## AS

### Algebraic Expressions

• Laws of indices
• Expanding Brackets
• Factorising
• Negative and Fractional Indices
• Surds
• Rationalising Denominators

• Completing the Square
• Functions
• The Discriminant
• Equations and inequalities
• Linear Simultaneous Equations
• Simultaneous Equations on Graphs
• Linear inequalities
• Inequalities on graphs
• Regions
• Graphs and Transformations
• Cubic graphs
• Quartic graphs
• Reciprocal graphs
• Points of intersections
• Translating graphs
• Sketching Graphs
• Transforming functions
• Straight line graphs
• y=mx+c
• Equations of straight lines
• Parallel and perpendicular lines
• Length and area
• Modelling with Straight Lines
• Circles
• Midpoints and perpendicular bisectors
• Equation of a circle
• Intersections of straight lines and circles
• Use tangent and chord properties
• Circles and triangles
• Algebraic methods
• Algebraic fractions
• Dividing polynomials
• The factor theorem
• Mathematical Proof
• Methods of proof
• The Binomial Expansion
• Pascals Triangle
• Factorial Notation
• The binomial Expansion
• Solving binomial problems
• Binomial estimation
• Trigonometric ratios
• The Cosine rule
• The sine rule
• Areas of triangles
• Solving triangle problems
• Graphs for sine, Cosine and Tangent
• Transforming trigonometric graphs
• Trigonometric identities and equations
• Exact values of trigonometric ratios
• Trigonometric identities
• Simple trigonometric equations
• Harder trigonometric equations
• Equations and identities
• Vectors
• Vectors
• Representing Vectors
• Magnitude and direction
• Position vectors
• Solving geometric problems
• Modelling with vectors
• Differentiation
• Finding the derivative
• Differentiation
• Differentiating functions with two or more items
• Increasing and decreasing functions
• Second order derivatives
• Stationary points
• Modelling with differentiation
• Integration
• Indefinite integrals
• Finding functions
• Definite integrals
• Areas under curves
• Areas under the x-axis
• Areas between curves and lines
• Exponential and logarithms
• Exponential functions
• y=ex
• Exponential modelling
• Logarithms
• Laws of logarithms
• Solving questions using logarithms
• Working with natural logarithms
• Logarithms and non-linear data
• A Level
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