Mental Arithmetic Speed

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.

Why Speed Matters in CEM

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.

Key Number Facts to Know by Heart

Times Tables (up to 12 × 12)

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

Square Numbers

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

Division Facts

If you know your times tables, you also know your division facts:

56 ÷ 7 = 8 (because 7 × 8 = 56)
108 ÷ 9 = 12 (because 9 × 12 = 108)
96 ÷ 8 = 12 (because 8 × 12 = 96)

Mental Strategies for Addition

Partitioning

Break numbers into parts that are easy to add:

347 + 258 = 300 + 200 + 40 + 50 + 7 + 8 = 500 + 90 + 15 = 605

Compensating (Round and Adjust)

Round one number to make the addition easier, then adjust:

467 + 199 = 467 + 200 - 1 = 666

Near Doubles

When two numbers are close together:

76 + 78 = 76 + 76 + 2 = 152 + 2 = 154

Mental Strategies for Subtraction

Counting On (Shopkeeper's Method)

Find the difference by counting up from the smaller number:

503 - 287

287 → 300 = 13
300 → 500 = 200
500 → 503 = 3
Total: 13 + 200 + 3 = 216

Compensating

645 - 198 = 645 - 200 + 2 = 447

Mental Strategies for Multiplication

Doubling and Halving

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

Using Factors

Break the multiplier into factors:

24 × 15 = 24 × 5 × 3 = 120 × 3 = 360

Multiplying by 25

Multiply by 100, then divide by 4:

36 × 25 = 36 × 100 ÷ 4 = 3,600 ÷ 4 = 900

Mental Strategies for Division

Halving Repeatedly

To divide by 4, halve twice. To divide by 8, halve three times:

248 ÷ 4 = 248 ÷ 2 ÷ 2 = 124 ÷ 2 = 62

Using Known Facts

432 ÷ 12 — Think: what × 12 = 432? Since 12 × 36 = 432, the answer is 36.

Practising Under Time Pressure

The best way to build mental arithmetic speed is daily practice. Try the following routine:

Warm-up (2 minutes): Write answers to 20 random times table questions.
Sprint (3 minutes): Answer 15 mixed addition, subtraction, multiplication, and division questions.
Challenge (5 minutes): Answer 10 multi-step questions (e.g. "What is 7 × 8 + 15 - 9?").

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.

Practice Checklist

I know all times tables up to 12 × 12 instantly
I know square numbers up to 15²
I can add and subtract three-digit numbers in my head
I can multiply two-digit numbers using mental strategies
I can divide using halving and known facts
I practise mental arithmetic under timed conditions regularly

Summary

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.