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Year 10 Algebra Mastery

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Year 10 Algebra Mastery worksheet preview

Year 10 Algebra Mastery

📚 Part A: Algebraic Expressions & Exponent Laws

Worked Example: Simplify 3x² × 2x³ = 3 × 2 × x² × x³ = 6x⁵ (add exponents when multiplying)

1. Simplify: 4a³ × 2a²
2. Simplify: (3x²y)³
3. Expand and simplify: 3(2x - 5) + 4(x + 1)
4. Factorise: 6x² - 9x

✏️ Part B: Linear Equations & Inequalities

Worked Example: Solve 2x + 7 = 15. Subtract 7: 2x = 8. Divide by 2: x = 4

5. Solve: 3x - 8 = 19
6. Solve: 2(x - 3) = 4x + 10
7. Solve the inequality: 5x - 3 ≤ 17
8. A mobile phone plan costs $25 per month plus $0.50 per text message. If Jake's monthly bill was $37, how many text messages did he send?

🔧 Part C: Simultaneous Equations & Challenge

Worked Example: Solve x + y = 5 and 2x - y = 1. Add equations: 3x = 6, so x = 2. Substitute: 2 + y = 5, so y = 3

9. Solve the simultaneous equations: x + 2y = 8 and 3x - y = 5
10. Solve: 2x + 3y = 11 and x - y = 2
Challenge: 11. A rectangular garden has a perimeter of 24 metres. The length is 2 metres more than twice the width. Find the dimensions of the garden.
Challenge: 12. Simplify: (2x³y²)² ÷ (4xy)²

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