Calculusmental math

Mental math techniques

Tricks to calculate faster in your head, sorted by level. Each one comes with a worked example, step by step.

Level 5 · Legend 4 techniques

Remember

Squaring a neighbour

For a number right next to a ten: (m ± 1)² = m² ± 2m + 1.

31² = 961

  1. 30 × 30 = 900
  2. 2 × 30 + 1 = 61
  3. 900 + 61 = 961
Practise →
Remember

Powers of 2

Remember two landmarks, 2⁵ = 32 and 2¹⁰ = 1024, then double or halve.

2⁸ = 256

  1. 2¹⁰ = 1024
  2. 1024 ÷ 2 = 512
  3. 512 ÷ 2 = 256
Practise →
Remember

Square roots by bracketing

Squeeze the number between the squares of two tens, then look at its last digit.

√576 = 24

  1. 20 × 20 = 400
  2. 30 × 30 = 900
  3. 25 × 25 = 625
  4. 24 × 24 = 576
Practise →
Remember

Multiplying by 15

× 15 is × 10 plus half of that.

18 × 15 = 270

  1. 18 × 10 = 180
  2. 180 ÷ 2 = 90
  3. 180 + 90 = 270
Practise →