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Cooper and Caulcott Ltd Mathematical and Scientific Consultants

AS Further Maths - Pure

Chapter 1: Matrices

1.1 Matrix Addition and Subtraction

1.2 Matrix Multiplication

1.3 Matrix Inverses

1.4a Determinants of 3x3 Matrices

1.4b Inverses of 3x3 Matrices

Chapter 2: Further Vectors

2.1 Vector Equation of the Line

2.2 Cartesian Equation of the Line

2.3 Intersecting Lines

2.4 The Scalar Product

2.5 The Vector Product

Chapter 3: Applications of Matrices

3.1 Solving Linear Simultaneous equations

3.2 Matrix Transformations

3.3 Further Matrix Transformations

3.4 Invariant Points and Lines

3.5 3D Transformations

also 3D Transformations Example

Chapter 4: Complex Numbers

4.1 An Introduction to Complex Numbers

4.2 Division and Complex Conjugates

4.3 The Argand Diagram

also Argand Diagram Example

4.4a Radians

4.4b Modulus and Argument

4.5 Loci also Complex Loci Example also Complex Loci Example 2

4.6 Operations in Modulus-Argument form

Chapter 5: Roots of Polynomials

5.1 Factorising Polynomials.

5.2 Complex Solutions to Polynomial Equations

5.3 Roots and Coefficients

5.4 Finding an Equation also Example of Finding a New Equation

5.5 Transforming Equations

Chapter 6: Mathematical Induction

6.1 Mathematical Induction

6.2 Induction for Matrices also Example Ex 6A Q9 also Vector Example

6.3 Induction for divisibility also Example 6B Q5 and 6

6.4 Induction for inequalities

Complex Numbers example MP6 Q9

 

 

 

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© 2020 Neill S Cooper
@NeillCooper
Last changed on April 14 2020