Who this is for: Cambridge IGCSE Mathematics (0580/0607) students who want travel graphs — distance-time and speed-time interpretation — to become a reliable source of marks instead of a topic they only half-remember.
What query it owns: how to understand and revise travel graphs in Cambridge IGCSE Mathematics.
Why this is safe: this page owns the travel graphs revision-guide angle, while Tutopiya’s Travel Graphs subtopic page owns the learning resource and the free travel graphs quiz owns the practice.

Travel graphs turn motion into lines on a grid. In Cambridge IGCSE Mathematics (0580/0607) you read distance-time graphs for speed and rest periods, and speed-time graphs for acceleration and total distance. The gradient and area rules are worth easy marks when you know them cold. This guide explains the subtopic, the exam wording, and where to practise.

Key takeaways

• On a distance-time graph, gradient = speed; a horizontal line means stationary.
• On a speed-time graph, gradient = acceleration; area under the graph = distance travelled.
• A steeper line on a distance-time graph means higher speed.
• Always state units when the question asks for speed, acceleration or distance.

What are travel graphs in Cambridge IGCSE Maths?

Travel graphs show how a journey changes over time. A distance-time graph plots distance from a starting point against time; a speed-time graph plots speed against time. In Cambridge IGCSE Mathematics you interpret these graphs, calculate speed and acceleration from gradients, find distance from areas, and sketch journeys described in words.

Read the worked examples on Tutopiya’s Travel Graphs subtopic page before attempting questions.

The core ideas you must master

Graph type	Gradient means	Area means	Horizontal line means
Distance-time	Speed	Not used for distance	Stationary (not moving)
Speed-time	Acceleration	Distance travelled	Constant speed
Speed-time (below axis)	Negative acceleration	Distance (take care with signs)	—

How to read a distance-time graph — step by step

1. Identify the axes — distance (usually metres or km) on the vertical, time on the horizontal.
2. Calculate speed from the gradient of a sloped section: speed = change in distance ÷ change in time.
3. A horizontal section means the object is not moving (rest).
4. A steeper slope means faster motion.
5. Total distance for a one-way journey is the final distance value, not the sum of all slopes.

Test yourself with the free Travel Graphs quiz.

How to read a speed-time graph

1. Gradient of each section = acceleration (or deceleration if negative).
2. Area under the graph between two times = distance travelled in that interval.
3. For a triangle: area = ½ × base × height. For a trapezium: average speed × time.
4. A horizontal line = constant speed (zero acceleration).
5. Add areas of sections for total distance.

Travel graphs in past-paper wording: command words that matter

Command word / phrase	What the question wants	Typical stem
Work out the speed	Gradient of distance-time section	”Work out the speed between t = 2 and t = 5.”
Describe the motion	Explain each section in words	”Describe the motion of the cyclist.”
Calculate the acceleration	Gradient of speed-time graph	”Calculate the acceleration during the first 10 seconds.”
Find the total distance	Area under speed-time graph	”Find the total distance travelled in the first 30 seconds.”
Sketch the graph	Draw distance-time or speed-time from a description	”Sketch a distance-time graph for a car that…”

Worked exam-style stems (how to answer the wording)

1. “The distance-time graph is a straight line from (0, 0) to (20, 400). Work out the speed.” Speed = 400 ÷ 20 = 20 m/s. Reward: correct gradient calculation with units.
2. “Between t = 10 and t = 30 the speed-time graph is horizontal at 15 m/s. Find the distance travelled.” Distance = 15 × 20 = 300 m. Reward: area = speed × time.
3. “Describe the motion between t = 0 and t = 5.” “The object moves at constant speed” or “accelerates uniformly” — match the graph shape. Reward: accurate description linked to gradient.
4. “A speed-time graph shows a straight line from (0, 0) to (8, 20). Calculate the acceleration.” Acceleration = gradient = 20 ÷ 8 = 2.5 m/s². Reward: gradient as acceleration with correct units.
5. “On a distance-time graph, the line is horizontal from t = 6 to t = 10. What happens during this time?” The object is stationary — distance does not change, so speed is zero. Reward: linking horizontal section to rest, not constant speed.

When you can recognise the wording instantly, work the full set on the Algebra topical past-paper questions and the Travel Graphs quiz.

How travel graphs connect to the wider syllabus

Travel graphs link to Rate in Number and gradient work in Coordinate Geometry. Questions that ask you to “calculate the average speed for the whole journey” need total distance divided by total time — not the average of section speeds. The Cambridge IGCSE Maths resource hub connects all Algebra subtopics.

Common mistakes students make

• Using distance instead of gradient for speed on a distance-time graph.
• Forgetting that horizontal on distance-time means stopped, but horizontal on speed-time means constant speed.
• Calculating area on a distance-time graph when the question wants gradient.
• Not converting minutes to seconds (or vice versa) before calculating.
• Describing a return journey incorrectly when distance drops on the graph.

When you need more support

If travel graph questions keep tripping you up, retake the Travel Graphs quiz, work through the Algebra topical past-paper questions, and ask a Cambridge IGCSE Maths tutor to clarify gradient versus area.

Frequently asked questions

What does the gradient of a distance-time graph represent? Speed. Calculate it as change in distance divided by change in time for that section.

What does the area under a speed-time graph represent? Distance travelled. Find the area of each section and add them for the total journey.

What does a horizontal line on a distance-time graph mean? The object is stationary — distance is not changing, so speed is zero.

How do I revise travel graphs effectively? Practise distance-time (gradient) and speed-time (area) separately, then mixed questions. Use the travel graphs quiz to confirm each skill.

Ready to master Cambridge IGCSE Maths travel graphs?

Start with the Travel Graphs subtopic page, then book a free trial with a Cambridge IGCSE Maths specialist.

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