After going through this course, you will be able to understand how calculus (differentiation and antidifferentiation/integration) works at an Australian VCE Maths Methods Units 1-4 level, and apply such knowledge on exam questions. Each lecture includes many clearly annotated diagrams to make mathematical concepts easier to understand, and will be followed by a quiz to test your understanding.

The lectures are designed to cater for both unit 1/2 students and unit 3/4 students, with unit 1/2 and unit 3/4 content indicated in the ‘lecture description’ and the beginning of each lecture. Unit 1/2 students only need to watch the unit 1/2 content of each lecture, although you may go on to watch the unit 3/4 content if you want to get a head start. Unit 3/4 students may find the unit 1/2 content a good revision for them.

You are encouraged to go through the lectures in order since the content from the earlier lectures is often required in the later lectures.

### Introduction to calculus - Limits

This lecture provides an introduction to the course.

Content: All covered in __unit 1/2__

- What are limits?

- When do limits exist?

- Theorem on limits

- Calculations of limits

### Differentiation

Content: All covered in __unit 1/2__

- Introduction to differentiation (including notation)

- The derivative of a function using first principles

- Examples

The content in this lecture is covered in ** unit 1/2**. You will learn how to differentiate x^n, and the more complicated form of this rule which is (ax+b)^n.

The content in this lecture is covered in ** unit 3/4**. You will learn how to differentiate e^x, log(x), sin(x), cos(x) and tan(x).

The content in this lecture is covered in ** unit 1/2**. You will learn how to find the average rate of change and (instantaneous) rate of change of a graph. Take note that although the concept is taught in unit 1/2, the second worked example provided in the lecture is suitable only for unit 3/4 students since it assumes knowledge from the lecture entitled “Differentiation by rule – e^x, log(x), sin(x), cos(x), tan(x)”. This means that unit 1/2 students should only watch the first

*4 minutes and 52 seconds*of the lecture, while unit 3/4 students can watch the entire lecture.

Content: All covered in __unit 3/4__

- When do we use chain rule?

- What is chain rule?

- Long method
- Short method (recommended)

- More examples

Content: All covered in __unit 3/4__

- When do we use product and quotient rule?

- What is product rule and quotient rule?

- Mixed examples (including chain rule, product rule and quotient rule)

Content: All covered in __unit 1/2__

- Features of a derivative graph

- Sketching the derivative graph of a polynomial function

- Determining the domain of a derivative graph

- Sketching the derivative graph of a hybrid function

The content in this lecture is covered in ** unit 1/2**. You will learn how to find the equation of the tangent and normal line of a graph at a particular point. Take note that although the concept is taught in unit 1/2, the second worked example provided in the lecture is suitable only for unit 3/4 students since it assumes knowledge from a maths methods unit 3/4 level. This means that unit 1/2 students should only watch the first

*8 minutes and 36 seconds*of the lecture, while unit 3/4 students can watch the entire lecture.

Content: All covered in __unit 1/2__

- Finding the stationary points of a function

- Sign test: Verifying the nature of a stationary point

- More complicated examples (recommended for unit 3/4 students to watch as well! – from *8 minutes and 32 seconds *onwards)

This lecture goes through three worded problems, which involve deriving a function and using calculus to find the maximum or minimum value of the function. The main focus in this lecture is on how to derive the function from the worded problem. *Examples one* and *two* are suitable for unit 1/2 students, while example three is suitable for unit 3/4 students (although unit 1/2 students are encouraged to watch *example three* as well to improve their problem solving skills).

This lecture goes through two worded problems, with *example one* relating to motion graphs (unit 1/2) and *example two* relating to rate of change problems (unit 3/4). Just like in the previous lecture, the main focus in this lecture is on how to derive the function from the worded problem.

### Antidifferentiation (integration)

The content in this lecture is covered in ** unit 1/2**. You will learn how to antidifferentiate x^n, and the more complicated form of this rule which is (ax+b)^n. You will also learn how to find the value of the constant ‘c’ in the antidifferentiated equation given the additional information provided.

The content in this lecture is covered in ** unit 3/4**. You will learn how to antidifferentiate e^x, 1/x, sin(x) and cos(x).

Content: All covered in __unit 3/4__

- Features of an antiderivative graph

- Sketching the antiderivative graph of a polynomial function

The concept of integration by recognition is covered in ** unit 3/4**.

Content: All covered in __unit 3/4__

- Indefinite integrals vs. definite integrals

- Evaluating definite integrals

- Properties of definite integrals

- More complicated examples

This lecture is covered in ** unit 1/2**, and covers the left-rectangle and right-rectangle methods in approximating the area beneath a graph. Note that in the final example in this lecture, a knowledge of exponential functions and graphs is required.

Content: All covered in __unit 3/4__

- Fundamental theorem of integral calculus (in part one)

- Area beneath a graph (in part one)

- Area between two graphs (in part two)

- More complicated area calculations (in part two)

Warning: This lecture is quite content-heavy! So make sure you give yourself enough time to go through this lecture. This lecture also assumes a knowledge on the sketching of basic graphs, including quadratic graphs, exponential graphs, hyperbolic graphs etc.

Content: All covered in __unit 3/4__

- Fundamental theorem of integral calculus (in part one)

- Area beneath a graph (in part one)

- Area between two graphs (in part two)

- More complicated area calculations (in part two)

Warning: This lecture is quite content-heavy! So make sure you give yourself enough time to go through this lecture. This lecture also assumes a knowledge on the sketching of basic graphs, including quadratic graphs, exponential graphs, hyperbolic graphs etc.

The content of this lecture is covered in ** unit 3/4**.

This lecture goes through three worded problems, with *example one* relating to motion graphs (unit 1/2), *example two* relating to rate of change problems (unit 3/4), and *example three* relating to area calculations (unit 3/4). Note, unit 3/4 students may find *example three* highly useful as an exam-style question, as it combines concepts from both differentiation and antidifferentiation.