AS/A2 Pure 4 Pure 5

Edexcel allows use of a graphic calculator. In specifications for OCR, WJFC and NICCEA a graphic calculator is allowed too. AQA permits a scientific calculator only.
1. Complex Numbers 2. Matrix algebra 3. Vectors	4. Maclaurin and Taylor series 5. Numerical Methods 6. Proof Summary

1. Complex Numbers
Euler's relation	eiq = cos q + i sin q
	Relations between trigonometric functions and hyperbolic functions.
	De Moivre’s theorem and its application to trigonometric identities and to roots of a complex number.
	nth roots of unity
Loci	circle loci 1
	circle loci 2
	straight line loci 1
	straight line loci 2
	straight line loci 3
	straight line loci 4
	arc loci 1
Regions	circle region 1
	circle region 2
	complex transformations of the circle
2. Matrix algebra
	Linear transformations of column vectors in two and three dimensions and their matrix representation. Combination of transformations.
	sums and products
	transpose of a matrix
	2 x 2 and 3 x 3 determinants
	2 x 2 inverses and determinants 1
	2 x 2 inverses and determinants 2
	3 x 3 determinants
	3 x 3 inverses and determinants
	linear transformations of column vectors in two dimensions
	transformations of shapes
	The inverse (when it exists) of a given transformation or combination of transformations
	eigenvalues and eigenvectors of 2 x 2 matrices
	eigenvalues of 2 x 2 matrices
	Reduction of symmetric matrices to diagonal form
3. Vectors
Cross product	definition
	illustration
Triple scalar product	definition
	volumes
	Use of vectors in problems involving points, lines and planes. The equation of a line in the form (r - a) ´ b = 0. Applications to include (i) distance from a point to a plane, (ii) line of intersection of two planes, (iii) shortest distance between two skew lines.
	The equation of a plane in the forms r.n = p, r = a + sb + tc
4. Maclaurin and Taylor series
Some power series	ex
	sin x
	cos x
	ln(1+x)
	arctan x
	hyperbolic functions
	Third and higher order derivatives
	Derivation and use of Maclaurin series.
	Derivation and use of Taylor series.
	Use of Taylor series method for series solutions of differential equations
5. Numerical Methods
	Numerical solution of first and second order differential equations by step-by-step methods.
6. Proof
	proof by mathematical induction		OCR P4
Summary
	the formulae

Credits
	=Javamath graphs		=WebEQ equations		=HotEqn equations
	=Cinderella graphs		=JavaScript		=other Java applets
	=PGC graphic calculator		=Hot Potatoes dynamic HTML		=Cabri Geometre
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