Free Elementary Education: Mathematics Subtest Practice Questions

Sample Practice Questions

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

1. 1In 62.407, what value is represented by the digit 4?

   1. A.4
   2. B.0.4Correct answer: B
   3. C.0.04
   4. D.0.004

   Explanation: The standards give decimal expanded form using "3 × (1/10) + 9 × (1/100) + 2 × (1/1000)." The first position to the right of the decimal point is tenths, so the 4 in 62.407 represents 4 × 1/10 = 0.4. The other values assign the digit to ones, hundredths, or thousandths.

   Reference: Common Core State Standards for Mathematics — 5.NBT.3a, p. 35

2. 2Which expression means seven less than three times x?

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

   Explanation: The standards illustrate subtraction language: "Subtract y from 5" is written as "5 – y." Three times x is 3x, and seven less than that is 3x − 7. The alternatives reverse the subtraction or multiply a different quantity.

   Reference: Common Core State Standards for Mathematics — 6.EE.2a, p. 43

3. 3Two distinct lines in the same plane never meet, even when extended indefinitely. What are they called?

   1. A.Parallel linesCorrect answer: A
   2. B.Perpendicular lines
   3. C.Intersecting lines
   4. D.Coincident lines

   Explanation: The glossary defines parallel lines as "Lines in a plane that never meet." Perpendicular and other intersecting lines meet, while coincident lines share all their points and are not distinct lines.

   Reference: Connected Mathematics Project — CMP3 Glossary: All Grades, All Units — Parallel lines

4. 4Which base-ten numeral correctly writes the number named five hundred six?

   1. A.56
   2. B.506Correct answer: B
   3. C.560
   4. D.5,006

   Explanation: The standards explain that three-digit numbers represent "amounts of hundreds, tens, and ones". Five hundred six has 5 hundreds, 0 tens, and 6 ones: 500 + 0 + 6 = 506. The zero preserves the unoccupied tens position.

   Reference: Common Core State Standards for Mathematics — p. 19

5. 5Distribute the negative factor across both terms in −3(2x − 5). Which expression results?

   1. A.Negative six x minus fifteen
   2. B.Negative six x plus fifteenCorrect answer: B
   3. C.Negative six x minus five
   4. D.Negative six x plus five

   Explanation: The distributive property is "a × (b + c) = a × b + a × c". Distributing −3 to both terms gives −6x + 15. Missing the second multiplication or mishandling the product of two negative numbers produces the other expressions.

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

6. 6What relationship holds between two lines that intersect at a right angle?

   1. A.They are parallel.
   2. B.They are perpendicular.Correct answer: B
   3. C.They are coincident.
   4. D.They are skew.

   Explanation: The glossary defines perpendicular lines as "Lines that meet at right angles." Parallel lines do not meet, coincident lines overlap, and skew lines do not intersect. A right-angle intersection uniquely identifies perpendicular lines.

   Reference: Connected Mathematics Project — CMP3 Glossary: All Grades, All Units — Perpendicular lines

7. 7A number is represented by 7 tens and 24 ones. What is the same quantity written with fewer than 10 ones?

   1. A.7 tens and 4 ones
   2. B.8 tens and 14 ones
   3. C.9 tens and 4 onesCorrect answer: C
   4. D.10 tens and 4 ones

   Explanation: The place-value standard states that a digit represents "10 times as much as it represents in the place to its right". A ten is 10 ones; regrouping 20 of the 24 ones creates 2 additional tens. Thus 7 tens and 24 ones equals 9 tens and 4 ones. Eight tens and 14 ones is equal in value but does not meet the requested fewer-than-10-ones condition.

   Reference: Common Core State Standards for Mathematics — p. 35

8. 8Combine the variable terms and constants in 4x + 7 + 3x − 2. What is the simplified expression?

   1. A.7x + 5Correct answer: A
   2. B.7x + 9
   3. C.12x + 5
   4. D.12x + 9

   Explanation: The standards illustrate combining repeated variable terms to "produce the equivalent expression 3y." Combining like terms here gives (4 + 3)x + (7 − 2) = 7x + 5. Coefficients are added rather than multiplied, and constants retain their signs.

   Reference: Common Core State Standards for Mathematics — 6.EE.3, p. 44

9. 9An angle opens through one hundred thirty-five degrees. Which angle classification describes its measure?

   1. A.Acute
   2. B.Right
   3. C.ObtuseCorrect answer: C
   4. D.Straight

   Explanation: The official glossary describes an obtuse angle as "an angle greater than 90o but less than 180o." Since 90 < 135 < 180, the angle is obtuse. Acute angles are below 90°, right angles measure 90°, and straight angles measure 180°.

   Reference: New Zealand Ministry of Education — NZC: Glossary of mathematics terms — Triangles, classification by angles

10. 10Which expression is the expanded form of 8.053?

    1. A.8 + 5/10 + 3/100
    2. B.8 + 5/100 + 3/1000Correct answer: B
    3. C.8 + 5/1000 + 3/100
    4. D.8 + 5/10 + 3/1000

    Explanation: The standards illustrate decimal expansion with "3 × (1/10) + 9 × (1/100) + 2 × (1/1000)." Applying those place units, 8.053 contains 8 ones, 0 tenths, 5 hundredths, and 3 thousandths. Its expanded form is 8 + 5/100 + 3/1000.

    Reference: Common Core State Standards for Mathematics — 5.NBT.3a, p. 35