Free Middle School Mathematics (5164) Practice Questions

Sample Practice Questions

Try these 10 sample questions from the Middle School Mathematics (5164) practice bank. Each includes the answer and explanation. Continue with the interactive practice above to review the full question set.

1. 1At sunrise the temperature was −6°C. By noon it had risen 11°C. What was the temperature at noon?

   1. A.Negative 17°C
   2. B.Negative 5°C
   3. C.Positive 5°CCorrect answer: C
   4. D.Positive 17°C

   Explanation: OpenStax explains, "When the signs are different, some counters would make neutral pairs; subtract to see how many are left." The change is added to the initial temperature: −6 + 11 = 5. Subtracting magnitudes gives 5, and the larger magnitude is positive.

   Reference: Prealgebra 2e — 3.2 Add Integers — Addition of Positive and Negative Integers — 3.2 Add Integers — Addition of Positive and Negative Integers

2. 2What is the simplified sum (3x² + 2x − 5) + (x² − 7x + 8)?

   1. A.4x squared plus 9x plus 3
   2. B.4x squared minus 5x minus 13
   3. C.4x to the fourth power minus 5x plus 3
   4. D.4x squared minus 5x plus 3Correct answer: D

   Explanation: The text states, "We can add and subtract polynomials by combining like terms." The quadratic coefficients add to 4, the linear coefficients add to −5, and the constants add to 3. Adding terms does not add the exponents of their variables.

   Reference: College Algebra 2e — 1.4 Polynomials — 1.4 Polynomials

3. 3Which of these sets of ordered pairs defines a function with x as the input?

   1. A.{(1, 2), (1, 3), (2, 4)}
   2. B.{(−1, 0), (0, 0), (1, 0)}Correct answer: B
   3. C.{(2, 1), (2, −1), (3, 4)}
   4. D.{(0, 2), (0, 5), (1, 6)}

   Explanation: The source defines a function as a relation in which "each domain value, or input, leads to exactly one range value, or output." The inputs −1, 0, and 1 each have one output, even though the output is the same. Each other relation assigns two distinct outputs to one input.

   Reference: College Algebra 2e — 3.1 Functions and Function Notation — 3.1 Functions and Function Notation

4. 4Two adjacent angles form a straight angle. If one measures 67°, what is the measure of the other?

   1. A.23°
   2. B.67°
   3. C.113°Correct answer: C
   4. D.293°

   Explanation: OpenStax states, "If the sum of the measures of two angles is 180°, then the angles are supplementary." A straight angle measures 180°, so the missing measure is 180° − 67° = 113°. Subtracting from 90° would instead find a complementary angle.

   Reference: Prealgebra 2e — 9.3 Supplementary and Complementary Angles — 9.3 Supplementary and Complementary Angles

5. 5Which question is statistical because it anticipates variation among the observations?

   1. A.How many lockers are installed in this classroom?
   2. B.How many hours do students in this school sleep on school nights?Correct answer: B
   3. C.What is the room number of the principal's office?
   4. D.How many minutes is one class period scheduled to last?

   Explanation: The standards describe a statistical question as one that "anticipates variability in the data related to the question and accounts for it in the answers." Students' sleep durations are expected to differ and require a distribution of observations. The other questions ask for a single fixed count, identifier, or scheduled duration.

   Reference: Common Core State Standards for Mathematics — p. 45, Statistics and Probability — Develop understanding of statistical variability

6. 6A 6-meter ribbon is cut into pieces that are each 3/4 meter long. How many complete pieces are obtained?

   1. A.4
   2. B.6
   3. C.9
   4. D.8Correct answer: D

   Explanation: The rule is, "To divide fractions, multiply the first fraction by the reciprocal of the second." Thus 6 ÷ (3/4) = 6 × (4/3) = 8 complete pieces. Multiplying by 3/4 instead would find a fraction of the ribbon rather than the number of pieces.

   Reference: Prealgebra 2e — 4.2 Multiply and Divide Fractions — Fraction Division — 4.2 Multiply and Divide Fractions — Fraction Division

7. 7A student rewrites −(2x² − 3x + 4) as −2x² − 3x + 4. Which expression correctly removes the parentheses?

   1. A.Negative 2x squared plus 3x minus 4Correct answer: A
   2. B.Negative 2x squared minus 3x minus 4
   3. C.Positive 2x squared plus 3x minus 4
   4. D.Negative 2x squared plus 3x plus 4

   Explanation: The distributive rule requires multiplying "each term" in the grouped polynomial. Multiplying every term by −1 changes the signs of all three terms: −2x² + 3x − 4. The student's work changes only the first sign.

   Reference: College Algebra 2e — 1.4 Polynomials — multiplication by distribution — 1.4 Polynomials — multiplication by distribution

8. 8For x = 0, 1, 2, 3, and 4, a function's outputs are 2, 5, 10, 17, and 26. Which feature identifies these values as consistent with a quadratic model rather than a linear or exponential model?

   1. A.The outputs have a constant first difference.
   2. B.The outputs have a constant ratio.
   3. C.The outputs decrease at a constant rate.
   4. D.The outputs have a constant nonzero second difference.Correct answer: D

   Explanation: ETS notes that "the second differences of a quadratic function are constant". With equally spaced inputs, the first differences here are 3, 5, 7, and 9; the second differences are all 2. Neither the first differences nor successive output ratios are constant.

   Reference: The Praxis Middle School Mathematics (5164) Study Companion — p. 11, Discussion Questions: Functions, indicators of function type

9. 9Two lines intersect. A pair of vertical angles has measures (3x + 8)° and (5x − 22)°. What is x?

   1. A.Positive 15Correct answer: A
   2. B.Negative 15
   3. C.Positive 24.25
   4. D.Positive 7

   Explanation: The standards state, "vertical angles are congruent". Equate their measures: 3x + 8 = 5x − 22, so 30 = 2x and x = 15. Their common measure is 53°; treating the vertical pair as supplementary gives the wrong equation.

   Reference: Common Core State Standards for Mathematics — High School Geometry, G-CO.9

10. 10A researcher wants to estimate the average commute time of all 4,000 students in a district and surveys 120 randomly selected district students. What is the population of interest?

    1. A.The 120 surveyed students
    2. B.The recorded commute times of the 120 students
    3. C.The average computed from the 120 responses
    4. D.All 4,000 students in the districtCorrect answer: D

    Explanation: OpenStax states, "researchers use samples to represent the population." The 120 selected students are the sample. The group the researcher intends to describe is all 4,000 district students, which is the population of interest; a list of sample observations and their average are different statistical objects.

    Reference: Introductory Statistics 2e — 1.2 Data, Sampling, and Variation in Data and Sampling — 1.2 Data, Sampling, and Variation in Data and Sampling