**The following contents will in covered in great depth within the course of the year **

**Algebra**

The Factor Theorem

Quadratic Equations

Cubic Equations

Factorising

Completing the Square

Solving by Substitution

Simultaneous Equations -Linear

Simultaneous Equations – Non-Linear

Irrational Equations

Modulus Equations

Linear Inequalities

Quadratic Inequalities

Rational Inequalities

The Discriminant

Modulus Inequalities

Abstract Inequalities

Exponential Equations

Logarithmic Equations

**Proof By Induction** Series

Divisibility

Inequality

**Complex Numbers** Addition – Subtraction

Conjugate and Division

Modulus and Polar Form

De Moivre and Powers – Whole Number Power

De Moivre and Powers – Fraction Power

Complex Roots

Transformations

**Functions**

Inputs and Outputs

Crossing the Axes

Composite Functions

Point of Intersection

Functions Injective; Surjective; Bijective

Inverse Functions

**Calculus**

Limits

Asymptotes

Differentiation from First Principles

Differentiation by Rule

Product and Quotient Rule

Chain Rule

Second Derivative

Applications of Differentiation

Increasing/Decreasing Functions

Equation of the Tangent to a Curve

Maximum/Minimum Points

Point of Inflection

Rates of Change

Distance/Speed/Acceleration

Integration by Rule

Chain Integration

Trapezoidal Rule

Area Under a Curve

Area Between Two Curves

**Calculus/Sequences**

Average Value of a Function

Repeating Patterns

Types of Sequences

General Term of a Sequence

Recurring Decimals

**Arithmetic**

Rounding

Relative Error

Currency Exchange

Income Deductions

Index Notation

**Financial Maths** Final Value

Present Value

Non-Annual Interest Rates

Amortisation

Geometric Series – Savings

Geometric Series – Loans

**Geometry**

Angles

Triangles

Quadrilaterals

Circles

Congruent Triangles

Similar Triangles

Transformations

Enlargements

**Trigonometry**

SOH-CAH-TOA

Pythagoras

Cosine Rule

Sine Rule

Area of a Triangle

Solving Triangles

The Unit Circle

Trigonometric Equations

Trigonometric Functions

**Co-Ordinate Geometry** The Line

**Co-Ordinate Geometry** The Circle

**Probability**

Fundamental Principal of Counting

Counting Outcomes

Combinations

Permutations

Basic Probability

Conditional Probability

Independent Events

Mutually Exclusive Events

Bernoulli Trials

**Probability/Statistics**

Expected Value

Data Types

Sampling Types

Measures of Centre

Measures of Spread

Graphical Representations

Correlation Coefficient

Line of Best Fit

**Statistics Empirical Rule**

Normal Distribution

Hypothesis Testing