A printable sheet of the maths facts to know without a calculator
These are the facts that make a non-calculator paper faster rather than harder: squares to 15, cubes to 10, the primes below 50, the fraction, decimal and percentage conversions worth knowing on sight, angle rules and the usual unit conversions. None of it is exotic. Recall speed is what it buys you, and speed is marks on a paper you are short of time on.
Last updated 20 August 2026 · Written and checked by the GCSEwiz team
What is on the sheet
- Squares, cubes and the primes below 50, to recognise instantly
- Fraction, decimal and percentage conversions in one table
- Angle rules, plus the metric and imperial conversions GCSE uses
3 sheets · A4 portrait · black and white
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Squares, cubes and primes
Page 1 of 3Not a formula sheet. These are the ones worth knowing on sight.
Squares, cubes and roots
| n | n² | n³ |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 4 | 8 |
| 3 | 9 | 27 |
| 4 | 16 | 64 |
| 5 | 25 | 125 |
| 6 | 36 | 216 |
| 7 | 49 | 343 |
| 8 | 64 | 512 |
| 9 | 81 | 729 |
| 10 | 100 | 1000 |
| 11 | 121 | |
| 12 | 144 | |
| 13 | 169 | |
| 14 | 196 | |
| 15 | 225 |
Primes below 50
| Primes |
|---|
| 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 |
Fractions, percentages and angles
Page 2 of 3The conversions worth recognising instantly, and the angle rules behind the geometry.
Fractions, decimals and percentages
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333… | 33.3% |
| 2/3 | 0.666… | 66.7% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 2/5 | 0.4 | 40% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
| 1/10 | 0.1 | 10% |
| 1/20 | 0.05 | 5% |
Angles
| Fact | Value |
|---|---|
| Angles on a straight line | 180° |
| Angles around a point | 360° |
| Angles in a triangle | 180° |
| Angles in a quadrilateral | 360° |
| Exterior angles, any polygon | add to 360° |
| Interior angles, n-sided polygon | (n − 2) × 180° |
| One interior angle, regular n-gon | 180° − (360° ÷ n) |
Conversions
Page 3 of 3The metric ones are exact. The imperial ones are the approximations GCSE uses.
Conversions
| From | To |
|---|---|
| 1 cm³ | 1 ml |
| 1 litre | 1000 cm³ |
| 1 km | 1000 m |
| 1 tonne | 1000 kg |
| 1 m² | 10 000 cm² |
| 1 hour | 3600 seconds |
| 1 inch | about 2.5 cm |
| 1 foot | about 30 cm |
| 1 mile | about 1.6 km |
| 1 kg | about 2.2 pounds |
| 1 gallon | about 4.5 litres |
Facts I keep forgetting
This is not the formulae sheet, and it does not tell you which formulae your board hands you in the paper. That split differs by board and has changed more than once, so check it against your board’s current specification.
Why recall speed is worth marks
Recognising 169 as 13 squared takes no time at all. Working it out costs perhaps twenty seconds and some working-out space, and on a ninety-minute paper you will do something like that thirty times. The arithmetic is not the hard part of any question, so every second it takes is a second stolen from the part that is.
There is a second effect that matters more. Recognising 0.375 as three eighths often shows you what a question is really about, and a student who has to convert it laboriously frequently misses that.
How to learn a sheet like this
Not by reading it. Cover a column and write it out, check, repeat tomorrow. Ten minutes of that across a week is enough for most of the tables here, and the fraction conversions are the ones that pay back fastest.
The interior-angle rules are worth understanding rather than memorising. If you know that exterior angles always add to 360°, the rest of the polygon results can be rebuilt in a few seconds even if the memory goes.
The imperial conversions
GCSE uses approximate conversions for the imperial units, which is why the sheet says "about". Questions that need them normally give the conversion in the question itself, so treat these as a sense check rather than something to rely on.