Year 11 - Maths
Improving the estimate of the gradient of a curve
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 improve the estimate of the gradient by considering the gradient of the tangent at a fixed point.
Key Notes
- Since the gradient is improved by moving the points closer together, you could consider a point.
- By drawing the tangent to the graph at a given point, you can estimate the gradient at that point.
- The gradient at that point is estimated by calculating the gradient of the tangent.
Vocabulary To Learn
- Tangent: A tangent to a curve at a given point is a line that intersects the curve at that point. Both the tangent and the curve have the same gradient at the given point.
Common Mistakes To Avoid
- Pupils may think a tangent to a curve at a given point cannot intersect the curve at another point.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Since the gradient is improved by moving the points closer together, you could consider a point. By drawing the tangent to the graph at a given point, you can estimate the gradient at that point.
2. Use this key word in a maths sentence and explain it clearly. 'Tangent'
A tangent to a curve at a given point is a line that intersects the curve at that point. Both the tangent and the curve have the same gradient at the given point. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Pupils may think a tangent to a curve at a given point cannot intersect the curve at another point. Correction: Define the tangent at a point as the line which has the same gradient as the curve at that point. If the graph is cubic then it is possible for the tangent at a point to intersect the graph again. There are examples in the lesson that show this.
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
- 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
- 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.