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Algebraic Concepts Introduction

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Algebraic Concepts Introduction

Algebraic expressions and variables illustration

📚 Part 1: Understanding Algebraic Terms

1. Match each term with its correct definition by circling the best answer:

Variable:

A letter that represents an unknown number

A number that never changes

A mathematical sentence with an equals sign

2. Which of these are algebraic expressions? (Check all that apply)

3x + 5

7 = 2 + 5

2y - 8

n + 12

3. In the expression 4x + 7, identify the parts:

The variable is: ________

The constant is: ________

The coefficient of x is: ________

4. Circle the correct way to write "three times a number n":

3 + n

3n

3 ÷ n

✏️ Part 2: Writing Algebraic Expressions

5. Write algebraic expressions for these real-world situations:

a) The cost of buying x apples at $2 each, plus $3 for a bag:

b) Sarah's age if she is 5 years older than her brother who is y years old:

c) The total distance travelled if you drive at 80 km/h for t hours:

6. A mobile phone plan costs $25 per month plus $0.50 for each text message sent.

Write an expression for the total monthly cost if you send n text messages:

🔢 Part 3: Substitution and Evaluation

7. Evaluate these expressions when x = 4:

a) 3x + 2 = ________

b) 5x - 7 = ________

c) 2x + 10 = ________

8. The expression for the perimeter of a rectangle is 2l + 2w, where l is length and w is width.

Find the perimeter when l = 8 metres and w = 5 metres:

9. Look at this pattern of dots:

Pattern 1: • (1 dot)

Pattern 2: ••• (3 dots)

Pattern 3: ••••• (5 dots)

Write an expression for the number of dots in pattern n:

10. Explain in your own words why algebra is useful in real life:

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