Core 1 Mathematics

Algebra and functions

1. Simplifying expressions by collecting like terms
2. The rules of indices
3. Expanding an expression
4. Factorising expressions
5. Factorising quadratic expressions
6. The rules of indices for all rational exponents
7. The use and manipulation of surds
8. Rationalising the denominator of a fraction when it is surd

Quadratic functions

1. Plotting the graphs of quadratic functions
2. Solving quadratic equations by factorisation
3. Completing the square
4. Solving quadratic equations by completing the square
5. Solving quadratic equations by using the formula
6. Sketching graphs of quadratic equations

Equations and inequalities

1. Solving simultaneous linear equations by elimination
2. Solving simultaneous linear equations by substitution
3. Using substitution when one equation is linear and the other is quadratic
4. Solving lineare inequalities
5. Solving quadratic inequalities

Sketching curves

1. Sketching the graph of cubic functions
2. Interpreting graphs of cubic functions
3. Sketching reciprocal functions
4. Using the intersection points of graphs of functions to solve equations
5. The effect of the transformations f(x + a), f(x – a), and f(x)+a
6. The effect of the transformations f(ax) and af(x)
7. Performing transformations on the sketch of curves

Coordinate geometry in the (x, y) plane

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

Sequences and series

1. Introduction to sequence
2. The nth term of a sequence
3. Sequence generated by a recurrence relationship
4. Arithmetic sequences
5. Arithmetic series
6. The sum to n of an arithmetic series
7. Using Sigma notation

Differentiation

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

Integration

1. Integrating x to the power of n
2. Integrating simple expressions
3. Using the integral sign
4. Simplifying expressions before integrating
5. Finding the constant of integration

Core 2 Mathematics

Algebra and functions

1. Simplifying algebraic functions by division
2. Dividing a polynomial by (x±p)
3. Factorising a polynomial using the factor theorem
4. Using the remainder theorem

The sine and cosine rule

1. Using the sine rule to find missing sides
2. Using the sine rule to find unknown angels
3. The rule and finding two solutions for a missing angle
4. Using the cosine rule to find an unknown side
5. Using the cosine rule to find a missing angle
6. Using the sine rule, the cosine rule and Pythagora´s Theorem
7. Calculating the area of a triangle using sine

Exponentials and logarithms

1. The function y= a to the power of x
2. Writing expressions as a logarithm
3. Calculating using logarithm to base 10
4. Laws of logarithms
5. Solving equations of the form a to the power of x = b
6. Changing the base of logarithms

Coordinate geometry in the (x, y) plane

1. The mid-point of a line
2. The distance between two points on a line
3. The equation of a circle

The binomial expansion

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

Radian measure and its applications

1. Using radians to measure angels
2. The length of the arc of a circle
3. The area of a sector of a circle
4. The area of a segment of a circle

Geometric sequences and series

1. Geometric sequences
2. Geometric progressions and the nth term
3. Using geometric sequences to solve problems
4. The sum of a geometric series
5. The sum to infinity of a geometric series

Graphs of trigonometric functions

1. Sine, cosine and tangent functions
2. The values of trigonometric functions in the four quadrants
3. Exact values and surds for trigonometrical functions
4. Graphs of sine x, cos x and tan x
5. Simple transformations of sine x, cos x and tan x

Differentiation

1. Increasing and decreasing functions
2. Stationary points, maximum, minimum and points of inflexion
3. Using turning points to solve problems

Trigonometrical identities and simple equations

1. Simple trigonometrical identities
2. Solving simple trigonometrical equations
3. Solving equations of the form sin (nx+a), cos (nx+a) and tan (nx+a) = k
4. Solving quadratic trigonometrical equations

Integration

1. Simple definite integration
2. Area under a curve
3. Area under a curve that gives negative values
4. Area between a straight line and a curve
5. The trapezium rule

Core 3 Mathematics

Algebraic fractions

1. Simplify algebraic fractions by cancelling common factors
2. Multiplying and dividing algebraic fractions
3. Adding and subtracting algebraic fractions
4. Dividing algebraic fractions and the remainder theorem

Functions

1. Mapping diagrams and graphs of operations
2. Functions and function notation
3. Range, mapping diagrams, graphs and definitions of functions
4. Using composite functions
5. Finding and using inverse functions

The exponential and log functions

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

Numerical methods

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

Transformation graphs and functions

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

Trigonometry

1. The functions secant x, cosecant x and cotangent x
2. The graphs of secant x, cosecant x and cotangent x
3. Simplifying expressions, proving identities and solving equations using sec x, cosec x and cot x
4. Using the identities 1+tan² x =sec² x and 1+cot² x =cosec² x
5. Using inverse trigonometrical functions and theirs graphs

Further trigonometric identities and their applications

1. Using addition trigonometric formulae
2. Using double angle trigonometrical formulae
3. Solving equations and providing identities using double angle formulae
4. Using the form a cos x + b sin x in solving trigonometrical problems
5. The factor formulae

Differentiation

1. Differentiating using the chain rule
2. Differentiating using the product rule
3. Differentiating using the quotient rule
4. Differentiating the exponential function
5. Finding the differential of the logarithmic function
6. Differentiating sin x
7. Differentiating cos x
8. Differentiating tan x
9. Differentiating further trigonometrical functions
10. Differentiating functions formed by combining trigonometrical, exponential, logarithmic and polynomial functions