Mathematics
NCEA Level 1 Mathematics assesses how confidently you choose and apply numerical, algebraic, geometric, measurement, and probability methods in unfamiliar contexts. External questions reward clear working and correct rounding, not just a final answer.
Core rules and concepts
- Use order of operations: brackets, exponents, multiplication/division, addition/subtraction. Keep exact values until the final step.
- Rearrange formulas by doing the same operation to both sides. When solving inequalities, reverse the sign if you multiply or divide by a negative.
- Expand using the distributive law: a(b + c) = ab + ac. Factorise by finding common factors and using the difference of two squares.
- For right triangles, use Pythagoras a² + b² = c² and trigonometry: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent.
- Probability of an event = favourable outcomes ÷ total outcomes when outcomes are equally likely. Probabilities sum to 1.
Worked example
Solve 3(2x − 5) = 4x + 7. Expand: 6x − 15 = 4x + 7. Subtract 4x: 2x − 15 = 7. Add 15: 2x = 22. Divide by 2: x = 11. Check by substitution: LHS = 3(22 − 5) = 3 × 17 = 51; RHS = 4 × 11 + 7 = 51. The solution is consistent.
Traps
- Sign errors when expanding a negative bracket: −2(x − 3) = −2x + 6, not −2x − 6.
- Forgetting to reverse an inequality: −3x < 12 gives x > −4.
- Using diameter as radius in A = πr² or V = πr²h.
- Rounding mid-calculation and then rounding again at the end.
- Mixing units such as cm and m before adding or comparing.