Year 11 - Maths
Calculating the rate of change
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 the gradient and interpret this as the rate of change for real life contexts.
Key Notes
- For straight-line sections of a graph, it is easy to calculate the gradient.
- The gradient tells us the rate that one quantity changes with respect to the other.
- The gradient gives the rate that the $$y$$ variable changes with respect to the $$x$$ variable.
- The gradient can be interpreted in context and should be for real life contexts.
Vocabulary To Learn
- Rate of change: The rate of change is how one variable changes with respect to another. If the change is constant, there is a linear relationship between the variables.
- 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
- Gradient is change in $$y$$ divided by change in $$x$$.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
For straight-line sections of a graph, it is easy to calculate the gradient. The gradient tells us the rate that one quantity changes with respect to the other.
2. Use this key word in a maths sentence and explain it clearly. 'Rate of change'
The rate of change is how one variable changes with respect to another. If the change is constant, there is a linear relationship between the variables. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Gradient is change in $$y$$ divided by change in $$x$$. Correction: The gradient is calculated by considering the change in $$y$$ when moving one unit in the positive $$x$$ direction.
More Lessons In This Unit
- Advanced problem solving with real-life graphs Study Guide
- Calculating journeys from linear speed-time graphs 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
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