Q1. Find the sum:

Background

Topic: Adding Polynomials

This question tests your ability to add two polynomials by combining like terms.

Key Terms and Formulas:

• Like terms: Terms with the same variable(s) raised to the same power(s).

• To add polynomials: Combine like terms by adding their coefficients.

Step-by-Step Guidance

1. Write both polynomials in a single expression:

2. Remove the parentheses (since addition does not affect the signs):

3. Group like terms together:

4. Add the coefficients of each group to simplify.

Try solving on your own before revealing the answer!

Q2. Find the difference:

Background

Topic: Subtracting Polynomials

This question tests your ability to subtract one polynomial from another by distributing the negative sign and combining like terms.

Key Terms and Formulas:

• Subtracting polynomials: Distribute the negative sign to each term in the second polynomial, then combine like terms.

Step-by-Step Guidance

1. Write the expression:

2. Distribute the negative sign to each term in the second polynomial:

3. Group like terms:

4. Simplify each group by adding/subtracting the coefficients.

Try solving on your own before revealing the answer!

Q3. Given the perimeter and two sides and , find the measure of the missing side.

Background

Topic: Perimeter of Polygons (Algebraic Expressions)

This question tests your ability to use the perimeter formula and solve for a missing side when the perimeter and other sides are given as algebraic expressions.

Key Terms and Formulas:

• Perimeter (): The sum of all side lengths of a polygon.

• To find a missing side:

Step-by-Step Guidance

1. Write the equation for the perimeter:

2. Plug in the given values:

3. Add the known sides:

4. Subtract the sum of the known sides from the perimeter to solve for the missing side.

Try solving on your own before revealing the answer!

Q4. Given the perimeter and two sides and , find the measure of the missing side.

Background

Topic: Perimeter of Polygons (Algebraic Expressions)

This question tests your ability to solve for a missing side using the perimeter and other side lengths expressed as polynomials.

Key Terms and Formulas:

• Perimeter (): The sum of all side lengths.

• To find a missing side:

Step-by-Step Guidance

1. Write the equation:

2. Add the known sides:

3. Simplify the sum: , ,

4. Subtract this sum from the perimeter to solve for the missing side.

Try solving on your own before revealing the answer!

Q5. The sides of a triangle have lengths , , and . What is the perimeter in terms of ?

Background

Topic: Perimeter of Triangles (Algebraic Expressions)

This question tests your ability to add algebraic expressions to find the perimeter of a triangle.

Key Terms and Formulas:

• Perimeter (): The sum of all side lengths.

Step-by-Step Guidance

1. Write the perimeter as the sum:

2. Group like terms:

3. Add the coefficients of and the constants separately.

Try solving on your own before revealing the answer!

Q6. A hexagon has 3 sides of length and 3 sides of length . What is the perimeter in terms of ?

Background

Topic: Perimeter of Polygons (Algebraic Expressions)

This question tests your ability to multiply and add algebraic expressions to find the perimeter of a hexagon.

Key Terms and Formulas:

• Perimeter (): The sum of all side lengths.

Step-by-Step Guidance

1. There are 3 sides of each length, so multiply each expression by 3: and

2. Expand both products: , , ,

3. Add the results:

4. Combine like terms to simplify the perimeter expression.

Try solving on your own before revealing the answer!