# 2 Unit Mathematics Online Bridging Course

Welcome to the 2 Unit online mathematics bridging course.

Each day consists of audio visual modules on a number of mathematical topics for you to play and study. These modules are supplemented by notes and links to other useful sites. We have also included a booklet of exercises for you to work through, with solutions to selected exercises available each day.

2 Unit Mathematics Bridging Course Exercise Booklet

We have included a version of the modules without a commentary if you prefer.

NB: If you use a Mac you may need to download some software such as VLC to play the audio visual modules.

## Day 1 – Introduction to functions

#### Audio visual modules

- Day 1 Module 1 Introduction to functions
- Day 1 Module 2 More on functions

#### Modules without a commentary

- Day 1 Module 1 Introduction to functions
- Day 1 Module 2 More on functions

#### Additional materials and solutions to selected exercises

## Day 2 – Linear functions

#### Audio visual modules

- Day 2 Module 1 Linear functions I: Gradients
- Day 2 Module 2 Linear functions II: Finding equations

#### Modules without a commentary

- Day 2 Module 1 Linear functions I: Gradients
- Day 2 Module 2 Linear functions II: Finding equations

#### Additional materials and solution to selected exercises

## Day 3 – Factorisation and solving quadratic equations

#### Audio visual modules

- Day 3 Module 1 Factorisation and Expansion
- Day 3 Module 2 Quadratics
- Day 3 Module 3 Quadratic equations

#### Modules without a commentary

- Day 3 Module 1 Factorisation and expansion
- Day 3 Module 2 Quadratics
- Day 3 Module 3 Quadratic equations

#### Additional materials and solutions to selected exercises

## Day 4 – Introduction to the derivative

#### Audio visual modules

- Day 4 Module 1 The derivative of a function
- Day 4 Module 2 Stationary points and quadratic functions

#### Modules without a commentary

- Day 4 Module 1 The derivative of a function
- Day 4 Module 2 Stationary points and quadratic functions

#### Additional materials and solution to selected exercises

- Notes: Stationary points and their nature
- Solutions to selected exercises in the bridging course notes

## Day 5 – Derivative of a general polynomial function and applications of the derivative

#### Audio visual modules

- Day 5 Module 1 The derivative of a polynomial
- Day 5 Module 2 Applications of calculus I
- Day 5 Module 3 Applications of calculus II: Curve sketching

#### Modules without a commentary

- Day 5 Module 1 The derivative of a polynomial
- Day 5 Module 2 Applications of calculus I
- Day 5 Module 3 Applications of calculus II: Curve sketching

#### Additional materials and solutions to selected exercises

- Notes: Graphs of polynomials
- Notes: Introduction to the rules of calculus up to page 4
- Notes: Optimisation using calculus
- Notes: Curve sketching using calculus
- Solutions to selected exercises in the bridging course notes

## Day 6 – Second derivatives and their applications

#### Audio visual modules

- Day 6 Module 1 The second derivative
- Day 6 Module 2 Application of the second derivative: Curve sketching
- Day 6 Module 3 Application of the second derivatuve: A moving body

#### Modules without a commentary

- Day 6 Module 1 The second derivative
- Day 6 Module 2 Application of the second derivative: Curve sketching
- Day 6 Module 3 Application of the second derivative: A moving body

#### Additional materials and solutions to selected exercises

- Notes: The second derivative, concavity and points of inflection
- Solutions to selected exercises in the bridging course notes

## Day 7 — Index laws and power law of differentiation

#### Audio visual modules

- Day 7 Module 1 Index laws I
- Day 7 Module 2 Index laws II: Examples and the power law for differentiation

#### Modules without a commentary

- Day 7 Module 1 Index laws I
- Day 7 Module 2 Index laws II: Examples and the power law for differentiation

#### Additional materials and solutions to selected exercises

## Day 8 — The exponential function and derivatives

#### Audio visual modules

- Day 8 Module 1 Exponential functions
- Day 8 Module 2 Applications of the exponential function
- Day 8 Module 3 Composite functions

#### Modules without a commentary

- Day 8 Module 1 Exponential functions
- Day 8 Module 2 Applications of the exponential function
- Day 8 Module 3 Composite functions

#### Additional materials and solutions to selected exercises

## Day 9 — More rules of differentiation

#### Audio visual modules

- Day 9 Module 1 The derivative of a composite function
- Day 9 Module 2 The product rule of differentiation
- Day 9 Module 3 The quotient rule of differentiation

#### Modules without a commentary

- Day 9 Module 1 The derivative of a composite function
- Day 9 Module 2 The product rule of differentiation
- Day 9 Module 3 The quotient rule of differentiation

#### Additional materials and solutions to selected exercises

- Notes: Composite functions and their derivatives
- Notes: Differentiation of the exp and log functions
- Notes: Introduction to the rules of calculus from page 5
- Solutions to selected exercises in the bridging course notes

## Day 10 — The circular functions

#### Audio visual modules

- Day 10 Module 1 Circular functions I: The sine function
- Day 10 Module 2 Circular functions II: The general sine function
- Day 10 Module 3 Circular functions III: The cosine function, identities and derivatives

#### Modules without a commentary

- Day 10 Module 1 Circular functions I: The sine function
- Day10 Module 2 Circular functions II: The general sine function
- Day 10 Module 3 Circular functions III: The cosine function, identities and derivatives

#### Additional materials and solutions to selected exercises

## Day 11 — Inverse functions and the logarithm function

#### Audio visual modules

- Day 11 Module 1 Inverse functions
- Day 11 Module 2 Logarithms
- Day 11 Module 3 The logarithm function
- Day 11 Module 4 Differentiating the logarithm function

#### Modules without a commentary

- Day 11 Module 1 Inverse functions
- Day 11 Module 2 Logarithms
- Day 11 Module 3 The logarithm function
- Day 11 Module 4 Differentiating the logarithm function

#### Additional materials and solutions to selected exercises

- Notes: Logarithmic functions and the log laws
- Solutions to selected exercises in the bridging course notes

#### Day 12 — Absolute value

#### Audio visual module

- Day 12 Module 1 Absolute values

#### Module without a commentary

- Day 12 Module 1Absolute values