Year 11 - Maths
Finding the equation of a radius of a circle
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 find the equation of a radius of a circle.
Key Notes
- The equation of a circle gives the coordinates of the centre of the circle.
- Using this and the coordinates of a point on the circle, you can calculate the gradient of the radius.
- Using the gradient and the centre of the circle, you can find the equation of this radius.
Vocabulary To Learn
- Radius: The radius is any line segment that joins the centre of a circle to its edge.
- 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 think that a circle with equation $$(x+a)^2 + (y+b)^2=r^2$$ has centre $$(a,b)$$
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
The equation of a circle gives the coordinates of the centre of the circle. Using this and the coordinates of a point on the circle, you can calculate the gradient of the radius.
2. Use this key word in a maths sentence and explain it clearly. 'Radius'
The radius is any line segment that joins the centre of a circle to its edge. 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 that a circle with equation $$(x+a)^2 + (y+b)^2=r^2$$ has centre $$(a,b)$$. Correction: The general form of an equation of a circle is $$(x-a)^2 + (y-b)^2=r^2$$ where $$(a,b)$$ is then the centre. Graphing software will be useful to show and explore this general form.
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 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.