Year 11 - Maths
Efficiently estimating journeys from non-linear 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 efficiently estimate the distance travelled for non-linear speed-time graphs.
Key Notes
- The more trapezia used, the better the estimate.
- Multiple trapezia can be calculated efficiently.
- A formula for this can be deduced from the sum of the areas of multiple trapezia.
Vocabulary To Learn
- Estimate: A quick estimate for a calculation is obtained from using approximate values, often rounded to 1 significant figure.
- Generalisation: A generalisation is a statement or rule that applies correctly to all relevant cases.
Common Mistakes To Avoid
- When pupils see four, five or six trapezia they want to work each one out individually, then, do another calculation adding those four, five, six areas together.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
The more trapezia used, the better the estimate. Multiple trapezia can be calculated efficiently.
2. Use this key word in a maths sentence and explain it clearly. 'Estimate'
A quick estimate for a calculation is obtained from using approximate values, often rounded to 1 significant figure. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: When pupils see four, five or six trapezia they want to work each one out individually, then, do another calculation adding those four, five, six areas together. Correction: This is hugely inefficient. Write out the sum of the area of multiple trapeziums then, from there, look for efficiencies. This is where applying knowledge of factorisation can be beneficial as it reduces the work.
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
- 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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