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AQASpec R11-R16Foundation & Higher~30 min

Rates of Change & Growth

Mathematics · Topic revision workspace

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Read the notes, score 80% and know 75% of the cards.

Topic overview

What you need to know

Rates of Change & Growth is a key part of GCSE Mathematics. Build fluency with the method, then apply it to unfamiliar and multi-step problems. Distance travelled per unit of time. Speed = distance ÷ time. Measured in m/s or km/h. Mass per unit volume. Density = mass ÷ volume. Measured in g/cm³ or kg/m³. Force per unit area. Pressure = force ÷ area. Measured in N/m² or Pascals.

Exam tip

Write every stage of your method. Method marks can still be earned when the final answer is wrong.

Revision notes

Core ideas

Secure these ideas first. Say each definition in your own words, then connect it to the topic overview.

  • Speed: Distance travelled per unit of time. Speed = distance ÷ time. Measured in m/s or km/h.
  • Density: Mass per unit volume. Density = mass ÷ volume. Measured in g/cm³ or kg/m³.
  • Pressure: Force per unit area. Pressure = force ÷ area. Measured in N/m² or Pascals.
  • Compound Measures: Measures involving two or more units, such as speed (m/s), density (g/cm³), and flow rate (litres/min).

Revision notes

Apply it in the exam

The exam will rarely ask for an isolated definition. Practise selecting the right idea and using it as part of a complete explanation or method.

  • Percentage Growth: After n periods at r% growth: final = original × (1 + r/100)ⁿ. The multiplier compounds.
  • Depreciation: Decrease in value over time. After n years at r% depreciation: value = original × (1 − r/100)ⁿ.
  • Gradient of a Curve: The rate of change at a point on a curve, found by drawing a tangent line at that point and calculating its gradient.
  • Area Under a Graph: For a speed-time graph, the area under the curve represents the total distance travelled.

Core knowledge

Key facts for Rates of Change & Growth

1

Speed

Distance travelled per unit of time. Speed = distance ÷ time. Measured in m/s or km/h.

2

Density

Mass per unit volume. Density = mass ÷ volume. Measured in g/cm³ or kg/m³.

3

Pressure

Force per unit area. Pressure = force ÷ area. Measured in N/m² or Pascals.

4

Compound Measures

Measures involving two or more units, such as speed (m/s), density (g/cm³), and flow rate (litres/min).

5

Percentage Growth

After n periods at r% growth: final = original × (1 + r/100)ⁿ. The multiplier compounds.

6

Depreciation

Decrease in value over time. After n years at r% depreciation: value = original × (1 − r/100)ⁿ.

7

Gradient of a Curve

The rate of change at a point on a curve, found by drawing a tangent line at that point and calculating its gradient.

8

Area Under a Graph

For a speed-time graph, the area under the curve represents the total distance travelled.

Active recall

Close the notes and answer these

  1. 1.Without looking, explain speed and give one example or consequence.
  2. 2.Without looking, explain density and give one example or consequence.
  3. 3.Without looking, explain pressure and give one example or consequence.
  4. 4.Without looking, explain compound measures and give one example or consequence.

Content reviewed 23 July 2026 against the current linked specification.

Finished learning?

Mark the notes complete, then test what you can recall.

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