Mathematics
Core content
You need confident arithmetic with whole numbers, decimals and fractions; place value; ordering negative numbers; the order of operations (brackets, indices, division and multiplication, then addition and subtraction); equivalence between fractions, decimals and percentages; ratio and proportion; simple algebra (substitution and one- and two-step equations); unit conversion; perimeter, area and volume; angle facts (angles on a straight line, in a triangle, vertically opposite); coordinates; averages (mean, median, mode, range); simple probability; and problems involving time and money.
Traps
- Mixed units: centimetres alongside metres, minutes alongside hours.
- 'How many more' versus 'how many altogether'.
- A percentage of an amount versus a percentage increase.
- Perimeter and area confused; forgetting to convert before calculating.
- Ratio sharing: find the number of parts first, then divide, then multiply - never divide by the number of shares.
- Answers left in the wrong form (not simplified, wrong number of decimal places, no units).
Rule of thumb
Write the unit beside every number, estimate the answer before calculating, and check afterwards by working backwards or substituting.
Worked example
Share £84 in the ratio 3:4. The parts total 3 + 4 = 7, so one part is £84 ÷ 7 = £12. The shares are 3 × £12 = £36 and 4 × £12 = £48. Check: £36 + £48 = £84 and 36:48 simplifies to 3:4.