## Topic 1 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

Exponential Functions Basic shape and Translations

Exponential Functions Dilations

Exponential functions 2 Sketching

Exponential functions sketching part 2

Exponential functions 3 Finding equation from a sketch

Exponential Model and Applications

## Topic 2: Arithmetic and Geometric 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

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

## Topic 3: Introduction to Differential Calculus

Variable and constant rates of change

Average rates of change

Intro to instantaneous rates of change

The Gradient function

Differentiation from first principles

Differentiating polynomials by rule

Finding Stationary points

Nature of Stationary points

Optimisation when the function is unknown

Introduction to Kinematics

Finding the equation of a tangent

Finding the equation of a normal