📚 Part 1: Algebraic Vocabulary

1. Match each algebraic term with its correct definition:

1. Variable

2. Coefficient

3. Expression

4. Equation

A. A mathematical statement with an equals sign

B. A letter that represents an unknown number

C. The number in front of a variable

D. A combination of numbers, variables, and operations

2. Circle the variable(s) in each expression:

a) 3x + 7

b) 2y - 5z + 12

c) 4a² + 3b - 8

🔢 Part 2: Simplifying and Expanding Expressions

3. Simplify the following expressions by collecting like terms:

a) 5x + 3x - 2x = ___________

b) 7y + 4 - 2y + 9 = ___________

c) 3a + 2b - a + 5b = ___________

4. Expand the following expressions using the distributive property:

a) 4(x + 3) = ___________

b) 5(2y - 7) = ___________

c) -3(4z + 1) = ___________

🔄 Part 3: Substitution

5. Substitute the given values into each expression and calculate the result:

a) If x = 4, find the value of 3x + 7

b) If y = -2, find the value of 5y - 3

c) If a = 6 and b = 3, find the value of 2a + 4b - 5

6. A rectangle has length (3x + 2) metres and width (x - 1) metres. If x = 5, what is the perimeter of the rectangle?

⚖️ Part 4: Solving Linear Equations

7. Solve the following linear equations. Show all working steps:

a) x + 8 = 15

b) 3y = 21

c) 2x + 5 = 17

d) 4z - 7 = 13

8. Check your answer for question 7c by substituting your solution back into the original equation:

🧠 Part 5: Problem Solving

9. Sarah is x years old. Her brother is 3 years younger than twice Sarah's age. Write an expression for her brother's age:

10. The cost of hiring a car is $45 plus $0.30 per kilometre driven. Write an expression for the total cost if you drive k kilometres:

11. A mobile phone plan costs $25 per month plus $0.15 per text message. If the total monthly bill is $37, how many text messages were sent? Set up and solve an equation:

✅ Part 6: Self-Assessment

12. Rate your confidence level for each skill (tick one box for each):

Identifying variables and coefficients:

Very confident

Somewhat confident

Need more practice

Simplifying expressions:

Very confident

Somewhat confident

Need more practice

Solving linear equations:

Very confident

Somewhat confident

Need more practice

13. What was the most challenging part of this worksheet for you?

14. Write one question you still have about algebra:

Advanced Algebra Foundations

Advanced Algebra Foundations

📚 Part 1: Algebraic Vocabulary

🔢 Part 2: Simplifying and Expanding Expressions

🔄 Part 3: Substitution

⚖️ Part 4: Solving Linear Equations

🧠 Part 5: Problem Solving

✅ Part 6: Self-Assessment

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