Year 11 - Maths
Interpreting and drawing more 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 interpret and draw more real-life graphs.
Key Notes
- Not all real-life graphs can be drawn using sections of different linear graphs.
- The graphs are models, which means that we want them to be useful.
Vocabulary To Learn
- Simple interest: Interest is money added to savings or loans. Simple interest is always calculated on the original amount.
- Compound interest: Compound interest is calculated on the original amount and the interest accumulated over the previous period.
- Exponential: The general form for an exponential equation is $$y = ab^x$$ where $$a$$ is the coefficient, $$b$$ is the base and $$x$$ is the exponent.
- Speed: Speed is the rate at which something is moving. It is measured as the distance travelled per unit of time.
- Acceleration: Acceleration is the rate of change of speed with respect to time.
Common Mistakes To Avoid
- Pupils may think the gradient of the line to model simple interest is always the interest rate.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Not all real-life graphs can be drawn using sections of different linear graphs. The graphs are models, which means that we want them to be useful.
2. Use this key word in a maths sentence and explain it clearly. 'Simple interest'
Interest is money added to savings or loans. Simple interest is always calculated on the original amount. 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 the gradient of the line to model simple interest is always the interest rate. Correction: This works when investing £100 but not with other start values. The gradient is the amount of interest added each time which depends on the amount invested and the interest rate. There are examples to show this in the lesson.
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
- Improving the estimate of the gradient of a curve 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.