C2 Revision Notes

These are my C2 Revison notes.

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  • Created by: John
  • Created on: 22-01-11 17:35
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Core 2 Revision notes
This is how I think about/answer some common exam questions. This does not necessarily
cover every question that could come up in your C2 exam. It does not include modelling
Differentiation questions
Type 1
Question just asks you to differentiate.
If , then for n and k are all real constants.
e.g.1 then
e.g.2 first change into indice form then use the ordinary rule
which is the same as
e.g. 3 first change into indice form then use the ordinary rule
which is the same as
Type 2
This type of question asks you to differentiate a given equation and then find the
gradient of the graph of the function at a given point. To do this, first differentiate
using the standard formula on the formula sheet and then substitute in the x
coordinate given.
E.g. Q: Find gradient of graph at the point (2,9).
A: , when x =2, gradient =
Type 3
This type of question asks you to find the turning or stationary points of a graph and
determine their nature. To do this you have to differentiate to find the gradient and
then find where the gradient is zero. Then differentiate again to find and use
the following table to determine the nature of the turning point.
The point is a maximum
The point is a minimum
The point could be a maximum, a minimum or a point of inflection

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E.g. Q: Find the coordinates and the nature of the turning points of the graph
A: , , , , or
Remember to substitute into original equation to find y coordinates of
turning points.
when ,
when ,
coordinates of turning points are and
To determine the nature,
Substitute in ,
Substitute in ,
If you find , then you have to use a different techniques for determining the
nature of a turning point. i.e.…read more

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Step 0: Sub the x value into the original equation to find the corresponding y vaule.
(You might be able to miss this step out if you already know from the question what
the y value is)
Step 1: Differentiate original curve.
Step 2: Sub in the x value. This gives you the value of m.
Stap 2(b): (Only do this step if trying to find normal.) Turn the gradient upside down
and change the sign.…read more

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Type 3
This type of question asks you to find the areas on graphs. Remember any area
under the x axis will come out negative. This means in many questions you will need
to divide the area up into sections and find each bit individually. Question may ask
for area between two curves, in this case subtract the two equations and integrate
the resulting function between the limits (normally found by finding the intersection of
the two curves.…read more

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These are simultaneous equations, to solve first rewrite as,
Trigonometric equations
First step for solving trigonometric equations is to re write equation so that it only
contains one trigonometric function. This can be achieved using trigonometric
identities. i.e. If have , use identity to re write equation
as .
After you have re arranged the equation to read either , or
equals a number, you can get the first answer from your calculator.…read more

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Solving equations when the unknown is the power.
Step 1: Make it as simple as possible.…read more


Dinah Iwo



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