Year 11 - Maths
Estimating 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 estimate the gradient of a curved part of the graph by considering the gradient of a straight line connecting two points.
Key Notes
- The gradient of a curve can be estimated.
- You can estimate by drawing a straight line between two points on the graph.
- The closer the points, the more accurate the estimate is.
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.
Common Mistakes To Avoid
- Pupils may estimate negative gradients incorrectly by drawing gradient triangles the wrong way round or ignoring the fact that the $$y$$ values are decreasing as $$x$$ increases.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
The gradient of a curve can be estimated. You can estimate by drawing a straight line between two points on the graph.
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: Pupils may estimate negative gradients incorrectly by drawing gradient triangles the wrong way round or ignoring the fact that the $$y$$ values are decreasing as $$x$$ increases. Correction: Pupils should look at the shape of the graph between two points and decide if it is positive or negative before calculating. If $$y$$ is decreasing as $$x$$ increases then the gradient is negative.
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
- 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.