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Real-Life GraphsCambridge IGCSE Maths: Revision notes

Section 1

Travel graphs and conversion graphs

Real-life graphs represent practical situations, most commonly:

  • Travel graphs (distance–time or speed–time), showing how a journey unfolds
  • Conversion graphs, showing the relationship between two related quantities (e.g. currencies, units)

Because questions must be solved without a picture, real-life graph problems on this platform give you data (a table of values, or a described situation) and ask you to interpret or calculate from it directly, rather than reading a plotted line.

Key termstravel graphconversion graph

Section 2

Interpreting gradient as rate of change

On a distance–time graph, the gradient at any point represents speed: gradient=change in distancechange in time\text{gradient} = \dfrac{\text{change in distance}}{\text{change in time}}.

  • A steeper line means a faster speed
  • A horizontal section (zero gradient) means the object is stationary
  • A negative gradient means the object is moving back towards the start

Example: A journey covers 60 km in the first 2 hours, giving a gradient (average speed) of 602=30\dfrac{60}{2}=30 km/h.

Key termsrate of change
Exam tip

Always state the units of a gradient (e.g. km/h, m/s) — a numerical gradient alone will not earn full marks in a context question.

Section 3

Speed–time graphs and acceleration (Extended)

On a speed–time graph, the gradient represents acceleration: acceleration=change in speedchange in time\text{acceleration} = \dfrac{\text{change in speed}}{\text{change in time}}.

  • A positive gradient means the object is accelerating (speeding up)
  • A negative gradient means the object is decelerating (slowing down)
  • A horizontal section means constant speed (zero acceleration)

Example: A car's speed increases from 0 to 20 m/s in 5 seconds: acceleration =20−05=4= \dfrac{20-0}{5}=4 m/s².

Key termsaccelerationdeceleration

Section 4

Distance from a speed–time graph (Extended)

For linear sections of a speed–time graph, the area between the line and the time axis represents the distance travelled.

  • For a constant-speed section, the area is a rectangle: distance=speed×time\text{distance} = \text{speed} \times \text{time}
  • For a section with changing speed (a straight sloped line), the area is a trapezium: distance=12(sum of parallel sides)×height\text{distance} = \frac{1}{2}(\text{sum of parallel sides}) \times \text{height}, where the parallel sides are the initial and final speeds and the height is the time interval

Example: A car accelerates from 0 to 10 m/s over 4 seconds (linear). Distance =12(0+10)(4)=20=\frac{1}{2}(0+10)(4)=20 m.

Key termsarea under a graph
Common mistake

Students often multiply speed by time directly even when the speed is changing — for a sloped section, you must use the trapezium (average speed) method, not a simple rectangle.

Must Know

  • Distance–time graph gradient = speed; speed–time graph gradient = acceleration
  • A horizontal section on a distance–time graph means stationary; on a speed–time graph it means constant speed
  • A negative gradient on a speed–time graph means deceleration
  • Area under a speed–time graph (linear sections) = distance travelled
  • Use the trapezium method for distance when speed changes linearly over an interval
  • Always give units alongside a calculated gradient or area in context questions

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