### Core 1 Mathematics

### Algebra and functions

- Simplifying expressions by collecting like terms
- The rules of indices
- Expanding an expression
- Factorising expressions
- Factorising quadratic expressions
- The rules of indices for all rational exponents
- The use and manipulation of surds
- Rationalising the denominator of a fraction when it is surd

### Quadratic functions

- Plotting the graphs of quadratic functions
- Solving quadratic equations by factorisation
- Completing the square
- Solving quadratic equations by completing the square
- Solving quadratic equations by using the formula
- Sketching graphs of quadratic equations

### Equations and inequalities

- Solving simultaneous linear equations by elimination
- Solving simultaneous linear equations by substitution
- Using substitution when one equation is linear and the other is quadratic
- Solving lineare inequalities
- Solving quadratic inequalities

### Sketching curves

- Sketching the graph of cubic functions
- Interpreting graphs of cubic functions
- Sketching reciprocal functions
- Using the intersection points of graphs of functions to solve equations
- The effect of the transformations f(x + a), f(x – a), and f(x)+a
- The effect of the transformations f(ax) and af(x)
- Performing transformations on the sketch of curves

### Coordinate geometry in the (x, y) plane

- The equation of a straight line in the form y=mx+b or ax+by+c=0
- The gradient of a straight line
- The equation of a straight line of the form y-y1=m(x-x1)
- The formula for finding the equation the equation of a straight line
- The conditions for two straight lines to be parallel or perpendicular

### Sequences and series

- Introduction to sequence
- The nth term of a sequence
- Sequence generated by a recurrence relationship
- Arithmetic sequences
- Arithmetic series
- The sum to n of an arithmetic series
- Using Sigma notation

### Differentiation

- The derivate of f(x) as the gradient of the tangent to the graph y=f(x)
- finding the formula for the gradient of x to the power of n
- Finding the gradient formula of simple functions
- The gradient formula for a function where the power of x are real numbers
- Expanding or simplifying functions to make them easier to differentiate
- Finding second order derivates
- Finding the rate of change of a function at a particular point
- Finding the equation of the tangent and normal to a curve at a point

### Integration

- Integrating x to the power of n
- Integrating simple expressions
- Using the integral sign
- Simplifying expressions before integrating
- Finding the constant of integration

### Core 2 Mathematics

### Algebra and functions

- Simplifying algebraic functions by division
- Dividing a polynomial by (x±p)
- Factorising a polynomial using the factor theorem
- Using the remainder theorem

### The sine and cosine rule

- Using the sine rule to find missing sides
- Using the sine rule to find unknown angels
- The rule and finding two solutions for a missing angle
- Using the cosine rule to find an unknown side
- Using the cosine rule to find a missing angle
- Using the sine rule, the cosine rule and Pythagora´s Theorem
- Calculating the area of a triangle using sine

### Exponentials and logarithms

- The function y= a to the power of x
- Writing expressions as a logarithm
- Calculating using logarithm to base 10
- Laws of logarithms
- Solving equations of the form a to the power of x = b
- Changing the base of logarithms

### Coordinate geometry in the (x, y) plane

- The mid-point of a line
- The distance between two points on a line
- The equation of a circle

### The binomial expansion

- Pascal´s triangle
- Combinations and factorial notation
- Using ncr in the binomial expansion
- Expanding (a+bx) to the power of n using the binomial expansion

### Radian measure and its applications

- Using radians to measure angels
- The length of the arc of a circle
- The area of a sector of a circle
- The area of a segment of a circle

### Geometric sequences and series

- Geometric sequences
- Geometric progressions and the nth term
- Using geometric sequences to solve problems
- The sum of a geometric series
- The sum to infinity of a geometric series

### Graphs of trigonometric functions

- Sine, cosine and tangent functions
- The values of trigonometric functions in the four quadrants
- Exact values and surds for trigonometrical functions
- Graphs of sine x, cos x and tan x
- Simple transformations of sine x, cos x and tan x

### Differentiation

- Increasing and decreasing functions
- Stationary points, maximum, minimum and points of inflexion
- Using turning points to solve problems

### Trigonometrical identities and simple equations

- Simple trigonometrical identities
- Solving simple trigonometrical equations
- Solving equations of the form sin (nx+a), cos (nx+a) and tan (nx+a) = k
- Solving quadratic trigonometrical equations

### Integration

- Simple definite integration
- Area under a curve
- Area under a curve that gives negative values
- Area between a straight line and a curve
- The trapezium rule

### Core 3 Mathematics

### Algebraic fractions

- Simplify algebraic fractions by cancelling common factors
- Multiplying and dividing algebraic fractions
- Adding and subtracting algebraic fractions
- Dividing algebraic fractions and the remainder theorem

### Functions

- Mapping diagrams and graphs of operations
- Functions and function notation
- Range, mapping diagrams, graphs and definitions of functions
- Using composite functions
- Finding and using inverse functions

### The exponential and log functions

- Introducing exponential functions of the form y=a to the power of x
- Graphs of exponential functions and modelling using y=e to the power of x
- Using e to the power of x and the inverse of the exponential function ln x

### Numerical methods

- finding approximate roots of f(x)=0 graphically
- Using iterative and algebraic methods to find approximate roots of f(x)=0

### Transformation graphs and functions

- Sketching graphs of the modulus function y=|f(x)|
- Sketching graphs of the function y=f(|x|)
- Solving equations involving a modulus
- Applying a combination of transformations to sketch curves
- Sketching transformations and labelling the coordinates of given point

### Trigonometry

- The functions secant x, cosecant x and cotangent x
- The graphs of secant x, cosecant x and cotangent x
- Simplifying expressions, proving identities and solving equations using sec x, cosec x and cot x
- Using the identities 1+tan
^{2 }x =sec^{2 }x and 1+cot^{2 }x =cosec^{2 }x - Using inverse trigonometrical functions and theirs graphs

### Further trigonometric identities and their applications

- Using addition trigonometric formulae
- Using double angle trigonometrical formulae
- Solving equations and providing identities using double angle formulae
- Using the form a cos x + b sin x in solving trigonometrical problems
- The factor formulae

### Differentiation

- Differentiating using the chain rule
- Differentiating using the product rule
- Differentiating using the quotient rule
- Differentiating the exponential function
- Finding the differential of the logarithmic function
- Differentiating sin x
- Differentiating cos x
- Differentiating tan x
- Differentiating further trigonometrical functions
- Differentiating functions formed by combining trigonometrical, exponential, logarithmic and polynomial functions