Year 11 - Maths
Distance-time graphs
Real-life graphs
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit pupils expand upon knowledge developed in the linear graphs unit. Pupils are introduced to rates of change and the gradient of the tangent as a way of estimating the gradient of a curve.
Lesson Summary
You will learn to calculate time intervals and speed of sections of a distance-time graph.
Key Notes
- On a distance-time graph, a horizontal line means no distance was travelled for that time.
- A slanted line means that the distance from the start is changing over time.
- The distance travelled divided by the time taken gives the speed.
- You find this by considering the change in distance with respect to the change in time.
- This is how you find the gradient of the line, which is also the speed.
Vocabulary To Learn
- Gradient: The gradient is a measure of how steep a line is. It is calculated by finding the rate of change in the $$y$$-direction with respect to the positive $$x$$-direction.
- Displacement: Displacement is the distance from the starting point when measured in a straight line.
Common Mistakes To Avoid
- Not looking at units when calculating the gradient of the line to find speed.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
On a distance-time graph, a horizontal line means no distance was travelled for that time. A slanted line means that the distance from the start is changing over time.
2. Use this key word in a maths sentence and explain it clearly. 'Gradient'
The gradient is a measure of how steep a line is. It is calculated by finding the rate of change in the $$y$$-direction with respect to the positive $$x$$-direction. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Not looking at units when calculating the gradient of the line to find speed. Correction: A recap on compound measures and units may be helpful here. The units of compound measures tell us how to calculate the measure. E.g. km/h is the distance in km/ time in hours. Pupils need to check the units on their graphs and convert if needed.
More Lessons In This Unit
- Advanced problem solving with real-life graphs Study Guide
- Calculating journeys from linear speed-time graphs Study Guide
- Calculating the rate of change Study Guide
- Checking and securing understanding of drawing distance-time graphs Study Guide
- Checking and securing understanding of reading from context-based graphs Study Guide
- Efficiently estimating journeys from non-linear graphs Study Guide
- Estimating journeys from non-linear graphs Study Guide
- Estimating the gradient of a curve Study Guide
- Finding the equation of a radius of a circle Study Guide
- Finding the equation of the tangent to a circle Study Guide
- Improving the estimate of the gradient of a curve Study Guide
- Interpreting and drawing more real-life graphs Study Guide
- Interpreting and drawing real-life graphs Study Guide
- Non-linear distance-time graphs Study Guide
- Problem solving with real-life graphs Study Guide
- Speed-time graphs Study Guide
Browse all guides in the Year 11 Maths guide library.