficients, and Like Terms

5. 5Between which two consecutive integers does √35 lie on the number line?

   1. A.4 and 5
   2. B.5 and 6Correct answer: B
   3. C.6 and 7
   4. D.7 and 8

   Explanation: OpenStax explains: "To get a numerical estimate of a square root, we look for perfect square numbers closest to the radicand." Since 25 < 35 < 36 and 25 = 5² while 36 = 6², the root is between 5 and 6.

   Reference: Intermediate Algebra, 8.1 Simplify Expressions with Roots — Approximate Square Roots

6. 6What is the image of the point (3, −5) after reflection across the x-axis?

   1. A.(negative 3, negative 5)
   2. B.(3, 5)Correct answer: B
   3. C.(negative 3, 5)
   4. D.(5, negative 3)

   Explanation: OpenStax states: "A shape is reflected about a line and the new shape becomes a mirror image." Reflection across the x-axis preserves the x-coordinate and reverses the sign of the y-coordinate.

   Reference: Contemporary Mathematics, 10.5 Tessellations — Reflection

7. 7A data set of home prices contains one extremely expensive property. Which measure of center is generally less affected by the size of that extreme value?

   1. A.Mean
   2. B.MedianCorrect answer: B
   3. C.Range
   4. D.Total

   Explanation: OpenStax states: "The median is generally a better measure of the center when there are extreme values or outliers because it is not affected by the precise numerical values of the outliers." The median depends on order rather than the exact magnitude of the extreme observation.

   Reference: Introductory Statistics 2e, 2.5 Measures of the Center — Measures of the Center

8. 8A delivery fee is modeled by 12 + 4n dollars for n packages. What does the constant term represent?

   1. A.A fixed $12 chargeCorrect answer: A
   2. B.A charge of $4 per package
   3. C.The number of packages
   4. D.The total cost of n packages

   Explanation: OpenStax says: "A term is a constant or the product of a constant and one or more variables." In this model 12 does not vary with n and is the fixed charge.

   Reference: Prealgebra 2e, 2.2 Expressions — Identify Terms, Coefficients, and Like Terms

9. 9Which equation illustrates the commutative property of addition?

   1. A.(4 + 7) + 2 = 4 + (7 + 2)
   2. B.4 + 0 = 4
   3. C.4 + 7 = 7 + 4Correct answer: C
   4. D.4 + (−4) = 0

   Explanation: OpenStax states: "When adding or multiplying, changing the order gives the same result." The equation 4 + 7 = 7 + 4 reverses the order of the addends while preserving their sum.

   Reference: Intermediate Algebra 2e, 1.5 Properties of Real Numbers — Commutative Property

10. 10A triangle is rotated and then translated. What relationship must hold between the original and final triangles?

    1. A.They are congruent.Correct answer: A
    2. B.They have the same area but different side lengths.
    3. C.They are similar only if the rotation is 180°.
    4. D.They have proportional but unequal corresponding angles.

    Explanation: The HiSET framework describes congruent figures as ones "obtained from the first by a sequence of rotations, reflections, and translations". Rotation and translation preserve lengths and angles, so the triangles are congruent.

    Reference: HiSET Test at a Glance — Mathematics, p. 18, 8.G.2