Reading scales (AQA GCSE Maths): Revision Notes

Worked Example: Semicircular Gauge

On a semicircular gauge, there are 5 divisions between 100g and 150g.

Step 1: Find the range Range = 150g - 100g = 50g

Step 2: Apply the formula Division value = $\frac{50g}{5} = 10g$

Therefore, each division represents 10g.

Worked Example: Measuring Tape

On a measuring tape showing a brick wall, there are 5 divisions between 3.9m and 4m.

Step 1: Calculate the range Range = 4.0m - 3.9m = 0.1m

Step 2: Find the division value Division value = $\frac{0.1m}{5} = 0.02m$

Step 3: Convert to practical units 0.02m = 2cm per division

This means each small division represents 2 centimetres, not a round number like 5cm or 10cm.

Worked Example: Measuring Cylinder

In a measuring cylinder, if the liquid level appears to be about one-third of the way between 30ml and 40ml:

Step 1: Identify the range From 30ml to 40ml = 10ml range

Step 2: Calculate the fraction One-third of 10ml = $\frac{10ml}{3} ≈ 3.3ml$

Step 3: Add to the lower value Estimated reading = 30ml + 3.3ml = approximately 33ml

Worked Example: Balance Scale Problem

Given:

• Scale 1: 4 cubes + 1 tetrahedron = 9kg
• Scale 2: 3 cubes = 6kg

Step 1: Find the weight of one cube From Scale 2: $\frac{6kg}{3} = 2kg$ per cube

Step 2: Use substitution in Scale 1 4 cubes + 1 tetrahedron = 9kg $(4 × 2kg)$ + 1 tetrahedron = 9kg 8kg + 1 tetrahedron = 9kg

Step 3: Solve for tetrahedron 1 tetrahedron = 9kg - 8kg = 1kg

Step 4: Verify the solution

• Scale 1: $(4 × 2kg) + 1kg = 9kg$ ✓
• Scale 2: $(3 × 2kg) = 6kg$ ✓