College Algebra Unit 1 Review – Step-by-Step Guidance

Q1a. Use the correct order of operations to simplify the given expression.

Background

Topic: Order of Operations (PEMDAS/BODMAS)

This question tests your ability to correctly apply the order of operations to simplify an algebraic expression.

Key Terms and Formulas:

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

• PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction

Step-by-Step Guidance

1. Identify any parentheses or grouping symbols in the expression and simplify inside them first.

2. Next, look for exponents and evaluate them.

3. Perform multiplication and division from left to right.

4. Finally, perform addition and subtraction from left to right.

Try solving on your own before revealing the answer!

Q1b. Use the correct order of operations to simplify the given expression.

Background

Topic: Order of Operations

This question also tests your understanding of the order of operations in algebraic expressions.

Key Terms and Formulas:

• Order of Operations: PEMDAS/BODMAS

Step-by-Step Guidance

1. Start by simplifying any expressions inside parentheses or brackets.

2. Evaluate exponents next.

3. Carry out multiplication and division as they appear from left to right.

4. Finish with addition and subtraction from left to right.

Try solving on your own before revealing the answer!

Q2a. Evaluate the given expression for the specified values.

Background

Topic: Substitution and Evaluation

This question tests your ability to substitute values into an algebraic expression and evaluate it.

Key Terms and Formulas:

• Substitution: Replacing variables with given values.

Step-by-Step Guidance

1. Identify the values for each variable provided in the question.

2. Substitute these values into the expression.

3. Follow the order of operations to simplify the expression.

Try solving on your own before revealing the answer!

Q2b. Evaluate the given expression for the specified values.

Background

Topic: Substitution and Evaluation

This question tests your ability to substitute values into an algebraic expression and evaluate it.

Key Terms and Formulas:

• Substitution: Replacing variables with given values.

Step-by-Step Guidance

1. Identify the values for each variable provided in the question.

2. Substitute these values into the expression.

3. Apply the order of operations to simplify the expression.

Try solving on your own before revealing the answer!

Q3a. Write an expression that represents the discount amount for an orange label.

Background

Topic: Percentages and Algebraic Expressions

This question tests your ability to write an algebraic expression for a percentage discount.

Key Terms and Formulas:

• Discount Amount = (Discount Rate) × (Original Price)

Step-by-Step Guidance

1. Identify the discount rate for the orange label (as a decimal or fraction).

2. Let $p$ represent the original price.

3. Write the expression for the discount amount: $\text{Discount} = \text{Rate} \times p$.

Try solving on your own before revealing the answer!

Q3b. Write an expression that represents the discount amount for a green label.

Background

Topic: Percentages and Algebraic Expressions

This question tests your ability to write an algebraic expression for a percentage discount.

Key Terms and Formulas:

• Discount Amount = (Discount Rate) × (Original Price)

Step-by-Step Guidance

1. Identify the discount rate for the green label (as a decimal or fraction).

2. Let $p$ represent the original price.

3. Write the expression for the discount amount: $\text{Discount} = \text{Rate} \times p$.

Try solving on your own before revealing the answer!

Q4. Perform the indicated operation and write the answer in standard form.

Background

Topic: Polynomial Operations

This question tests your ability to add, subtract, and combine like terms in polynomial expressions.

Key Terms and Formulas:

• Standard Form: Arrange terms in descending order of degree.

• Combine like terms: Add or subtract coefficients of terms with the same variable and exponent.

Step-by-Step Guidance

1. Write out all terms from the expression.

2. Identify and group like terms (same variable and exponent).

3. Add or subtract the coefficients of like terms.

4. Arrange the resulting expression in standard form (descending order of degree).

Try solving on your own before revealing the answer!

Q5a. Simplify using rules of exponents. Express using positive exponents only.

Background

Topic: Exponent Rules

This question tests your understanding of exponent properties and how to simplify expressions with exponents.

Key Terms and Formulas:

• Product Rule: $a^m \times a^n = a^{m+n}$

• Quotient Rule: $\frac{a^m}{a^n} = a^{m-n}$

• Negative Exponent Rule: $a^{-n} = \frac{1}{a^n}$

Step-by-Step Guidance

1. Identify the base and exponents in the expression.

2. Apply the product or quotient rule as appropriate.

3. If any exponents are negative, rewrite them as positive exponents using the negative exponent rule.

Try solving on your own before revealing the answer!

Q5b. Simplify using rules of exponents. Express using positive exponents only.

Background

Topic: Exponent Rules

This question tests your ability to simplify expressions with exponents and write them with positive exponents.

Key Terms and Formulas:

• Product Rule: $a^m \times a^n = a^{m+n}$

• Quotient Rule: $\frac{a^m}{a^n} = a^{m-n}$

• Negative Exponent Rule: $a^{-n} = \frac{1}{a^n}$

Step-by-Step Guidance

1. Identify the base and exponents in the expression.

2. Apply the product or quotient rule as appropriate.

3. Rewrite any negative exponents as positive exponents.

Try solving on your own before revealing the answer!

Q5c. Simplify using rules of exponents. Express using positive exponents only.

Background

Topic: Exponent Rules

This question tests your ability to simplify expressions with exponents and write them with positive exponents.

Key Terms and Formulas:

• Product Rule: $a^m \times a^n = a^{m+n}$

• Quotient Rule: $\frac{a^m}{a^n} = a^{m-n}$

• Negative Exponent Rule: $a^{-n} = \frac{1}{a^n}$

Step-by-Step Guidance

1. Identify the base and exponents in the expression.

2. Apply the product or quotient rule as appropriate.

3. Rewrite any negative exponents as positive exponents.

Try solving on your own before revealing the answer!