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AQA GCSE · Question 21.3 · Geometry and Measures
Is your estimate from the previous question an overestimate or an underestimate?
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Give a reason for your answer.
Is your estimate from the previous question an overestimate or an underestimate?
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Give a reason for your answer.
How to approach this question
1. Look at the method you used to estimate the area in part (b). The only estimation was for the curved section from t=0 to t=4.
2. If you approximated this section with a trapezium (a straight line from (0,0) to (4,8)), compare this straight line to the actual curve.
3. Is the curve above or below the straight line you used for your approximation?
4. If the curve is above the line, your estimate missed some area, so it's an underestimate. If the curve were below the line, it would be an overestimate.
Full Answer
**Underestimate.**
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**Reason:**
In the first section (t=0 to t=4), the curve is above the straight line of the trapezium used for the estimation. This means the area of the trapezium is smaller than the true area under the curve. The other sections were calculated exactly. Therefore, the total estimated area is an underestimate of the true distance.
The estimate for the total distance involved approximating the area under the curve from t=0 to t=4. The most common method is to use a single trapezium, which is equivalent to drawing a straight line from the point (0, 0) to (4, 8).
If we look at the graph, the actual curve between t=0 and t=4 is bowed upwards, above the straight line connecting (0,0) and (4,8).
This means that the area of the trapezium is slightly less than the actual area under the curve. Since we calculated the areas of the other two sections (the rectangle and triangle) exactly, our overall estimate for the total distance is an **underestimate**.
The reason is that the trapezium model excludes the small sliver of area between the curve and the straight line.
Common mistakes
✗ Choosing overestimate.
✗ Giving a reason that is not related to the shape of the curve vs. the estimation method. For example, "because it's just an estimate" is not a valid reason.
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