2.5 Real-life graphs
Real-life graphs
Everything on real-life graphs that can come up in the WJEC GCSE Mathematics and Numeracy, in all three units. Each skill below has the method, the mistake that costs the most marks, a worked example, and free practice marked the way WJEC marks it.
Practise real-life graphs free
The exam skills (5)
Travel graphs
- Find the distance travelled on that part of the graph.
- Find the time it took, in hours.
- Speed = distance ÷ time.
Watch out: Using minutes instead of hours for km/h.
Conversion graphs
- Find the amount on one axis.
- Go across (or up) to the line, then down (or across) to the other axis.
- For a value off the graph, convert a smaller amount and multiply.
Watch out: Reading the wrong axis.
Velocity-time graphs
- Distance = area under a velocity-time graph.
- Split it into triangles and rectangles (or trapeziums).
- Add up the areas.
Watch out: Using the gradient. That gives acceleration, not distance.
Rates of change
- The rate of change at a point is the gradient of the tangent there.
- Use two points on the tangent: change in y ÷ change in x.
- Give units, e.g. m/s for a distance-time graph.
Watch out: Finding the gradient from the origin, which is the average rate.
Trapezium rule
- Find the strip width h.
- Area ≈ h/2 × [first + last + 2 × (all the middle values)].
- For a speed-time graph, the area is the distance.
Watch out: Forgetting to double the middle values, or using h instead of h/2.
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