Estimation (AQA GCSE Maths): Revision Notes

Worked Example: Basic Multiplication

Original calculation: $4.32 \times 18.09$

Step 1: Round to 1 significant figure: $4 \times 20$ Step 2: Calculate the estimate: $4 \times 20 = 80$ Result: $4.32 \times 18.09 \approx 80$

Worked Example: Squaring Numbers

Original calculation: $327^2$

Step 1: Round to 1 significant figure: $300^2$ Step 2: Calculate the estimate: $300^2 = 90,000$ Result: $327^2 \approx 90,000$

Worked Example: Mixed Operations

Calculate an estimate for: $4.31 \times 278 \div 0.487$

Step 1: Round to 1 significant figure

• $4.31 \approx 4$
• $278 \approx 300$
• $0.487 \approx 0.5$

Step 2: Write the calculation $4 \times 300 \div 0.5$

Step 3: Calculate $4 \times 300 \div 0.5 = 1200 \div 0.5 = 2400$

Worked Example: Removing Decimals

Instead of calculating $1200 \div 0.5$:

• Multiply both by 10: $12000 \div 5 = 2400$
• This is much easier to calculate without a calculator!

Worked Example: Estimating Cubes

Calculate an estimate for $37.4^3$

Step 1: Round to 1 significant figure: $37.4 \approx 40$

Step 2: Use laws of indices to break down $40^3$

• $40^3 = (4 \times 10)^3$
• $= 4^3 \times 10^3$
• $= 64 \times 1000$
• $= 64,000$

Result: $37.4^3 \approx 64,000$

Worked Example: Formula Estimation

For a sphere with radius 2.35cm, estimate the surface area:

Step 1: Use the formula: $4\pi r^2$ Step 2: Substitute and round: $4 \times 3 \times 2^2 = 4 \times 3 \times 4 = 48$ cm²

Result: Surface area $\approx 48$ cm²

Worked Example: Analysis of Estimation Accuracy

For our sphere calculation: $4 \times 3 \times 2^2$

• $\pi = 3.142$: we rounded down to 3
• $r = 2.35$: we rounded down to 2
• Since we rounded both numbers down, our answer is an underestimate