€20.00
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
