6th Grade Exponents and Order of Operations Test with Point Values (PDF)

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

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This exponents test 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.

This 45-minute test has 9 questions worth 20 points. It covers powers, order of operations, evaluating expressions with variables, and formulas such as cube volume (Common Core 6.EE.A.1 and 6.EE.A.2c). Show your steps.

Time and points

About this test

Grade: Grade 6
Chapter: Exponents and Order of Operations
Standards: 6.EE.A.1, 6.EE.A.2c
Time: 45 minutes
Total: 20 points

Exponents test: questions

Question 1 – Write and evaluate powers [2 pts]

Write \(7 \times 7 \times 7\) as a power.
Evaluate \(2^{6}\).

Question 2 – Evaluate powers [2 pts]

Evaluate \(5^{3}\).
Evaluate \(\left(\frac{2}{3}\right)^{2}\).

Question 3 – Order of operations [2 pts]

Order of operations.

Evaluate \(30 – 4 \times 3 + 2\).

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

Evaluate \(2 \times 3^{2} + 8 \div 4\).

Question 5 – Parentheses [2 pts]

Evaluate \((9 – 3)^{2} \div 4\).

Question 6 – Substitution [2 pts]

Evaluate \(4n^{2} – 7\) when \(n = 3\).

Question 7 – Cube volume [2 pts]

A cube.

Use \(V = s^{3}\) to find the volume of a cube with edge length 5 centimeters.

Question 8 – Formula [3 pts]

Equipment rental.

The cost in dollars to rent a kayak is \(C = 15 + 4h\), where h is the number of hours. Find the cost for 2, 5, and 8 hours.

Question 9 – Multi-step expression [3 pts]

Maya evaluated \(5 + 3 \times 2^{3}\) as 64. Find the correct value, and explain Maya’s mistake.

Key facts behind this exponents test

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

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All Grade 6 chapters: Grade 6 math.

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