Free Core Academic Skills for Educators: Mathematics Practice Questions

Sample Practice Questions

Try these 10 sample questions from the Core Academic Skills for Educators: Mathematics practice bank. Each includes the answer and explanation. Continue with the interactive practice above to review the full question set.

1. 1Subtract negative twelve from negative seven. What result does this signed subtraction produce?

   1. A.Negative nineteen
   2. B.Positive fiveCorrect answer: B
   3. C.Positive nineteen
   4. D.Negative five

   Explanation: The standards state, "Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q)." Therefore, −7 − (−12) = −7 + 12 = 5. Adding the two negative magnitudes gives −19; reversing the subtraction gives −5.

   Reference: Common Core State Standards for Mathematics — p. 48, The Number System, item 1(c)

2. 2A stem-and-leaf plot has stem 2 with leaves 1, 4, 4 and stem 3 with leaves 0, 5. The key is 2 | 1 = 21. How many observations are at least 30?

   1. A.3
   2. B.4
   3. C.2Correct answer: C
   4. D.5

   Explanation: OpenStax explains, "To create the plot, divide each observation of data into a stem and a leaf." The observations are 21, 24, 24, 30, and 35. Exactly 30 and 35 meet the threshold. Three counts the other stem, 4 may include the two 24s, and 5 counts every observation.

   Reference: OpenStax Introductory Statistics 2e — 2.1 Stem-and-Leaf Graphs, Line Graphs, and Bar Graphs — §2.1, opening paragraph

3. 3Which expression is equivalent to 4(2x − 3) for every real x?

   1. A.8x minus 3
   2. B.8x minus 12Correct answer: B
   3. C.6x minus 12
   4. D.8x plus 12

   Explanation: The standards give "a × (b + c) = a × b + a × c". Distribute 4 to both terms, treating subtraction as addition of −3: 4 × 2x + 4 × (−3) = 8x − 12. The alternatives omit a multiplication, add coefficients, or change the sign.

   Reference: Common Core State Standards for Mathematics — p. 90, Table 3, distributive property

4. 4What is 5/6 + 3/4, expressed as a single fraction in lowest terms?

   1. A.4/5
   2. B.2/3
   3. C.19/12Correct answer: C
   4. D.5/8

   Explanation: The standards give the rule "(In general, a/b + c/d = (ad + bc)/bd.)" Converting to twelfths gives 10/12 + 9/12 = 19/12. Adding numerators and denominators gives 4/5; adding numerators while keeping 12 gives 2/3; multiplying instead gives 5/8.

   Reference: Common Core State Standards for Mathematics — p. 36, 5.NF.1

5. 5Delivery times, in minutes, are 8, 9, 10, 10, 11, and 39. Which observation is most clearly an outlier relative to the rest of this data set?

   1. A.8 minutes
   2. B.10 minutes
   3. C.11 minutes
   4. D.39 minutesCorrect answer: D

   Explanation: OpenStax states, "An outlier is an observation of data that does not fit the rest of the data." Five observations cluster from 8 to 11, while 39 is far outside that cluster. The remaining choices are within the cluster; being a minimum, repeated value, or local maximum does not itself make an observation an outlier.

   Reference: OpenStax Introductory Statistics 2e — 2.1 Stem-and-Leaf Graphs, Line Graphs, and Bar Graphs — §2.1, paragraph following Try It 2.1

6. 6Which expression equals a + (b + c) for all real a, b, and c?

   1. A.Subtract b from a, then add c.
   2. B.Add a and b, then subtract c.
   3. C.Multiply b by c, then add a.
   4. D.Add a and b, then add c.Correct answer: D

   Explanation: The standards state, "(a + b) + c = a + (b + c)". Regrouping addition leaves the sum unchanged. The other expressions replace addition with subtraction or multiplication, which does not preserve the value for all choices of the variables.

   Reference: Common Core State Standards for Mathematics — p. 90, Table 3, associative property of addition

7. 7A container holds 7/8 liter of juice. How many 1/4-liter portions does this amount represent, allowing a fractional portion?

   1. A.7/32
   2. B.7/8
   3. C.2/7
   4. D.7/2Correct answer: D

   Explanation: The standards state, "(In general, (a/b) ÷ (c/d) = ad/bc.)" Divide the available amount by the portion size: (7/8) ÷ (1/4) = 28/8 = 7/2. Multiplication gives 7/32; 7/8 leaves the amount unconverted; 2/7 reverses the division.

   Reference: Common Core State Standards for Mathematics — p. 42, 6.NS.1

8. 8A frequency table lists 5 books read with frequency 2, 6 books with frequency 4, and 7 books with frequency 3. How many people are represented by the table?

   1. A.9Correct answer: A
   2. B.18
   3. C.55
   4. D.3

   Explanation: OpenStax defines n as the "total number of data values (or the sum of the individual frequencies)". Add frequencies: 2 + 4 + 3 = 9 people. Eighteen sums book-count labels, 55 is the total books read, and 3 is the number of categories.

   Reference: OpenStax Introductory Statistics 2e — 2.2 Histograms, Frequency Polygons, and Time Series Graphs — §2.2, relative-frequency definitions

9. 9What is the value of 6 + 3 × 4²?

   1. A.54Correct answer: A
   2. B.144
   3. C.150
   4. D.30

   Explanation: The standards require operations "in the conventional order when there are no parentheses to specify a particular order (Order of Operations)." Evaluate the exponent first: 4² = 16; then multiply 3 × 16 = 48 and add 6 to get 54. The alternatives add before multiplying, square 3 × 4, or replace squaring with doubling.

   Reference: Common Core State Standards for Mathematics — p. 44, Expressions and Equations, item 2(c)

10. 10Which value results from multiplying the two decimal numbers 2.4 and 0.35?

    1. A.0.84Correct answer: A
    2. B.0.084
    3. C.8.4
    4. D.0.0084

    Explanation: The standards state, "(In general, (a/b) × (c/d) = ac/bd.)" Write the decimals as 24/10 and 35/100. Their product is 840/1,000 = 0.84. The distractors 0.084, 8.4, and 0.0084 are respectively one tenth, ten times, and one hundredth of the correct product.

    Reference: Common Core State Standards for Mathematics — p. 36, 5.NF.4a