Number
Overview
The Number domain of CCEA GCSE Mathematics tests fluency with integers, fractions, decimals, percentages, ratio and proportion, and exact values. Foundation tier concentrates on secure arithmetic and proportional reasoning; Higher tier adds surds, standard form, bounds and negative/fractional indices. Questions appear both with and without a calculator, so method marks depend on clear intermediate steps.
Core rules
- Use BIDMAS: brackets, indices, then ×/÷, then +/−.
- Fraction arithmetic needs a common denominator for addition/subtraction; division means multiply by the reciprocal.
- A percentage change uses a multiplier: +15% is ×1.15, −15% is ×0.85. For a reverse percentage, divide by the multiplier.
- Ratio problems: find the value of one part, then scale; keep the order of the ratio.
- Standard form is a × 10^n with 1 ≤ a < 10.
- For a number rounded to 1 d.p., the upper bound is the stated value + 0.05; the lower bound is − 0.05. For division, divide by the lower bound to maximise, divide by the upper bound to minimise.
Worked example
A coat is reduced by 15% and now costs £68. Find the original price. The sale price is 85% of the original, so original × 0.85 = 68. Divide: 68 ÷ 0.85 = 80. The original price was £80. Check: 80 × 0.85 = 68.
Traps
Adding 15% to £68 instead of dividing; using 1.15 for a reduction; rounding too early in a multi-step calculation; treating a percentage as a fraction of the new amount; mixing up upper and lower bounds when subtracting.