In general one topic will be covered in one week
C1 Curriculum Map
Surds and indices
Surds
Manipulation of surds
Rationalising the denominator 13
Rules for indices
Algebra with indices
Indices
Algebraic expressions
Algebraic expressions
Function notation
Polynomials- adding and subtracting algebraic
expressions
Multiplication of algebraic expressions
Factorising
Cancelling fractions
Factorising by grouping
Factorising a quadratic
Fractions
Adding and subtracting fractions
Multiplying fractions
Dividing fractions
Equations and quadratic functions
Relationships
Equations, inequalities and identities
Solving linear equations
Cross multiplying
Solving quadratic equations
Completing the square
Using the quadratic equation formula
Sketching quadratic functions
Use of the discriminant
Inequalities
Linear inequalities
Quadratic inequalities
Simultaneous equations
Simultaneous equations: Linear equations
Solving two linear simultaneous equations:
Elimination method
Solving two linear simultaneous equations:
Substitution method
Further examples of simultaneous
equations
Solving simultaneous equations: One linear and one
quadratic
Intersection of linear and quadratic curves:
Three cases of the discriminant
Coordinate geometry and the straight line
Coordinate geometry of a plane
The length of a line segment
The mid-point of a line segment
The gradient of a line
Gradient as tan θ
Special cases: zero and infinite gradients
Parallel and perpendicular lines
Equation of a curve: To test if a point lies on a curve
Equation of a straight line:
To find the equation of a line given one point on the line
and its gradient
To find the equation of a line given two points on the line
Forms of equations of straight lines
Sketching straight lines
Applications
Graphs of functions
Graphs of standard functions
Continuous and discontinuous functions; asymptotes
Transformation of graphs
Sketching curves 1
Geometrical interpretation of the solution of equations
Solving a pair of equations
Solving an equation in one unknown
Sequences and series: arithmetic series
Sequences
Finding the formula for the terms of a sequence
Series and Ʃ notation
Arithmetic series
Formulae for arithmetic series
Differentiation
Rates of change
Tangent to a curve
Gradient of a curve Differentiation notation
Function notation
Vocabulary
Differentiating from first principles
Differentiation of polynomials
Tangents and normals
Integration
The reverse of differentiation
Finding the constant c
Using the integral sign
Rules for differentiating and integrating x"
Integration of a polynomial
Applying integration
Revision using Past Papers
Mock Examination
C2 Curriculum Map
More algebra
Identities
Division of polynomials
Alternative method of division
Remainder and factor theorems
Factorising polynomials
Coordinate geometry of the circle
Properties of a circle
The equation of a circle
Tangents to a circle
Binomial expansion
Binomial expansion using Pascal's triangle
Notation n! and n
r
Formula for binomial expansion
Application of differentiation
Increasing and decreasing functions
Stationary points
Identifying the type of a stationary point
Maximum and minimum problems
Sketching curves 2
Trigonometric functions
Definition of a radian
Converting radians to degrees
Converting degrees to radians
Angles of any size
Trigonometric ratios for any angle
To determine the sign of any trigonometric ratio
To determine the magnitude of any trigonometric
ratio
Special cases
Graphs of trigonometric functions
Transformation of trigonometric graphs
Special triangles: Trigonometric ratios of 30°, 45°
and 60°
Trigonometric identities
Solution of trigonometric equations
Solving trigonometric equations which are quadratic
Applications of trigonometry
Area of sector and length of arc
Area of a triangle
Solution of triangles
The sine and cosine rules
Exponentials and logarithms
Definition of a logarithm
Combining logs
Exponentials and their graphs
Change the base of a log
Solving equations involving indices and logs
Further Integration and the Trapezium Rule
Indefinite and definite integrals
Area 'under' a curve
To find an area using integration
Area between a curve and a straight line
Area between two curves
The trapezium rule
Formula for the trapezium rule
Geometric series
Geometric sequences and series
Geometric series
Formulae for geometric series
Infinite geometric series
Revision using Past Papers
Mock Examination