Q1. Evaluate the expression if , , and :

\[ \frac{\lvert 2y \rvert - \lvert x \rvert^2}{(y - 3z)^2} \]

Background

Topic: Evaluating Algebraic Expressions

This question tests your ability to substitute given values into an algebraic expression, use absolute values, and apply the order of operations correctly.

Key Terms and Formulas:

• Absolute Value: is the non-negative value of .

• Order of Operations: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction (PEMDAS).

Step-by-Step Guidance

1. Substitute , , and into the expression.

2. Calculate and then find .

3. Find and then square it to get .

4. Subtract from for the numerator.

5. Calculate and then square the result for the denominator.

Try solving on your own before revealing the answer!

Q2. Evaluate the expression if , , and :

\[ \frac{-4|2x + 3y|}{2y^2 - z} \]

Background

Topic: Evaluating Algebraic Expressions

This question focuses on substituting values, using absolute values, and simplifying the result using the correct order of operations.

Key Terms and Formulas:

• Absolute Value:

• Order of Operations (PEMDAS)

Step-by-Step Guidance

1. Substitute , , into the expression.

2. Calculate and then take the absolute value .

3. Multiply the result by for the numerator.

4. Calculate for the denominator.

Try solving on your own before revealing the answer!

Q3. Evaluate the expression if , , and :

\[ \frac{-(x^2 + 3)|y|}{x(y + 2z)} \]

Background

Topic: Evaluating Algebraic Expressions

This question tests substitution, absolute value, and simplifying expressions with both positive and negative numbers.

Key Terms and Formulas:

• Absolute Value:

• Order of Operations (PEMDAS)

Step-by-Step Guidance

1. Substitute , , into the expression.

2. Calculate and then multiply by for the numerator.

3. Calculate and then multiply by for the denominator.

Try solving on your own before revealing the answer!