Sheet № 197 · Foundation + Higher · AQA · Edexcel · OCR
Real-Life Graphs –
Real-life graphs appear frequently in GCSE Maths exams because they test your ability to interpret mathematical information in everyday contexts. From currency conversion to filling containers, these questions are about reading and understanding graphs rather than plotting them.
§Key definitions
Question:
A conversion graph shows that 5 miles is approximately 8 kilometres. Use the graph to convert 20 miles to kilometres.
Answer:
20 miles ≈ 32 kilometres
Q1 (Foundation):
A conversion graph shows 10 litres equals 2.2 gallons. Convert 35 litres to gallons.
Q2 (Foundation):
A taxi charges a £3 base fare plus £1.50 per mile. What is the cost for a 6-mile journey?
Q3 (Higher):
A graph shows the depth of water in a swimming pool over 5 hours. The gradient of the first section is 0.4. What does this represent?
§Formulas to memorise
Gradient = change in y / change in x — represents the rate of change in context
Worked example
A conversion graph shows that 5 miles is approximately 8 kilometres. Use the graph to convert 20 miles to kilometres.
Working:
⚠ Common mistakes
- ✗Misreading the scale on the axes. Always check what each square or gridline represents before reading values.
- ✗Ignoring units. If one axis is in pence and the other in minutes, do not confuse pence with pounds.
- ✗Describing the gradient without context. Saying "the gradient is 3" is not enough — you must say what it means, e.g. "the cost increases by £3 per kilogram."
✦ Exam tips
- →Use a ruler to draw lines from the axes to the graph when reading values — this improves accuracy.
- →If asked to "interpret the gradient," always include the units from both axes in your answer.
- →For container-filling graphs, think about whether the container is getting wider or narrower to decide if the graph is getting flatter or steeper.