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Term 1
Term 2
Term 3
Term 4
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Topics
Binomial Theorem
Circular Measure
Partial Fractions
Probability
Vectors
Further Trigo

Trigo Formula Sheet
Standard Graphs
Differentiation

Limits

Techniques of Differentiation

Tangent and Normal

Max/Min Points and 2nd Derivative

Rate of Change

Curve Sketching

Mensuration Formula Sheet
(for max/min problems)
Quizzes
Integration

Basic Integration
+ Substitution + By Parts (SMTP)
Further Integration (Trigo, Exp, Log, f '(x)type)

Area under curve
+ Volume of revolution (SMTP)

Kinematics

Differentiation & Integration Formula Sheet
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Area under curve
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Area under curve2.pptx
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678 KB
Use Geogebra (Free download:
http://www.geogebra.org/cms/en/installers
) to open this file and see the effect of increasing the no. of rectangles 'n'.
(Download the offline installer, not the webstart, which is not as good.)
Area under Curve.ggb
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4 KB
You should see a straight line graph, f(x) = x. Move the slider to see the effect of increasing 'n'
Click on View > Algebra View to open the panel on the left. You can click on f(x) = x and change it to f(x) = x^2 to see the curve f(x) = x^2 instead.
The main idea is to know that as you increase the no. of rectangles, the total area of the rectangles will become the area under the curve as n tend towards infinity.
That is the idea of how Integration is derived to find area under curve.
Note: Area under curve is not quite the correct term. It is used out of convenience. It should be "Area bounded by the curve, xaxis and the lines x = a and x = b". If the area is above the xaxis, it will be a positive value, if it's underneath the xaxis, it will be negative, in which case you just need to take its absolute value (Modulus).
Integration notes (Area).pdf
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integration notes (solutions to area examples).pdf
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79 KB
For SMTP (2015 onwards), Volume of revolution is included in the syllabus
integration notes (volume).pdf
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59 KB
integration notes (solutions to volume examples).pdf
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197 KB
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