## IGCSE only

Autumn Term 1Rational and irrational numbersConvert 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 2Kinematicsalculus to linear kinematics- C - Differentiation with respect to time Functions- Mapping, function, domain, range, composite, inverse - Function notation Transformations of Graphstretch f(ax) and af(x)- S - Translation f(x+a) and f(x)+a - Reflection f(-x) and -f(x) Direct and Inverse Proportionroblems involving direct or inverse proportion- P - Equation of direct and inverse proportion - Speed, density and pressure |

Spring Term 1Vectors- 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 2Circle Theorems- Alternate segment theorem - Internal and external intersecting chord properties Revision will take place in this term |

## IGCSE & Ad Maths

Autumn Term 1Functions 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 2Identities 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 1Integration- 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≡sinθ/cosθ - 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 2Revision will take place in this half term |