Fractions 

Inequalities 
Number 
Title 
Description 
5 
Solving inequalities 
Using algebra to solve simple inequalities, drawing graphs, introduction of the modulus symbol and quadratic inequalities. 
6 
Solving inequalities 
How to manipulate inequalities, and using algebraic and graphical methods to solve inequalities. 
7 
Linear inequalities 
How to sketch regions defined by linear inequalities. 
8 
Manipulating inequalities 
Another explanation on the inequality symbols < and >, and how we can manipulate inequalities. 


Indices 
Number 
Title 
Description 
9.1 
The laws of indices 
How to simplify expressions involving numbers raised to a specific power, including algebraic examples. 
9.2 
Negative and fractional powers 
How to approach negative and fractional powers, and what this notation means. 
9.3 
Powers and roots 
An explanation of how to use index notation to express roots of numbers, including square roots and cube roots. 
9.4 
Indicial equations 
Equations where the power is unknown, often used in calculating compound interest. 


Trigonometrical functions 

Trigonometry 
Number 
Title 
Description 
18 
Trigonometric ratios of an angle of any size 
Definitions of the ratios sine, cosine and tangent with reference to sides and angles, and how to use these in problems involving triangles. 
19 
Trigonometric equations 
How to approach equations involving trigonometric equations, using known values of trig functions and graphical techniques. 


Linear equations 

Rearranging formulae 

Functions and graphs 

Factorising 

Partial fractions 

Polynomials 

Logarithms 

Differentiation 

Integration 

Vectors 
Number 
Title 
Description 
47 
Introduction to vectors 
The definition of a vector, how to add and subtract them, recognising multiples of vectors and how we can use them in geometrical problems. 
48 
The scalar product 
Defining the scalar product and its properties. 
49 
The vector product 
Defining the vector product and its properties. 
50 
Cartesian components of vectors 
Expressing vectors in Cartesian components, by defining unit vectors in the directions of the coordinate axes. 


Matrices 
Number 
Title 
Description 
51 
Determinants 
The definition of a determinant and how it can be applied mathematically. 
52 
Cramer's Rule 
A method for solving linear simultaneous equations using determinants. 
53 
Multiplying matrices 
How to multiply matrices. 


Power series 
Number 
Title 
Description 
54 
Sequences and Series 
The definitions and properties of sequences and series. 
55 
Infinite Series 
The definition of an infinite series and what is meant by convergence. 
56 
The Binomial Series 
How to calculate the Binomial series of functions of the form (b+a)^{n}. 
57 
Power Series 
The definition of a power series and how to obtain their radius of convergence. 
58 
Maclaurin and Taylor Series 
How to write a generic (smooth) function as a power series. 


Complex numbers 

Differential equations 
