Step-by-Step Guidance for Mixed Review Algebra Worksheet

Q1. Find the value of the expression $3^{(12 - 11)}$.

Background

Topic: Exponents

This question tests your understanding of exponent rules and evaluating expressions with exponents.

Key Terms and Formulas:

• Exponent: The number that indicates how many times to multiply the base by itself.

• $a^n$ means multiply $a$ by itself $n$ times.

Step-by-Step Guidance

1. First, evaluate the expression inside the exponent: $12 - 11$.

2. Substitute the result into the exponent: $3^{(12 - 11)}$ becomes $3^{ ext{result}}$.

3. Recall that any number to the first power is itself: $a^1 = a$.

Try solving on your own before revealing the answer!

Q2. Simplify the inequality to determine whether it is true or false: $5(4 + 6) \\leq 80$.

Background

Topic: Inequalities and Order of Operations

This question tests your ability to simplify expressions using the order of operations and compare values using inequalities.

Key Terms and Formulas:

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

• Inequality: A mathematical statement that compares two values.

Step-by-Step Guidance

1. Simplify inside the parentheses: $4 + 6$.

2. Multiply the result by 5: $5 imes ( ext{result})$.

3. Compare the final value to 80 using the $\\leq$ symbol.

Try solving on your own before revealing the answer!

Q3. Simplify the following: $\\frac{4y + 2y - 3y + 7y}{9y + 2}$

Background

Topic: Combining Like Terms and Simplifying Rational Expressions

This question tests your ability to combine like terms in the numerator and simplify the resulting fraction.

Key Terms and Formulas:

• Like Terms: Terms that have the same variable raised to the same power.

• Rational Expression: A fraction where the numerator and denominator are polynomials.

Step-by-Step Guidance

1. Combine all the $y$ terms in the numerator: $4y + 2y - 3y + 7y$.

2. Write the simplified numerator over the denominator $9y + 2$.

3. Check if the fraction can be simplified further.

Try solving on your own before revealing the answer!

Q4. Evaluate the following for $x = 2$ and $y = 6$: $\\frac{7(x + 6)}{6}$

Background

Topic: Substitution and Evaluation of Expressions

This question tests your ability to substitute values for variables and evaluate the resulting expression.

Key Terms and Formulas:

• Substitution: Replacing variables with their given values.

• Evaluation: Calculating the value of an expression.

Step-by-Step Guidance

1. Substitute $x = 2$ and $y = 6$ into the expression: $7(x + 6)$.

2. Add the values inside the parentheses: $x + 6$.

3. Multiply the result by 7.

4. Divide the result by 6.

Try solving on your own before revealing the answer!

Q5. Find the value of the expression $\\frac{2^2}{6^2}$.

Background

Topic: Exponents and Simplifying Fractions

This question tests your ability to evaluate exponents and simplify fractions.

Key Terms and Formulas:

• Exponent: $a^n$ means multiply $a$ by itself $n$ times.

• Simplifying Fractions: Reduce the fraction to lowest terms if possible.

Step-by-Step Guidance

1. Evaluate $2^2$ and $6^2$ separately.

2. Write the fraction with the evaluated numerator and denominator.

3. Check if the fraction can be simplified further.

Try solving on your own before revealing the answer!