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Graphs are given with areas underneath them shaded. The area of the shaded regions are given and from this the value of various integrals are to be deduced.
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England schools
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England university
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Scotland schools
Taxonomy: mathcentre
Taxonomy: Kind of activity
Taxonomy: Context
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History
Lovkush Agarwal 7 years, 7 months ago
Created this.| Name | Status | Author | Last Modified | |
|---|---|---|---|---|
| Algebra: functions, approximate area under graph | draft | Lovkush Agarwal | 31/01/2020 09:12 | |
| blackfyre's copy of Functions: approximate area under graph | draft | blackfyre blackfyre | 21/11/2017 03:33 |
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| Name | Type | Generated Value |
|---|
| a | integer |
3
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| b | integer |
-5
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| c | integer |
3
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| x0 | integer |
1
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| x | list |
List of 8 items
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| fx | vector |
Vector with 8 components
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| total | number |
90
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Generated value: integer
This variable doesn't seem to be used anywhere.
Gap-fill
Ask the student a question, and give any hints about how they should answer this part.
Below is the graph of the function v(t)={{a}(t−{b})({c}−t)}. We would like to calculate the area of the shaded region.
{plotgraph(a,b,c,1)}
You will learn how to do this in Maths 2 (using so-called integration), but for now we will just estimate the area. We do this by calculating the area of the strips in the diagram below:
{plotgraph(a,b,c,2)}
To save you scrolling, the function was v(t)={{a}(t−{b})({c}−t)}.
(i) What are the coordinates of the points A and B?
A.
B.
(ii) Determine the total area of the strips. Do this by determining the area of each strip and adding them together. Remember to do simple estimates to check for big errors.
Total area of columns =
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This question is used in the following exams:
- CLE 5 by Lovkush Agarwal in 17/18 Assessments.
- CLE 4 by Lovkush Agarwal in 17/18 Assessments.
- CLE 5 by Lovkush Agarwal in 18/19 Assessments.
- CLE 12 by Lovkush Agarwal in 18/19 Assessments.
- Maths 1 CLE6 assessed by Lovkush Agarwal in 19/20 Assessments.
- Demo by Lovkush Agarwal in Lovkush's workspace.
- Maths 2 CLE13 practice by Lovkush Agarwal in 19/20 Assessments.