Treena Exams Courses

Mathematics

Foundations

Sets and Numbers

Introduction to Set Theory Set Theory Operations Numeric Sets The Real Numbers The Cartesian Plane

Arithmetic and Expressions

Expressions and Multiplication The Index Laws Special Expansions Factorizing Expressions Fraction Arithmetic Surd Arithmetic

Algebraic Techniques

Simple Algebraic Techniques Algebra With Quadratics Simultaneous Equations

Working with Functions

Introducing Functions

Functions and Relations Visualizing Functions Domain and Range Algebra with Functions Composite Functions Solving for Zeroes

Linear and Quadratic Functions

Lines and Gradients Quadratic Features

Further Functions and Relations

Introducing Polynomials Hyperbolic Functions Absolute Values Circular Relations

Trigonometric Functions

Trigonometric Functions

Measures of Angle Unit Circle Trigonometry Special Ratios (soh, cah, toa)Trigonometric Graphs Reciprocal Trigonometry

Applications and Triangles

The Sine Rule The Cosine Rule Arcs, Sectors and Area Miscellaneous Triangles

Trigonometric Algebra

Trigonometric Identities Pythagorean Identities Trigonometric Equations

Introduction to Differentiation

Basics of Calculus

Gradients and Calculus Tangents and Secants Limits and Continuity

The Derivative

First Principals Basic Derivatives The Chain Rule The Product Rule The Quotient Rule General Derivatives

Exponentials and Logarithms

Exponentials

Introducing Exponentials Graphing Exponentials

Logarithms

Introducing Logarithms Logarithm Laws Graphing Logarithms

Discrete Probability Distributions

Introductory Set Theory

Introduction to Set Theory Set Theory Operations

Probability and Venn Diagrams

Introduction to Probability Disjoint Probabilities Tables and Trees Overlapping Probabilities Conditional Probability Multiplying Probabilities Independent Probability

Discrete Probability Distributions

Random Variables Probability Distributions Expected Value Measures of Spread

Graphing Techniques

Elementary Functions

Elementary Functions

Graphical Transformations

Translating Graphs Dilating Graphs Combined Graphical Transformations Applications of Graphing

Further Derivatives

Exponentials and Logarithms

Exponential Derivatives Logarithmic Derivatives

Trigonometric Derivatives

Trigonometric Derivatives

Derivative Applications

Stationary Points Second Derivatives Inflections and Extremes Simple Optimisation

Modelling Financial Situations

Series and Sequences

Introducing Sequences Introducing Series Arithmetic Sequences Geometric Sequences Limiting Sums

Financial Sequences

Compound Interest Periodic Investments Repaying Loans

Integral Calculus

Undoing Differentiation

Undoing Derivatives The Rules of Integration Evaluating Definite Integrals The Indefinite Integral The Fundamental Theorem of Calculus

Areas and Integration

Finding Areas Approximating Integrals

Further Explicit Integrals

The Reverse Chain Rule Exponential Integrals Hyperbolic Integrals Trigonometric Functions General Integrals

Descriptive Statistics and Bivariate Data

Univariate Data Analysis

Random Variables and Data Visualising Univariate Data Quartile Analysis

Bivariate Datasets

Bivariate Data Calculating Correlations Linear Regression

Continuous Random Variables

Continuous Random Variables

Probability Density Functions Cumulative Density Functions Statistical Analysis of Distributions

The Normal Distribution

Normally Distributed Data Modelling Normal Distributions Z-Scores Probability and Normal Distributions