Almost every mark your child drops in an 11+ maths paper comes down to one of two things: not knowing a fact cold, or knowing it but running out of time to use it. In a typical GL Assessment paper that means answering around 50 multiple-choice questions in about 50 minutes, roughly a minute each, with no calculator and answers marked A to E on a separate sheet. Under that pressure there is no time to derive the area of a triangle from first principles. This page gathers every formula and number fact your child genuinely needs into one free reference: area, perimeter, volume, averages, angle facts and the key conversions, each with a worked example and the exam traps that catch children out.
The core formula sheet
Learn these until they are automatic. If your child has to stop and think about which one to use, that is a second saved by practising and a mark saved in the exam.
| What you want | Formula | Worked example |
|---|---|---|
| Perimeter of a rectangle | 2 × (length + width) | 2 × (8 + 5) = 26 cm |
| Area of a rectangle | length × width | 8 × 5 = 40 cm² |
| Area of a triangle | (base × height) ÷ 2 | (6 × 4) ÷ 2 = 12 cm² |
| Volume of a cuboid | length × width × height | 3 × 4 × 2 = 24 cm³ |
| Mean average | total of values ÷ number of values | (4+6+8+2) ÷ 4 = 5 |
| Speed | distance ÷ time | 120 km ÷ 2 h = 60 km/h |
| Percentage of an amount | (percent ÷ 100) × amount | 15% of 80 = 0.15 × 80 = 12 |
Exam trap: mixing up area and perimeter is the single most common geometry error. Perimeter is the distance around the edge (measured in cm); area is the space inside (measured in cm²). If the answer needs a squared unit, you want area.
Perimeter, area and compound shapes
Compound (L-shaped) shapes are a top mark-loser because children apply one rectangle's formula to the whole thing. The method is always the same: split the shape into rectangles, or subtract a missing piece.
Worked example. An L-shape is a 10 cm by 6 cm rectangle with a 4 cm by 3 cm corner cut out. Splitting method: the full rectangle is 10 × 6 = 60 cm²; the cut-out is 4 × 3 = 12 cm²; so the area is 60 − 12 = 48 cm². For the perimeter, add every outer edge all the way round — do not forget the two short edges created by the notch. Our step-by-step compound shapes guide and the area and perimeter worksheets drill this until it is second nature.
Exam trap: missing sides. When a shape has hidden lengths, work them out from the sides you are given (opposite sides of the full rectangle must total the same) before adding up the perimeter.
The angle facts to memorise
Angle questions are pure recall plus one subtraction. Learn this table and most angle questions become a ten-second calculation.
| Fact | Total |
|---|---|
| Angles on a straight line | 180° |
| Angles around a point | 360° |
| Angles in a triangle | 180° |
| Angles in a quadrilateral | 360° |
| Vertically opposite angles | equal |
| Angles in an equilateral triangle | 60° each |
Worked example. A triangle has angles of 90° and 35°. The third is 180 − 90 − 35 = 55°. Exam trap: an isosceles triangle has two equal base angles — if you are told the top angle is 40°, the other two share the remaining 140°, so each is 70°, not 140°.
Fractions: the named methods
Fractions appear everywhere, so drill these three methods by name.
- Equivalent-fraction ladder: multiply or divide the top and bottom by the same number. 3/4 = 6/8 = 9/12. To simplify, divide both by their highest common factor: 6/8 → divide by 2 → 3/4.
- Adding and subtracting: find a common denominator first. 1/3 + 1/4: rewrite as 4/12 + 3/12 = 7/12. You cannot add the bottoms.
- Keep-change-flip (dividing): 2/3 ÷ 4/5 becomes 2/3 × 5/4 = 10/12 = 5/6. Keep the first fraction, change ÷ to ×, flip the second.
- Fraction of an amount: divide by the bottom, multiply by the top. 3/5 of 40 = (40 ÷ 5) × 3 = 24.
Exam trap: forgetting to simplify. If your answer is 8/12 and the options show 2/3, they are the same value — always cancel down to match the multiple-choice option. More practice sits in the free worksheets library.
Fraction, decimal and percentage conversions
These equivalents come up constantly, and knowing them by heart turns a working-out question into instant recall.
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/3 | 0.333… | 33.3% |
| 1/5 | 0.2 | 20% |
| 2/5 | 0.4 | 40% |
| 1/10 | 0.1 | 10% |
| 1/100 | 0.01 | 1% |
To turn a fraction into a percentage, make the bottom into 100 or divide top by bottom and multiply by 100. To go from a decimal to a percentage, multiply by 100 (0.35 = 35%).
Averages and BIDMAS worked in full
Averages. From the data set 3, 7, 7, 2, 6: the mean is (3+7+7+2+6) ÷ 5 = 25 ÷ 5 = 5; the mode is 7 (most common); the range is 7 − 2 = 5. For the median, put them in order (2, 3, 6, 7, 7) and take the middle value, 6. With an even count of six numbers, the median is the mean of the middle two. Remember to reorder before finding the median — that is where marks vanish.
BIDMAS. Order of operations is Brackets, Indices, Division/Multiplication, Addition/Subtraction. Take 2 + 3 × 4. A child working left to right gets 5 × 4 = 20, which is wrong. Multiplication comes first: 3 × 4 = 12, then 2 + 12 = 14. The mental maths techniques guide pairs each of these with a speed shortcut.
Ratio, worded problems and the exam format
Sharing in a ratio. Share £60 between two children in the ratio 2:3. Add the parts: 2 + 3 = 5. One part is 60 ÷ 5 = £12. So they get 2 × 12 = £24 and 3 × 12 = £36 (which checks out: 24 + 36 = 60).
A method for worded problems: underline the actual question, list what you are given, choose the operation, do the maths, then check the units and re-read the final sentence. Exam trap: the last line often switches what is asked (“how many were left?” not “how many were used?”). Our word problems method walks through this in detail.
Remember how this appears: GL papers are multiple-choice with options A to E on a separate answer sheet, so if your worked-out answer is not one of the options, you have made a slip — recheck rather than guess. A raw score is converted to a Standard Age Score (roughly 69–141, where 100 is the national average and many grammar schools look for around 111 or above); the age adjustment gives younger children in the year a fair chance. Build broader skills through the revision hub, the full maths guide, and timed practice mocks.
Frequently asked questions
Is a calculator allowed in the 11+ maths paper?
No. GL Assessment maths papers are non-calculator, which is exactly why the formulas, times tables and conversions on this sheet need to be memorised. Fast, accurate mental methods are what protect your child's time.
How many questions are there and how long per question?
Formats vary by region, but a common GL maths paper is around 50 questions in about 50 minutes — roughly one minute each. Some questions take seconds, freeing time for multi-step problems, so pace matters as much as knowledge.
Which of these facts matter most?
Angle facts, the fraction-decimal-percentage table, and the area/perimeter/volume formulas give the best return because they appear in almost every paper. Probability is rarer in GL but common in CSSE and independent-school papers, so weight your practice to your target school.