C2 - Introduction

C2 is the second module, of the Alevel Maths which is core. It is in my opinion the hardest module of AS, for Edexcel, it is one of the longer modules of the whole course.The topics are :

Edexcel

1. Algebra and Functions - Algebraic Division, Factor Theorem, Remainder Theorem.
2. Coordinate Geometry - Equation of Circle, Use of certain circle properties
3. Sequences and Series - Geometric Series {Sum of a g. series, Sum to infinity, Proof of sum formula}, Binomial Expansion for (1+x)^n and (a+b) ^n.
4. Trigonometry - Sine and Cosine Rule, Area of Triangle, Radians, Arc length, area of a sector and segment, Sin,Cos and Tan Graphs, Use of Trig. Identities, Solving simple equations.
5. Exponentials and Logarithms - y=a* and the graph, Laws of Logarithms and Change of base formula.
6. Differentiation - Maxima and Minima problems, Stationery points, Increasing and Decreasing Functions.
7. Integration - Definite Integrals, Area under a curve is a definite integral, Trapezium Rule, Area bounded between a curve and line.

AQA

1. Algebra and Functions - Laws of Indices, Simple transformations on graphs
2. Sequences and Series - Arithmetic series {nth term, Sum of a. series}, Geometric series {Sum of finite g. series, sum to infinity}, Binomial Expansion (1+x)^n.
3. Trigonometry - Sine and Cosine Rule, Area of Triangle, Radians, Arc length, area of a sector and segment, Sin,Cos and Tan Graphs, Use of Trig. Identities, Solving simple equations.
4.  Exponentials and Logarithms - y=a* and the graph, Laws of Logarithms and Change of base formula.
5. Differentiation - Differentiate functions of form x^n. where n is a rational number.
6.  Integration - Integration of functions of form x^n, Trapezium Rule

OCR

1. Algebra - Factor theorem, Remainder theorem, algebraic division, a* graph, laws of logarithms, change of base of logs, and solving log equations.
2. Sequences and Series - Sigma Notation, Arithmetic & Geometric Series, Sum of arithmetic and geometric series, sum to infinity, Binomial Expansion.
3. Trigonometry - Sine and Cosine Rule, Area of Triangle, Radians, Arc length, area of a sector and segment, Sin,Cos and Tan Graphs, Use of Trig. Identities, Solving simple equations.
4.  Integration - Indefinite Integration, Evaluation of definite integrals, Finding area of a region bounded by a curve and line,. Trapezium Rule.

There is alot of new content, and alot which is expanded from the topics learnt in C1. To Achieve a top grade, you should ensure you can apply everything used in C1, these modules are synoptic, and they can ask you a c1 question in c2, or ask a question which relates to c1 content.

Indefinite Integration

•  Edexcel - C1, Integration
• AQA - C1, Integration
• OCR - C2, Integration

We already discussed one of the branches of calculus. The other is Integration, it's general purpose is to find the area between some given intervals. It can be used to find the area bounded by a curve, you will learn this in C2. Right now, we need to know what Indefinite Integration is. It is simply the reverse of Differentiation, if dy/dx is the derivative of some function, we can use integration to obtain the function y. It's also called Anti differentiation. When will integrate some function, we will add a constant c. (The constant of Integration).

That image is the general notation used for Integration. When we integrate, we first draw the S kind of line, then write the function, and then dx. (for now anyway). This shows we are integrating. We need to know how to integrate functions in the form : x^n.

As I said Integration is the reverse of Differentiation. So when we differentiate we multiply the power by the coefficient of the function, and subtract the power by 1. When integrating, we firstly raise the power by 1, and divide by this new power.


a)

      *We usually write c (instead of constant) [  + c ]


I will also post some further examples in my image notes. In my image notes, I will also show you how to derive a the equation of the curve, when given dy/dx and a point on the curve, these question are usually 5/6 easy marks.

With this we end C1 here. I shall start C2 next week... I have done all model solutions for the Edexcel C1 Papers (From Jan 2005 - June 2011), these are available on request. I will start working on the model solutions for Solomon Papers aswell.

C1 Introduction

C1. The first module of AS, of any Alevel Maths Course. Suppose to be the easiest, it generally forms on from the A-A* topics of gcse. However, you don't have a calculator... so brush up on general arithmetic skills, and fractions. Topics :

1)  Algebra and Functions
*Laws of Indices, Surds, Rationalising the Denominator, Quadratic Equations (Discriminant, Completing the Square, Quadratic Formula,Factorisation), Sketching Graphs and Transformations of Graphs.

2) Coordinate Geometry
*Equation of a Straight Line, Gradients, Perpendicular Lines

3) Sequences and Series
*Terms, nth Term, Arithmetic Series, Sum of Terms and Stigma Notations.

4)Differentiation
*Differentiating basic functions, and relation to Gradients.

5)Integration
*Indefinite Integration