Mathematics
What the paper tests
The Mathematics paper covers number operations, fractions and decimals, algebraic expressions, linear equations, ratio and proportion, geometry, measurement, and simple statistics. Marks are lost less often from unknown methods than from untidy substitution and unit errors.
Core rules
- Follow order of operations: brackets, powers, multiplication/division, then addition/subtraction.
- In an equation, do the same operation to both sides; collect variable terms on one side.
- Area of a triangle is ½ × base × height; circumference of a circle is 2πr.
- A ratio compares parts of the same whole; a proportion equates two ratios.
- Mean = sum of values ÷ number of values.
Worked example
Solve 3(x − 2) = 2x + 5. Reasoning: expand the bracket: 3x − 6 = 2x + 5. Subtract 2x from both sides: x − 6 = 5. Add 6: x = 11. Check by substitution: 3(11 − 2) = 27 and 2(11) + 5 = 27. Both sides agree, so x = 11.
Traps
- Distributing a negative incorrectly: −2(x − 3) = −2x + 6, not −2x − 6.
- Cancelling terms across a plus sign instead of factoring.
- Mixing units such as cm and m in area or speed questions.
- Rounding too early in a multi-step calculation.