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Algebra Expression Fundamentals

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Algebra Expression Fundamentals

Algebra Expression Fundamentals

Algebra symbols and expressions illustration

📚 Part 1: Algebra Vocabulary

1. Match each term with its correct definition:
1. Variable
2. Constant
3. Coefficient
4. Like terms
A. A number that doesn't change
B. Terms with the same variable and power
C. A letter representing an unknown number
D. The number in front of a variable
2. Circle the variables in these expressions:

Expression: 5x + 3y - 7

5

x

3

y

7

🔢 Part 2: Simplifying Expressions

3. Simplify these expressions by combining like terms:

a) 3x + 5x = _________

b) 7y - 2y + 4y = _________

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

d) 8m - 3m + 2n + 6m = _________

4. Show your working to simplify: 4x + 2(3x - 1) + 5
5. Which expression is equivalent to 6x + 9?

3(2x + 3)

3(2x + 6)

6(x + 3)

2(3x + 9)

🎯 Part 3: Evaluating Expressions

6. Evaluate these expressions when x = 4 and y = 2:

a) 3x + 5 = 3(____) + 5 = _________

b) 2x - y = 2(____) - ____ = _________

c) x² + 3y = (____) ² + 3(____) = _________

7. If a = 3 and b = 5, find the value of 2a + 3b - 4. Show your working:
8. The expression 5t + 20 represents the cost in dollars of hiring a bike for t hours. How much does it cost to hire the bike for 6 hours?

🧩 Part 4: Problem Solving

9. Sarah has x marbles. Tom has 3 more marbles than Sarah. Write an expression for:

a) The number of marbles Tom has: _________

b) The total number of marbles they have together: _________

10. A rectangle has length (2x + 3) metres and width (x - 1) metres. Write a simplified expression for the perimeter of the rectangle:
11. Check all the expressions that are equivalent to 12x + 8:

4(3x + 2)

2(6x + 4)

8(x + 4) + 4x

10x + 2x + 6 + 2

12. Create your own algebraic expression with at least 3 terms, then simplify it:

Original expression: _________________________

Simplified expression: _________________________

13. Explain in your own words what it means to "combine like terms":

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