IGCSE only

Autumn Term 1
Rational and irrational numbers
- Convert recurring decimals into fractions
- Surds
- Manipulate surds
- Rationalise the denominator
Gradients of Curves and Differentiation
- Find the gradients of non-linear graphs
- Differentiate kx^n
- Gradient function dy/dx
- Find stationary points on a curve
Autumn Term 2
Kinematics
- Calculus to linear kinematics
- Differentiation with respect to time
Functions
- Mapping, function, domain, range, composite, inverse
- Function notation
Transformations of Graphs
- Stretch f(ax) and af(x)
- Translation f(x+a) and f(x)+a
- Reflection f(-x) and -f(x)
Direct and Inverse Proportion
- Problems involving direct or inverse proportion
- Equation of direct and inverse proportion
​- Speed, density and pressure
Spring Term 1
Vectors
- A vector has both magnitude and direction
- Vector notation
- Multiply vectors by scalar quantities
- Add and subtract vectors
- Modulus (magnitude) of a vector
- Resultant of two or more vectors
Spring Term 2
Circle Theorems
- Alternate segment theorem
- Internal and external intersecting chord properties
​
Revision will take place in this term

IGCSE & Ad Maths

Autumn Term 1
Functions and polynomials
​- A function is a mapping between elements of two sets
- Function notation, f(x)
- Domain and range
- Composite and inverse function
- Transformations of graphs
- Operations with polynomials
- Factor Theorem
Direct and inverse proportion
- Problems involving direct or inverse proportion
- Relate to graphical representation of equations
Histograms
​- Construct and interpret histograms
Differentiation
- Gradients of non-linear graphs
- Variable rate of change
- Use a chord to estimate gradient of a tangent
- Differentiate integer powers of x 
- Gradients, rates of change, stationary points, turning points (maxima and minima) by differentiation and relate these to graphs plus equation of a tangent and normal
Autumn Term 2
Identities and Proof
- Use algebra to support and construct proofs
Vectors
- A vector has both magnitude and direction
- Vector notation including column vectors
- Multiply vectors by scalar quantities
- Add and subtract vectors
- Modulus (magnitude) of a vector
- Resultant of two or more vectors
Enumeration
- Binomial expansion
- Use the binomial distribution to enumerate outcomes
- Counting numbers of outcomes of combined events
- Permutations and nPr
- Combinations and nCr
Spring Term 1
Integration
- Integrate polynomials, as the reverse of differentiation
- Indefinite and a definite integral
- Area between a curve, two co-ordinates and the x-axis
- Area between two curves
- Estimate the area between a curve and the x-axis
- Trapezium rule
- Over or under estimate and calculate an improved estimate
Kinematics
- Calculus and linear kinematics
- Differentiation and integration for variable acceleration
- Recognise the special case where the use of constant acceleration formulae is appropriate
Exponentials and logarithms
- Graph of ka^x, where a is positive
- Logarithm as the inverse of a^x
- Laws of logarithms
- Linearising exponential graphs
- Solve equations of the form a^x = b for a>0
- Exponential growth and decay
Linear Programming
- Express real situations in terms of linear inequalities
- Maximization and minimization problems
- Objective function
Trigonometry
- tanθ≡sin⁡θ/cos⁡θ
- sin^2(⁡)θ+cos^2(θ)≡1
Recurrence relations and solving equations
- Recurrence relationships to describe and determine sequences, and use recurrence relationships in modelling (e.g. compound interest)
- Change of sign
- Decimal search
- Interval bisection
- Iterative method 
- Failure of numerical methods
Spring Term 2
Revision will take place in this half term