Chapter 1-1: Mental Arithmetic Techniques (Non-Calculator)

Foundation Higher Paper 1 - Non-Calculator

📝 Paper 1 Exam Technique (Non-Calculator - May 15, 2025)

  • Paper 1 is 100% non-calculator - mental arithmetic is ESSENTIAL for Grade 5+
  • Speed matters - you have ~1 minute per mark, mental methods save time
  • Mental arithmetic questions often appear early in Paper 1 (Questions 1-10)
  • 2-3 marks available in every paper for quick mental calculations
  • Foundation: Focus on addition, subtraction, multiplication, division up to 12×12
  • Higher: Must also handle fractions, decimals, percentages, negatives mentally
  • Show working - even for mental methods, write down intermediate steps

⏱️ Time Management

Target time for mental arithmetic questions: 30-60 seconds per mark

Paper 1 opens with 5-8 quick mental questions worth 1-2 marks each. Complete these in the first 10 minutes to build confidence and secure easy marks.

Essential Mental Arithmetic Techniques

1. Addition: Breaking Numbers Apart

Example: 47 + 38

Method: 47 + 40 = 87, then 87 - 2 = 85

Why it works: Adding 40 is easier than 38, then adjust by subtracting 2

2. Subtraction: Counting Up

Example: 83 - 56

Method: Count from 56 to 60 (+4), then 60 to 83 (+23), total = 27

Why it works: Often easier to count up than subtract down

3. Multiplication: Partitioning

Example: 24 × 6

Method: (20 × 6) + (4 × 6) = 120 + 24 = 144

Why it works: Breaking into tens and units makes calculation easier

4. Multiplication: Doubling and Halving

Example: 15 × 8

Method: 30 × 4 = 120 (doubled 15, halved 8)

Why it works: Multiplying by 4 is easier than 8

5. Division: Factor Method

Example: 144 ÷ 12

Method: 144 ÷ 6 = 24, then 24 ÷ 2 = 12

Why it works: Breaking division into steps (÷6 then ÷2 instead of ÷12)

6. Percentages: Using 10% and 1%

Example: 15% of 80

Method: 10% of 80 = 8, 5% of 80 = 4, so 15% = 8 + 4 = 12

Why it works: 10% is easy (÷10), 5% is half of 10%

Practice Questions

Question 1
Calculate mentally: 56 + 39
Question 2
Calculate mentally: 92 - 47
Question 3
Calculate mentally: 16 × 7
Question 4
Calculate mentally: 25 × 8
Question 5
Calculate mentally: 180 ÷ 12
Question 6
Calculate mentally: 20% of 45
Question 7
Calculate mentally: 7² + 5²
Question 8
Calculate mentally: 0.5 × 36
Question 9 (Higher)
Calculate mentally: -8 + 15 - 12
Question 10 (Higher)
Calculate mentally: 3/4 + 1/8

⚡ Quick Revision Summary

  • Addition: Add to nearest 10, then adjust (47+38: add 40, subtract 2)
  • Subtraction: Count up from smaller to larger number
  • Multiplication: Partition into 10s and units, or double and halve
  • Division: Break into factors (÷12 = ÷6 then ÷2)
  • Percentages: Use 10% as base, then adjust (10% = ÷10)
  • Squares: Memorize 1² to 15² for Paper 1
  • Key facts: 25×4=100, 0.5=half, 0.25=quarter
  • Exam strategy: Complete mental questions in first 10 minutes
  • Always show working - even brief steps can earn method marks