Mathematics (4024)
Expression: 3x + 2 (no equals sign) Equation: 3x + 2 = 14 (has equals sign, can be solved) Formula: A = πr² (a rule for calculating something)
Collect like terms: 3x + 2y + 5x - y = 8x + y Expand brackets: 3(2x + 4) = 6x + 12 Factorise (reverse of expanding): 6x + 12 = 3(2x + 4)
Subtract 7: 3x = 15 Divide by 3: x = 5
x² × x³ = x⁵ (add powers when multiplying) x⁶ ÷ x² = x⁴ (subtract powers when dividing) (x²)³ = x⁶ (multiply powers when raising to a power) x⁰ = 1 (anything to the power 0 equals 1)
Topic 3 of 5Cambridge O Levels
Algebra Basics
Using letters to represent unknown numbers
Algebra uses letters (variables) to represent unknown values. It's like solving a puzzle!
Expressions, Equations & Formulae:
Simplifying Expressions:
Solving Linear Equations:
Do the same thing to both sides to isolate x.
Example: 3x + 7 = 22
Substitution: Replace letters with numbers.
If a = 3 and b = -2, then 2a + 3b = 2(3) + 3(-2) = 6 - 6 = 0
Indices (Powers):
Key Points to Remember
- 1Like terms: same variable and power (3x and 5x, NOT 3x and 5x²)
- 2Expand: multiply each term inside brackets
- 3Solve equations by doing the same thing to both sides
- 4Index laws: multiply → add powers, divide → subtract powers
Pakistan Example
Mobile Data Plans
Jazz offers a data plan: Rs 200 base + Rs 15 per GB. You can write this as Cost = 200 + 15g (where g = number of GBs). If your budget is Rs 500, how many GBs can you get? Solve: 200 + 15g = 500 → 15g = 300 → g = 20 GB. Now compare with Zong's plan: Rs 100 base + Rs 20 per GB. Cost = 100 + 20g. When are they equal? 200 + 15g = 100 + 20g → 100 = 5g → g = 20. Below 20 GB, Zong is cheaper. Above 20 GB, Jazz is cheaper!