Step-by-step worked examples and graded practice questions on interpreting graphs — comparing graphs, reading rates of change, estimating values, and spotting misleading graphs.
📚 Foundation & Higher✅ 15 Practice Questions🔍 Full Worked Examples⚠️ Common Mistakes
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This final Graphs & Functions topic pulls together the skills from every graph type on this hub into one general ability: reading a graph accurately, comparing what it shows against another graph, and being critical of how a graph might mislead. Exam questions here often don't need any calculation at all — they're testing whether you can read a graph correctly.
Comparing two graphs on the same axes
When two graphs are drawn on the same axes, compare their steepness (rate of change) and their starting and finishing points. The steeper line always represents the faster rate of change, regardless of which one started first or looks longer.
Worked Example 1 — Comparing two travel graphs
Two hikers set off at the same time along the same 20 km trail. Compare their average speeds, and state which hiker finishes first.
1
Hiker A's line reaches 20 km at 4 hours: speed = 20 ÷ 4 = 5 km/h
2
Hiker B's line reaches 20 km at 2 hours: speed = 20 ÷ 2 = 10 km/h
3
Hiker B's line is steeper, confirming the faster speed, and reaches 20 km first
AnswerHiker B is faster (10 km/h vs 5 km/h) and finishes first, at 2 hours
Comparing two hikers' journeys: Hiker B's steeper line shows the faster speed.
Estimating values from a graph
Graphs let you estimate values between the points you actually know, by reading directly off the curve — this is called interpolation. It works for any graph, not just straight lines.
Worked Example 2 — Reading a curved graph
A graph shows the temperature over a 24-hour day. Use the graph to estimate the temperature at 10am.
1
Find 10 on the time axis and read up to the curve, then across to the temperature axis
2
The reading gives approximately 19.6°C
AnswerApproximately 19.6°C
Reading the temperature curve at 10am gives approximately 19.6°C.
Spotting misleading graphs
The same data can be made to look very different depending on how a graph is drawn — most commonly by not starting the axis at zero. Always check the axis scale before drawing conclusions from a graph, especially a bar chart.
Worked Example 3 — Comparing an honest and a misleading graph
Both graphs below show the same sales data: £84k in January, £86k in February, and £91k in March. Explain why Graph B makes the increase look far more dramatic than Graph A.
1
Graph A's y-axis starts at 0, so the bar heights are shown in true proportion to each other
2
Graph B's y-axis starts at 80, not 0 — this stretches the small differences between the bars, making them look much larger than they really are
AnswerGraph B's truncated (non-zero) axis exaggerates the visual size of the increase, even though the underlying data is identical
The same sales data, drawn two ways — only Graph A's zero-based axis gives a fair comparison.
Practice questions
Work through each question before checking the answers. Difficulty is shown for each question.
Foundation (Grade 3–5)
Q1A graph shows a straight line going up steeply from left to right. What does this tell you about the rate of change?Foundation
Q2A distance-time graph is flat for part of the journey. What is happening during this time?Foundation
Q3Two lines are drawn on the same distance-time graph. Line A is steeper than Line B. Which represents the faster speed?Foundation
Q4A bar chart's y-axis starts at 50 instead of 0. What effect does this have on how the differences between the bars appear?Foundation
Q5A temperature graph shows a curve that rises, reaches a peak, then falls. At what point is the temperature at its highest?Foundation
Higher (Grade 5–7)
Q6Using the hikers' graph from Worked Example 1, find how far ahead Hiker B is after 1 hour.Higher
Q7Using the same graph, at what time (other than the start) are the two hikers at the same distance from the start?Higher
Q8Using the temperature graph from Worked Example 2, estimate the temperature at 6pm.Higher
Q9Using the temperature graph, between which two times is the temperature increasing?Higher
Q10A company presents two bar charts of the same profit data, but one has a y-axis starting at 0 and the other starts at 90. Which chart gives a more honest impression of the change in profit, and why?Higher
Higher — Hard (Grade 8–9)
Q11Using the hikers' graph, find the equation of Hiker A's distance-time graph (distance y in km, after x hours), and use it to find how far Hiker A has travelled after 3.5 hours.Grade 8–9
Q12Using the graph below, which shows the same temperature curve from Worked Example 2, find the two times of day when the temperature is exactly 20°C, to 1 decimal place.Grade 8–9
Graph for Question 12 — the temperature curve with y = 20°C marked.
Q13Two distance-time lines on the same graph cross at (3, 15). Before this point, Line A is above Line B; after this point, Line B is above Line A. Describe what happens at the crossing point, in the context of two runners on a track.Grade 8–9
Q14The graph below shows a company's profit y = −2t² + 16t − 10 (£ thousand) over time t (years). Find the year(s), to 1 decimal place, when the company breaks even (profit = 0).Grade 8–9
Q15Using the same profit graph, find the maximum profit and the year it occurs.Grade 8–9
Graph for Questions 14–15 — the profit curve y = −2t² + 16t − 10.
Answers
Foundation (Q1–Q5)
Q1It is increasing quickly — a fast, constant rate of change
Q2The object is stationary — not moving
Q3Line A
Q4It makes the differences between the bars look bigger than they really are
Q5At the peak (turning point) of the curve
Higher (Q6–Q10)
Q65 km ahead(B: 10 km, A: 5 km at t = 1)
Q7At 4 hours, both at 20 km(B arrives at 20 km at t=2 and stays there; A reaches 20 km at t=4)
Q8Approximately 19.6°C
Q9Between the start of the day (midnight) and 2pm (14:00), where the peak occurs
Q10The chart starting at 0 — it doesn't exaggerate the visual size of the differences between the bars
Higher — Hard (Q11–Q15)
Q11y = 5x; 17.5 km after 3.5 hours(5 × 3.5)
Q12Approximately 10.3 and 17.7 (i.e. around 10:21am and 5:39pm)
Q13The runner who was behind (Line B) overtakes the runner who was ahead (Line A) at that point — they are at the same position at t = 3
Q14t ≈ 0.7 years and t ≈ 7.3 years(−2t²+16t−10=0 → t²−8t+5=0 → t=(8±√44)/2)
Q15Maximum profit £22,000, in year 4(vertex at t=−16/(2×−2)=4; profit = −32+64−10=22)
Common mistakes
These are the errors Alamin sees most frequently with graph interpretation at GCSE. Recognising them now will save you marks in the exam.
Common Mistake 1
Confusing "further along the x-axis" with "further along the graph"
A line reaching further to the right doesn't mean it's "winning" — always check what each axis actually measures before comparing two graphs.
Common Mistake 2
Not checking the axis scale before comparing bar heights
A truncated (non-zero) axis can make small differences look huge. Always check where the axis starts before concluding how big a change really is.
Common Mistake 3
Reading the wrong axis when estimating a value
Double-check which quantity you're being asked for before reading off a graph — it's easy to read across to the wrong axis, especially under time pressure.
Common Mistake 4
Assuming a curve's rate of change is constant
Unlike a straight line, a curve's steepness changes continuously. Describing a curved section as having "one" rate of change is incorrect — describe how the rate itself changes (e.g. "increasing, but more slowly").
Common Mistake 5
Giving a vague description instead of a specific one
"The graph goes up" is not a full answer. State how it changes — quickly, slowly, at a constant rate, accelerating — and reference specific values or time periods where possible.
Common Mistake 6
Missing the point where two graphs cross
The intersection of two graphs on the same axes is often the most important feature — it usually represents the moment two quantities are equal, such as one runner overtaking another.
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