*Jump straight to Past Examinations or Collected Tutorials*

*or read on for guidance and advice…*

So you’ve studied A level Mathematics. C1 and C2 lured you into a false sense of security and then we threw C3 and C4 at you. They’re hard, but not impossible. For one thing, you need to realise that C3 and C4 are basically courses in calculus and trigonometry. All the other topics are either stand alone techniques, or depend upon calculus and trig. So I thought I would break each down for you. Here is my quick guide to C4:

The main prerequisite stuff is the calculus from C1 and 2, and all of the trig from C3. So make sure you know:

- How to find maxima and minima (let the first derivative be 0)
- How to find equations of tangents and normals
**(y-y1=m(x-x1))** - The
**product**, the quotient and the**chain**rule - ALL your trig identities (bearing in mind many are in the formulae book)

Then start with…

**Implicit Differentiation**

- This basically uses differentiation techniques from C3 in an implicit situation. Nothing new to learn once you’ve got past
**how to do it implicitly**. You’ll use the first 3 prerequisites listed above.

Then move on to…

**Integration**

- Standard integrals you should know
**By substitution****By parts**- Using the
**“anti-chain rule”**including when**logarithms are needed** - Using trigonometric identities
- Area under a graph is same as C2, Volume of revolution is a formula to remember
- … and don’t forget the trapezia rule from C2

The reason I say master those first, is that the stand alone topics generally use these in part b and c type questions. Sometimes you think you can’t do parametric equation questions, when actually it’s just the integration that is throwing you….

**Parametric Equations has 2 or 3 simple results, and the rest is calculus**

- How to find dy/dx if y and x given separately
- How to integrate to find area or volume
- You will often find tangents and normals using C3 knowledge

**Binomial Expansion**

- This builds from C2 binomial expansions, use the formula from the booklet
- Remember for which values of x the formula is valid
- You often integrate your expansion, not related to formula but uses anti-chain rule or partial fractions

**Partial Fractions**

- A straight forward procedure to be learnt
- Uses
**algebraic division from C2**if you have an improper fraction - Often becomes an integration question using natural logarithms and anti-chain rule.

**Vectors**

- I always use column notation. Gets rid of i, j and k.
**Find the equation of a line****Find the angle between lines**a.b=|a||b|Cos**θ**where a and b are just directions (**Here’s a song to help you remember**)**Show points are collinear**(on the same line)- Find the shortest distance
**from a point on a line to another line**, and**from any point to a line.**

**Differential Equations**- Make differential equations from given context
**Find rates of change from connected variables****Solve Differential Equations by separating and solving**

And that is it! Doesn’t look too bad once you’ve broken it down! You can master Binomial expansion, partial fractions and Implicit stuff in an hour or two, but without being able to integrate everything you won’t be able to complete any exam, and without your trig knowledge from C3 there will be some things you find hard to integrate!

Good luck…

**See a walk through of January 2012**

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