6th Grade Exponents and Order of Operations Test Solutions and Scoring (PDF)

6th Grade math test solutions: Exponents and Order of Operations – Maths PDF

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This exponents test answers for 6th Grade covers exponents and order of operations (Common Core 6.EE.A.1, 6.EE.A.2c), with a free PDF to print.

Use this key to score the exponents test out of 20 points. Each solution is fully worked, and the scoring line explains how to award each point and partial credit for correct steps.

Grade 6 · Common Core State Standards: 6.EE.A.1, 6.EE.A.2c

Exponents test answers: worked solutions

Question 1 – Write and evaluate powers [2 pts]

(a) \(7^{3}\). (b) \(2^{6} = 64\).

Scoring: 1 point for each part.

Question 2 – Evaluate powers [2 pts]

(a) \(5 \times 5 \times 5 = 125\).

(b) \(\frac{2}{3} \times \frac{2}{3} = \frac{4}{9}\).

Scoring: 1 point for each part.

Question 3 – Order of operations [2 pts]

Multiply first: \(4 \times 3 = 12\).

\(30 – 12 + 2 = 20\)

Scoring: 1 point for multiplying first; 1 point for 20.

Question 4 – Exponents in order of operations [2 pts]

\(3^{2} = 9\), \(2 \times 9 = 18\), \(8 \div 4 = 2\).

\(18 + 2 = 20\)

Scoring: 1 point for the exponent and products; 1 point for 20.

Question 5 – Parentheses [2 pts]

\(9 – 3 = 6\), \(6^{2} = 36\).

\(36 \div 4 = 9\)

Scoring: 1 point for the parentheses and exponent; 1 point for 9.

Question 6 – Substitution [2 pts]

\(4 \times 3^{2} – 7 = 4 \times 9 – 7 = 36 – 7 = 29\)

Scoring: 1 point for substituting and using the exponent first; 1 point for 29.

Question 7 – Cube volume [2 pts]

\(V = 5^{3} = 5 \times 5 \times 5 = 125\).

The volume is \(125\text{ cm}^{3}\).

5 x 5 x 5 = 125 cubic centimeters.

Scoring: 1 point for the substitution; 1 point for 125 cm^3.

Question 8 – Formula [3 pts]

\(15 + 4 \times 2 = 23\), \(15 + 4 \times 5 = 35\), \(15 + 4 \times 8 = 47\).

Completed table.

Scoring: 1 point for each correct cost.

Question 9 – Multi-step expression [3 pts]

Exponent: \(2^{3} = 8\). Multiply: \(3 \times 8 = 24\). Add: \(5 + 24 = 29\).

Maya added 5 + 3 = 8 first and then did 8 x 8 = 64, ignoring the order of operations.

Scoring: 1 point for the correct value 29; 1 point for the correct steps; 1 point for identifying the mistake.

Total score

Total

20 points

Key facts behind this exponents test answers

Key facts

In b^n, the base b is used as a factor n times.
Squares and cubes: 3^2 = 9 and 2^3 = 8.
Order of operations: parentheses, exponents, multiply or divide, add or subtract.
Powers of 10 have as many zeros as the exponent.
To evaluate an expression with a variable, substitute then follow the order of operations.

How to use this exponents test answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

All Grade 6 chapters: Grade 6 math.

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