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Module Content

Algebra and Functions:
- Algebraic long division
- missing terms
- finding the remainder

- Factor theorem
- showing that x-1 is a factor of a cubic polynomial
- factorising a cubic polynomial
- solving a cubic equation
- finding constants in a polynomial given the factors

- Remainder theorem
- finding the remainder when a cubic polynomial is divided by x+1
- finding the remainder when a quartic polynomial is divided by 2x-1
- finding constants in a polynomial given the remainders

- Exponential functions

- Logarithms
- Rules of logs
- Simplifying
- Equations
- Equations with log terms
- Change of base type
- Quadratic type
- Inequalities
- Solving inequalities

Coordinate geometry:
- Circles
- Equation
- Finding the centre and radius
- Equation of a tangent
- Equation of a circle through 3 points
- Circle properties

Sequences and series:
- Geometric series
- consecutive terms
- investment example
- Proof of sum of first n terms Sn
- Sum to infinity

- Binomial expansion
- nCr method
- method of expanding
- finding particular terms
- Pascals triangle method
- Binomial formula

Trigonometry:
- Trigonometric Ratios
- Trig. ratios for 30, 45, 60 and 90 degrees
- Trig. ratios for multiples of 30, 45 and 60 degrees

- Graphs
- Trigonometric graphs
- Transformations
- Translations
- Reflections
- Stretches
- Combining transformations

- Applications
- Area of a triangle
- Sine Rule
- Cosine Rule
- Arcs, Sectors and Segments
- Radians
- Arc length and sector area
- Arc length and sector area
- Area of a segment

- Equations
- The quadrant rule
- How to solve sinθ, cosθ, tanθ = a positive or negative value in a given range
- How to solve multiple angles, example sin2x = a positive value
- Equations that factorise

- Identities
- Two basic trigonometric identities, tanθ ≡ sinθ/cosθ and sin²θ+cos²θ ≡ 1
- Proving trignometric identities
- The identities, cos(θ) ≡ cos(-θ), sin(θ) ≡ -sin(-θ)
- Solving equations using identities

Differentiation:
- Stationary points
- Finding stationary points (example)
- Nature of a stationary point using the first differential
- Nature of a stationary point using the second differential
- Finding stationary points and their nature example
on graphs
- Applications
on practical applications
- Increasing and Decreasing functions

Integration:
- Definite Integration
- Infinite integrals
- Application - Area
- Area under a curve
- Finding the area below the x-axis
- Finding the area above and below the x-axis
- Finding the area bounded by two curves

- Numerical Integration
- Trapezium rule
- Type of estimate