Q1. (15 + 5) + (26 - 6)² + 3²

Background

Topic: Order of Operations (PEMDAS/BODMAS)

This question tests your ability to correctly apply the order of operations to evaluate an expression with parentheses and exponents.

Key Terms and Formulas:

• PEMDAS/BODMAS: Parentheses/Brackets, Exponents/Orders, Multiplication & Division, Addition & Subtraction

• Evaluate expressions inside parentheses first, then exponents, followed by addition.

Step-by-Step Guidance

1. Start by evaluating the expressions inside each set of parentheses: and .

2. Next, apply the exponent to and to $3(26 - 6)^2).

3. Add the results from the previous steps together.

Try solving on your own before revealing the answer!

Q2. 6(2 + 18 - 9) + (3 × 4)^2

Background

Topic: Order of Operations

This question tests your ability to handle parentheses, multiplication, and exponents in a single expression.

Key Terms and Formulas:

• Evaluate inside parentheses first.

• Apply multiplication and exponents as indicated by PEMDAS.

Step-by-Step Guidance

1. Calculate the value inside the parentheses: .

2. Multiply the result by $6$.

3. Calculate , then raise it to the power of $2$.

4. Add the two results together.

Try solving on your own before revealing the answer!

Q3. ((3 + 2)² + (10 + 1)) + 2²

Background

Topic: Order of Operations

This question involves nested parentheses and exponents, requiring careful application of PEMDAS.

Key Terms and Formulas:

• Nested parentheses: Work from the innermost set outward.

• Exponents: Apply after evaluating parentheses.

Step-by-Step Guidance

1. Evaluate and inside the inner parentheses.

2. Apply the exponent to , i.e., .

3. Add the results from and .

4. Add to the sum from the previous step.

Try solving on your own before revealing the answer!

Q4. [-12 × (-4)] × [144 ÷ (15 - 3)]

Background

Topic: Order of Operations

This question tests your ability to handle multiplication, division, and negative numbers within brackets.

Key Terms and Formulas:

• Multiplication and division: Perform operations inside brackets first.

• Negative numbers: Remember the rules for multiplying negatives.

Step-by-Step Guidance

1. Calculate inside the first bracket.

2. Evaluate inside the second bracket.

3. Divide $144(15 - 3)$.

4. Multiply the results from the two brackets together.

Try solving on your own before revealing the answer!

Q5. (6 × 7) + 26 ÷ 12 = 5

Background

Topic: Order of Operations

This question tests your ability to apply multiplication and division before addition.

Key Terms and Formulas:

• Multiplication:

• Division:

• Addition: Add the results together.

Step-by-Step Guidance

1. Multiply .

2. Divide $26.

3. Add the two results together.

Try solving on your own before revealing the answer!

Q6. 5 + [3 × (35 + 7)]

Background

Topic: Order of Operations

This question involves nested brackets and multiplication.

Key Terms and Formulas:

• Brackets: Evaluate first.

• Multiplication: Multiply the result by $3$.

• Add $5$ to the result.

Step-by-Step Guidance

1. Calculate inside the brackets.

2. Multiply the result by $3$.

3. Add $5$ to the product.

Try solving on your own before revealing the answer!

Q7. 15 + 5 + (36 ÷ 12)² - 4

Background

Topic: Order of Operations

This question tests your ability to handle division, exponents, addition, and subtraction in a single expression.

Key Terms and Formulas:

• Division:

• Exponents: Apply to the result of division.

• Addition and subtraction: Combine all terms.

Step-by-Step Guidance

1. Divide $36.

2. Square the result from the division.

3. Add $15 to the squared value.

4. Subtract $4$ from the sum.

Try solving on your own before revealing the answer!

Q8. 8(5² + 15) - (7 + 13)

Background

Topic: Order of Operations

This question tests your ability to handle exponents, addition, multiplication, and subtraction.

Key Terms and Formulas:

• Exponents:

• Addition: and

• Multiplication: Multiply $8$ by the sum.

• Subtraction: Subtract the second sum.

Step-by-Step Guidance

1. Calculate .

2. Add $15$ to the result.

3. Multiply the sum by $8$.

4. Add and subtract from the previous result.

Try solving on your own before revealing the answer!

Q9. (9 × 4) ÷ 12 + 5 - 4²

Background

Topic: Order of Operations

This question tests your ability to handle multiplication, division, addition, and exponents.

Key Terms and Formulas:

• Multiplication:

• Division: Divide by $12$

• Add $5$

• Subtract

Step-by-Step Guidance

1. Multiply .

2. Divide the result by $12$.

3. Add $5$ to the quotient.

4. Subtract from the sum.

Try solving on your own before revealing the answer!

Q10. 3[(9 + 14) - (81 ÷ 9)]

Background

Topic: Order of Operations

This question tests your ability to handle nested brackets, addition, and division.

Key Terms and Formulas:

• Addition:

• Division:

• Subtract the division result from the sum.

• Multiply the difference by $3$.

Step-by-Step Guidance

1. Calculate .

2. Divide $81.

3. Subtract the division result from the sum.

4. Multiply the difference by $3$.

Try solving on your own before revealing the answer!