## ME-P1 Proof by Mathematical Induction

Summation notation or Sigma Notation

Why we need proof by mathematical induction

Proof by Mathematical Induction: Mathematical Dominoes

Proof by induction partial sums worked examples

Proof by Induction Divisibility proofs

## ME-V1 Introduction to vectors

#### – V1.1 Introduction to vectors

Vectors Introduction

Adding Vectors Graphically

Vectors Multiplying by a scalar

Vectors in 2D and 3D Shapes

Vectors in linear combinations

Vectors in component form

Adding Vectors in component form

Vectors multiplying by a scalar in component form

#### – ME-V1.2 Further Operations with Vectors

Vectors finding the magnitude

Vectors finding the unit vector

Finding direction of a vector

Defining a vector between 2 points

Vector Revision part 1

The dot product part 1

The dot product part 2

The dot product part 3

The scalar product or dot product of a vector revisited

Force Vector Diagrams

Resolving Force Vectors

Resolving forces into their components

Resolving Forces into components part 2

Vector midpoints

Vectors in component form recap

Vectors in polar form

What's a vector projection?

Calculating vector projections

Resolving a vector into components parallel and perpendicular to a second vector

Applications of vectors displacement and velocity

Applications of vectors displacement and velocity collisions

Applications of vectors relative velocity

Triangle of forces

Inclined plane recap part 1

Solving equilibrium questions using resolution of forces

#### – ME-V1.3 Projectile Motion

Vector Functions Introduction and converting vector functions to cartesian functions

Vector equations and finding collision points

Vector Calculus Displacement, velocity Acceleration

Vector Calculus Anti differentiation worked example

Vector Calculus Differentiation worked examples

Vector Calculus Motion in a straight line

Vector Calculus Projectile Motion Calculating Launch Angle

## ME-T3 Trigonometric Equations

Express the sum of trigonometric functions as a single function

Express the sum of trigonometric functions as a single function part 2

Solving trig equations of the form sin(ax+b) = c

Exact values of reciprocal trigonometric functions

Solving reciprocal trig functions

Proving Trigonometric identities

2 more pythagorean identities

Angle sum and difference indentities

Angle sum and difference identities part 2

Double angle identity proofs and an example

More proofs of trig identities

## ME-C2 Further Calculus Skills

Proofs of derivatives of Inverse Trigonometric Functions

Calculating derivatives of inverse trigonometric Functions

Integration by Substitution Introduction

Integration by substitution worked examples part 1

Integration by substitution worked examples part 2

Using trig identities for integration

## ME-C3 Applications of Calculus

#### – C3.1 Further Area & Volumes of Solids of Revolution

Volumes of solids of revolution introduction

Volume of solids of revolution: between 2 curves

Volumes of solids of revolution: Around the y axis

#### – C3.2 Differential Equations

Implicit differentiation

Solving differential equations

Solving differential equations given in terms of f(y)

Setting up differential equations

Isaac Newton & My Cup of Coffee: Differential Equations Applications

Differential equations: Mixing Problems

Modelling Population Growth: The Logistic Equation – Differential Equations

Verifying solutions to differential equations

Separable differential equations

Displacement velocity acceleration etc

Velocity in terms of displacement Acceleration in terms of velocity

Other Expressions for acceleration part 1

Other Expressions for acceleration part 2

Simple Harmonic Motion

Resultant forces

Momentum

Newton's laws of motion

Newtons laws of motion examples

Calculating the Normal Reaction Force in an Elevator

## ME-S1 The Binomial Distribution

#### – S1.1 Bernoulli & Binomial Distributions

Bernoulli sequence

Binomial distribution introduction

Developing Binomial Distribution Intuition

The binomial Probability Formula

Binomial Probability Distribution formula Worked Example

Binomial Probability formula at most and at least

Binomial Distribution on the Casio FX CG50AU

Binomial Probability Conditional Probability

Binomial distribution expected value variance and standard deviation

Construct a Binomial Distribution Graph

Binomial Distribution finding a sample size

#### – s1.2 Normal Approximation for the Sample Proportion

Why is sample proportion interesting and important

Sampling from a small population

Sampling from a large population

Sample proportion mean and standard deviation

Approximating the distribution of sample proportions using the normal distribution

Determining required Sample size for a given Margin of error

Binomial Approximation to the normal and sample proportion, one question two ways