Introduction | |
A toolbox | |
Circular functions | |
Solving right-angled triangles | |
The sine and cosine rules | |
Geometry prerequisites | |
Sequences and series | |
Circles | |
Ellipses and hyperbolae | |
Vectors | |
Introduction to vectors | |
Resolution of a vector into rectangular components | |
Scalar (or dot) product of vectors | |
Vector resolutes | |
Vector proofs | |
Circular functions | |
The tangent function | |
The reciprocal circular functions | |
Compound and double angle formulae | |
Inverses of circular functions | |
Solution of equations | |
Complex numbers | |
The set of complex numbers, C | |
The complex conjugate and division | |
The modulus-argument form of a complex number | |
Basic operations on complex numbers in the modulus-argument form | |
Factorisation of polynomials in C | |
Solution of polynomial equations | |
Using De Moivre's theorem to solve equations in the form zn=a where a = C | |
Relations and regions of the complex plane | |
Revision of chapters 2-4 | |
Summary of chapters 2-4 | |
Short answer questions | |
Multiple choice questions | |
Analysis questions | |
Differentiation and rational functions | |
A review | |
Derivatives of x=f(y) | |
Derivatives of inverse circular functions | |
Second derivatives | |
Related rates | |
Graphs of some rational functions | |
A summary of differentiation | |
Implicit differentiation | |
Antidifferentiation | |
Antidifferentiation | |
Antiderivatives involving inverse circular functions | |
Integration by substitution | |
Definite integrals by substitution | |
Use of trigonometric identities for integration | |
Partial fractions | |
Further techniques and miscellaneous exercises | |
Applications of integration | |
Areas of regions | |
Area of a region between two curves | |
Integration using a graphics calculator | |
Volumes of solids of revolution | |
Numerical methods of integration | |
Differential equations | |
An introduction to differential equations | |
Solution of differential equations of the form dy/dx=f(x) and d2y/dx2=f(x) | |
The solution of differential equations of the form dy/dx=f(y) | |
Application of differential equations | |
Differential equations with related rates | |
A numerical solution to a differential equation | |
Kinematics | |
Position velocity and acceleration | |
Constant acceleration | |
Velocity time graphs | |
Differential equations of the form v=f(x) and a=f(v) | |
Other expressions for acceleration | |
Revision of chapters 6-10 | |
Summary of chapters 6-10 | |
Short answer questions | |
Multiple choice questions | |
Analysis questions | |
Vector functions | |
Vector equations | |
Position vectors as a function of time | |
Vector calculus | |
Velocity and acceleration for motion along a curve | |
Distance travelled by a particle along a curve | |
Dynamics | |
Force | |
Newton's laws of motion | |
Resolution of forces and inclined planes | |
Connected particles | |
Variable forces | |
Equilibrium | |
Friction and equilibrium | |
Vector functions | |
Revision of chapters 12-13 | |
Summary of chapters 12-13 | |
Short answer questions | |
Multiple choice questions | |
Analysis questions | |
Graphics calculator appendix 1 | |
Answers | |
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