Testinar Grade 6 math

Exponents and Order of Operations

Students will build Grade 6 mastery of exponents and order of operations using models, equations, and test-style reasoning.

CH03-01 Expressions and Equations

Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

Evaluate: \(3^2+2\times(5-1)\)
1. \(9\)
2. \(17\)
3. \(25\)
4. \(40\)
What is \(2^4\) in expanded form?
1. \(2+2+2+2\)
2. \(2\times4\)
3. \(4\times4\)
4. \(2\times2\times2\times2\)
Evaluate: \(5^3\)
1. \(15\)
2. \(25\)
3. \(125\)
4. \(243\)
What is \(6^2\)?
1. \(12\)
2. \(36\)
3. \(42\)
4. \(62\)
Evaluate: \(10^2 \div 5 + 3\)
1. \(20\)
2. \(27\)
3. \(30\)
4. \(23\)
Which expression equals \(24\)?
1. \(2^3 + 4 \times 2\)
2. \(3^2 + 6 + 3\)
3. \(4^2 + 8\)
4. \(5^2 - 2\)
Evaluate: \((2+3)^2 - 5\)
1. \(10\)
2. \(20\)
3. \(25\)
4. \(30\)
Evaluate: \(8 + 2 \times 3^2\)
1. \(30\)
2. \(26\)
3. \(18\)
4. \(54\)

Teacher and parent reference

Answer key and explanations

B. \(17\)
Work inside the parentheses first: \(5-1=4\). Then exponent: \(3^2=9\). Then multiply: \(2\times4=8\). Finally add: \(9+8=17\).
D. \(2\times2\times2\times2\)
An exponent shows how many times to multiply the base by itself. \(2^4\) means \(2\) multiplied \(4\) times, which is \(2\times2\times2\times2=16\).
C. \(125\)
\(5^3 = 5 \times 5 \times 5 = 125\). The exponent 3 means we multiply 5 by itself 3 times (a cube).
B. \(36\)
\(6^2 = 6 \times 6 = 36\). A square exponent (power of 2) means multiply the base by itself once.
D. \(23\)
First, compute the exponent: \(10^2 = 100\). Then divide: \(100 \div 5 = 20\). Finally add: \(20 + 3 = 23\).
C. \(4^2 + 8\)
Evaluate each expression using order of operations. Choice C gives \(4^2+8=16+8=24\).
B. \(20\)
First, work inside the parentheses: \(2 + 3 = 5\). Then apply the exponent: \(5^2 = 25\). Finally subtract: \(25 - 5 = 20\).
B. \(26\)
First, evaluate the exponent: \(3^2 = 9\). Then multiply: \(2 \times 9 = 18\). Finally add: \(8 + 18 = 26\).