MathsNet: A Level Pure Mathematics FP1 Module contents

Further Pure Mathematics FP1

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All specifications allow use of a graphic calculator in module FP1. It is recommended that you have both a graphic and a scientific calculator with you.

Note that the specifications for AQA and OCR both differ significantly from Edexcel.

1. Inequalities
2. Series
3. Complex numbers
4. Numerical solutions
5. 1st Order Differential Equations

6. 2nd Order Differential Equations
7. Polar Coordinates
Summary
Examination paper

Glossary

A argand diagram argument arithmetic mean B binomial expansion C centre of gravity chain rule chord collinear commutative completing the square complex number conic conjugate cosine rule cubic D differential equation discontinuity discriminant dot product double angle formulae E even function exponential function I imaginary number implicit equation intercept L locus logarithm M modulus N natural numbers normal O odd function P parametric equations periodic point of inflexion polynomial Q quotient rule S surd T tangent transformation turning point V vector

= analytical, algebraic

= visual, graphical

= video

1. Inequalities

Using a graph	quadratic inequalities	rational inequalities 1	rational inequalities 2
	modulus inequalities 1	modulus inequalities 2	modulus inequalities 3
Using algebra	solving rational inequations 1	solving rational inequations 2	solving quadratic inequations

2. Series

Standard results	sum of the 1st n integers	summation formulae 1	summation formulae 2
	summations of finite series 1	summations of finite series 2
Method of differences	differences 1	differences 2	differences 3
	differences 4

3. Complex numbers

Functions of roots	quadratics 1	quadratics 2	quadratics 3
	quadratics 4	quadratics 5
[Not Edexcel]	cubics	cubics 1
Complex numbers	definitions
The Argand diagram	modulus and argument	modulus and argument 2	modulus and argument 3
	sum of complex numbers	subtraction of complex numbers	multiplication of complex numbers
	division of complex numbers
The Mandelbrot set	videos	the Mandelbrot set	understand the process
	zooming in on the Mandelbrot set	argand diagram summary
Complex algebra	sum	subtraction	product
	quotient	calculations	modulus properties
	complex algebra	simplifying expressions	real and imaginary parts 1
	real and imaginary parts 2	real and imaginary parts 3	a quick test
Complex equations	quadratic equations	conjugate complex roots	conjugate complex roots 2
	square roots






	intersecting circles	a fallacy

4. Numerical solution of equations

Interval bisection	interval bisection	interval bisection 2	interval bisection 3
	interval bisection 4	interval bisection 5
Newton's method	the Newton-Raphson process 1	the Newton-Raphson process 2	the Newton-Raphson process 3
	the Newton-Raphson process 4	the Newton-Raphson process 5
Linear interpolation	linear interpolation

5. First Order Differential Equations

Slope fields	"slope fields" 1	"slope fields" 2
Families of solutions	families of solutions 1	families of solutions 2	families of solutions 3
	families of solutions 4	families of solutions 5	families of solutions 6
Linear 1st order d.e.s	auxiliary equation 1	the auxiliary equation 2
Separable d.e.s	separable differential equations 1	separable differential equations 2	separable differential equations 3
Integrating factors	integrating factor 1	integrating factor 2

6. Second Order Differential Equations

Complementary functions	complementary function 1	complementary function 2
Particular integrals	the particular integral 1	the particular integral 2	the particular integral 3
	the particular integral 4	the failure case	use of substitution
General solutions	general solutions

7. Polar Coordinates

Various graphs	the coordinate system	investigate graphs	r = a
	r = cos at	spirals	logarithmic spirals
	r = A + Bsin t	r = A(1 + Bcos t)	r = A + Bcos t
	r = p sec(q-t)	r = a sec(t)+b	r² = cos(at)
	other polar curves
Area of sector	area of sector 1	area of sector 2

Summary

The FP1 mindmap

the formulae

paper