## Topic 1: Arithmetic Sequences and Series

Sequence Notation

Recurrence Relations

Using a recurrence relation

Defining a sequence in terms of n

Applications of recurrence relations

Applications of recurrence relations non arithmetic

Using a calculator with recurrence relations

Arithmetic sequence formula

Rearranging the arithmetic sequence formula

Arithmetic sequences using simultaneous equations

Arithmetic sequences and series

Simultaneous equations using arithmetic series and sequences

Application of the arithmetic sequence

Simple Interest using arithmetic sequences

The Middle Term as the arithmetic mean in an arithmetic sequence

Introduction to the Sum of an arithmetic series

Finding the number of terms in an arithmetic sequence

Arithmetic series Finding the number of terms that sum to a given number

Application of arithmetic series

## Topic 2: Functions and Graphs

Relations Domain and Range

Graphing on calculator using restricted domains

What's a function

Function notation

Function Transformations intro

Function transformation afx

Function transformation fx+a

Functions Transformation fx+a

Functions transformations fax

domain and range notation

Anatomy of a quadratic graph

Solving Quadratics 3 ways

Review of sketching quadratics two ways

Modelling and problem solving with quadratics

solving simultaneous equations using quadratic and linear graphs

Direct vs inverse proportion

Equations of hyperbola and sketching

Finding equation of reciprocal function from sketch

Finding a linear factor of a polynomial

## Topic 3: Counting and Probability

The Language of Sets

Theoretical Probability with sets

All Probabilities sum to 1

Venn Diagrams the complement

Experimental probability

simplified tree diagram

The Addition rule of probability

Probability Tables intro

Conditional Probability formula

Conditional Probability Do you watch the bachelorette

Conditional probability rearranging the formula

Conditional Probability and Tree Diagrams

Independent events intro and tests

Independent events 2

Pascal's Triangle and Selections

Binomial expansion using pascal's triangle

## Topic 4: Exponential Functions

Index Law 1 – multiplication of indices

Index Law 2 – dividing indices

Index Law 3 – raising to the power of zero

Index Law 4 – Raising a power to another power

Index Law 5 – worked examples using the fifth index law

Index Law 6 – expanding brackets around a fraction raised to a power

Index law 7 Negative Indices – converting Negative indices into positive indices using fractions

Index Laws Fractional indices

Index Laws Negative bases

Index Laws simplifying by decomposing

Scientific notation Converting to scientific notation

Scientific Notation Convert scientific notation to decimal

Scientific notation Multiplying and dividing

## Topic 5: Geometric Sequences and Series

Geometric sequences and the recursive definition

Geometric Sequence formula

Geometric sequences finding the common ratio

Geometric Sequences finding the value of n

Geometric Sequences and simultaneous equations

Geometric Sequences Geometric mean

Compound interest as a geometric sequence

Geometric series formula proof and example

Geometric series find the value of n

Regular deposits as a geometric series

Geometric Series Sum to Infinity and Zeno's Paradox

Geometric series sum to infinity application

Geometric Series Sum to infinity writing recurring decimals as fractions