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Mental arithmetic is one of the most important skills you need for the CEM 11+ exam. Unlike the GL exam, where questions are grouped by topic, the CEM exam mixes maths questions with non-verbal reasoning in a single booklet. You will need to switch quickly between different types of thinking, so being able to do calculations in your head — fast and accurately — is essential.
In the CEM 11+ exam, time pressure is intense. You may have as little as 30-40 seconds per question, and there is no separate calculator paper. The questions test whether you can recall number facts instantly and apply them under pressure.
CEM Tip: CEM questions are designed so that pupils who have practised mental arithmetic daily will have a significant advantage. Even a few seconds saved per question adds up across the whole paper.
You must know every times table fact instantly — not after counting on your fingers. Here is a reminder of the trickier ones:
| × | 6 | 7 | 8 | 9 | 12 |
|---|---|---|---|---|---|
| 6 | 36 | 42 | 48 | 54 | 72 |
| 7 | 42 | 49 | 56 | 63 | 84 |
| 8 | 48 | 56 | 64 | 72 | 96 |
| 9 | 54 | 63 | 72 | 81 | 108 |
| 12 | 72 | 84 | 96 | 108 | 144 |
| Number | Square |
|---|---|
| 1 | 1 |
| 2 | 4 |
| 3 | 9 |
| 4 | 16 |
| 5 | 25 |
| 6 | 36 |
| 7 | 49 |
| 8 | 64 |
| 9 | 81 |
| 10 | 100 |
| 11 | 121 |
| 12 | 144 |
| 13 | 169 |
| 15 | 225 |
If you know your times tables, you also know your division facts:
Break numbers into parts that are easy to add:
347 + 258 = 300 + 200 + 40 + 50 + 7 + 8 = 500 + 90 + 15 = 605
Round one number to make the addition easier, then adjust:
467 + 199 = 467 + 200 - 1 = 666
When two numbers are close together:
76 + 78 = 76 + 76 + 2 = 152 + 2 = 154
Find the difference by counting up from the smaller number:
503 - 287
645 - 198 = 645 - 200 + 2 = 447
To multiply by 4, double twice. To multiply by 8, double three times:
35 × 4 = 35 × 2 × 2 = 70 × 2 = 140
15 × 8 = 15 × 2 × 2 × 2 = 30 × 2 × 2 = 60 × 2 = 120
Break the multiplier into factors:
24 × 15 = 24 × 5 × 3 = 120 × 3 = 360
Multiply by 100, then divide by 4:
36 × 25 = 36 × 100 ÷ 4 = 3,600 ÷ 4 = 900
To divide by 4, halve twice. To divide by 8, halve three times:
248 ÷ 4 = 248 ÷ 2 ÷ 2 = 124 ÷ 2 = 62
432 ÷ 12 — Think: what × 12 = 432? Since 12 × 36 = 432, the answer is 36.
The best way to build mental arithmetic speed is daily practice. Try the following routine:
CEM Exam Insight: CEM papers often embed arithmetic inside word problems or present calculations in unfamiliar layouts. The faster your basic arithmetic, the more time you have to think about the trickier parts of each question.
Mental arithmetic speed is the engine that powers your performance in the CEM 11+ maths paper. By knowing your number facts by heart and using smart strategies — partitioning, compensating, doubling, halving, and using factors — you can answer questions quickly and move on to the trickier problems with time to spare. Practise every day, and your speed and accuracy will grow steadily.