Simplification Cheat Sheet

Simplification Cheat Sheet

Quick Revision

Simplification asks you to reduce a long expression to a single value. The whole topic rests on doing the operations in the correct order — the BODMAS rule.

Ready to practise? Take the Simplification quiz

1. BODMAS — the Order of Operations

Work through an expression in this order:

Division and multiplication rank together (left to right), as do addition and subtraction.

Order of brackets: solve ( ) first, then { }, then [ ].

Example

12 + 6 ÷ 2 × 3 − 4
= 12 + 3 × 3 − 4     (division first)
= 12 + 9 − 4         (then multiplication)
= 17

2. Approximation (fast answers)

In "find the approximate value" questions, round each number to a convenient figure, then compute.

Example

49.8 × 20.1 ≈ 50 × 20 = 1000

Round to the nearest easy number; the options are usually far enough apart to allow it.

3. Algebraic Identities

(a + b)² = a² + 2ab + b²
(a − b)² = a² − 2ab + b²
a² − b² = (a + b)(a − b)
(a + b)³ = a³ + 3a²b + 3ab² + b³
a³ + b³ = (a + b)(a² − ab + b²)
a³ − b³ = (a − b)(a² + ab + b²)

4. Values Worth Memorising

• Squares up to 30 and cubes up to 15.
• Common fraction–percentage pairs: 1/2 = 50%, 1/4 = 25%, 1/5 = 20%, 1/8 = 12.5%, 1/3 = 33⅓%.
• Square roots of 2 ≈ 1.414, 3 ≈ 1.732.

These turn long divisions into instant recall.

5. Exam Quick Tips

• Always follow BODMAS; a wrong order is the most common mistake.
• Open round brackets first, then curly, then square.
• For "approximate value", round early and compute with easy numbers.
• Memorised squares, cubes and fraction-percents save the most time.

Keep revising with the rest of the Maths section:

• All Maths topics
• Data Interpretation Cheat Sheet
• Partnership Cheat Sheet

How this was made: Drafted with AI assistance; spot-checked by the editor on 31 October 2026.