Year 11 - Maths
Advanced problem solving with real-life 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 use your knowledge of interpreting real-life graphs to solve problems.
Key Notes
- Different speed/time graphs can be interpreted and compared.
- The area under the graph can also be interpreted in context.
- Circle theorems can be demonstrated using coordinate geometry.
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.
- Tangent: A tangent of a circle is a line that intersects the circle exactly once.
Common Mistakes To Avoid
- The intersection of two different graphs on a speed-time graph is the point where the faster particle overtakes the slower moving particle.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Different speed/time graphs can be interpreted and compared. The area under the graph can also be interpreted in context.
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: The intersection of two different graphs on a speed-time graph is the point where the faster particle overtakes the slower moving particle. Correction: Remind pupils that this is a speed-time graph and ask, "How do we find the distance travelled on a speed-time graph?". Then, ask pupils to calculate how far each particle has travelled at the point of intersection.
More Lessons In This Unit
- 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
- Distance-time 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.