Year 11 - Maths
Interpreting and drawing 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 other 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.
- Different containers may need different graphs to model filling them.
- Volume of liquid changes over time and this is affected by container shape.
Vocabulary To Learn
- Time series graphs: Time series graphs show data over a time period. The time period is always shown on the $$x$$-axis. Data points are joined chronologically by line segments.
- Extrapolation: Extrapolation is the process of estimating unknown values that are outside the range of existing data.
- Interpolation: Interpolation is the process of estimating unknown values that are inside the range of existing data.
Common Mistakes To Avoid
- Interpolation is always more accurate than extrapolation.
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. 'Time series graphs'
Time series graphs show data over a time period. The time period is always shown on the $$x$$-axis. Data points are joined chronologically by line segments. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Interpolation is always more accurate than extrapolation. Correction: If a graph is plotting data collected at set points then there is no way to know what is happening between the points. The trend between the points could be a curve, a line or could fluctuate. Interpolation could therefore be inaccurate.
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 more 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.