How to use this. Do not read it through. Take one section, cover it, and ask your child to tell you everything they remember. Recalling from memory builds far stronger retention than re-reading — and it shows you instantly which section is shaky.
Area and perimeter
- Rectangle: area = length × width · perimeter = 2 × (length + width)
- Triangle: area = ½ × base × height — the perpendicular height, not the sloping side
- Parallelogram: base × perpendicular height
- Trapezium: ½ × (a + b) × height, where a and b are the parallel sides
- Circle: area = πr² · circumference = πd (use π ≈ 3.14)
- Compound shapes: split into rectangles and triangles, or take the big rectangle and subtract
Trap: double the sides of a square and the area increases ×4, not ×2. Triple them and it is ×9.
Angles
- Straight line = 180° · full turn = 360° · right angle = 90°
- Triangle = 180° · quadrilateral = 360°
- Isosceles triangle: two equal sides and two equal base angles
- Vertically opposite angles (across an X) are equal
- Parallel lines: alternate (Z) equal · corresponding (F) equal · co-interior (C) add to 180°
- Regular polygon: exterior angles total 360°, so each = 360 ÷ n, and interior = 180 − exterior
- Interior angle sum = (n − 2) × 180 → pentagon 540°, hexagon 720°
Fractions, decimals and percentages
Learn these by heart:
| Fraction | Decimal | Percentage |
|---|---|---|
| ½ | 0.5 | 50% |
| ¼ | 0.25 | 25% |
| ⅕ | 0.2 | 20% |
| ⅛ | 0.125 | 12.5% |
| ⅓ | 0.333… | 33⅓% |
| ⅜ | 0.375 | 37.5% |
| ⅝ | 0.625 | 62.5% |
- Add/subtract: match denominators first · multiply: straight across · divide: flip the second and multiply
- Fraction of an amount: divide by the bottom, times by the top (⅗ of 40 → 8 × 3 = 24)
- Percentage of an amount: 10% = ÷10 · 1% = ÷100 · 5% = half of 10% · 25% = ÷4
- Percentage change = (change ÷ original) × 100 — always the original
- Reverse percentage: if 25% is 17, then 100% is 68. Find 1% first
Trap: 0.2 × 0.4 = 0.08, not 0.8. Count the decimal places.
Ratio and proportion
- Simplify like a fraction: 12 : 18 → 2 : 3
- Sharing: add the parts to get total shares, divide, then multiply. 40 in 3 : 5 → 8 shares → 5 each → 15 and 25
- Best value: work out the price per unit
Trap: answer the part actually asked for — the larger share, the difference, or the total.
HCF and LCM
- HCF = the biggest number that divides into both. LCM = the first number they both go into.
- Use HCF for: simplifying fractions and ratios; splitting into the largest equal groups with none left over; the biggest square tile that fits exactly.
- Use LCM for: things happening together again — buses every 12 and 18 minutes meet after 36.
- Spot it: "largest / greatest / maximum" + "equal groups, nothing left over" → HCF.
- Sense check: HCF is smaller than your numbers, LCM is bigger.
- Method: prime factorise both and multiply the shared primes. 36 = 2×2×3×3, 60 = 2×2×3×5 → HCF = 12.
Number facts worth knowing instantly
- Squares to 20²: …169, 196, 225, 256, 289, 324, 361, 400
- Cubes to 10³: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000
- Primes under 50: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 — 1 is not prime
- Divisibility: by 3 if digits sum to a multiple of 3 · by 4 if last two digits divide by 4 · by 6 if it passes 2 and 3 · by 9 if digits sum to a multiple of 9
- BIDMAS: brackets, indices, division/multiplication, addition/subtraction
Averages, time and speed
- Mean = total ÷ how many · median = middle when ordered · mode = most common · range = biggest − smallest
- Missing value: total = mean × number of items, then subtract what you have
- Speed = distance ÷ time · distance = speed × time · time = distance ÷ speed
- Time runs in 60s: 2.5 hours = 2 h 30 min; 1.75 hours = 1 h 45 min
- Count time in chunks: 13:47 → 14:00 is 13 minutes, then on to 16:12
The habits that win marks
- Estimate first. If 15% of 260 comes out as 390, something is wrong.
- Answer the question asked. If it wants the width, do not stop at the perimeter.
- Units matter. Area in cm², volume in cm³, and never mix cm with m in one calculation.
- In multiple choice, the traps are the wrong answers. Work it out before looking at the options.
- Answer every question. GL papers carry no penalty for a wrong answer, so a blank is a wasted chance.