VCE Maths Methods Units 1-4: Calculus

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Includes differentiation and antidifferentiation (integration)

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What Will I Learn?

- Understand what limits are and evaluate limits [as an introduction to calculus]
- Differentiate using first principles
- Differentiate the following functions: x^n, e^x, loge(x), sin(x), cos(x), tan(x)
- Differentiate using the chain rule, product rule and quotient rule
- Calculate the average and instantaneous rate of change of a function
- Find the equation of a tangent and normal line
- Find the maximum and minimum of a function
- Apply the concepts on differentiation on worded problems (including maximum and minimum problems, rate of change problems and motion graphs)
- Sketch the derivative and antiderivative of a given graph
- Antidifferentiate the following functions: x^n, e^x, 1/x, sin(x), cos(x)
- Integrate by recognition
- Evaluate definite integrals
- Calculate the approximate and exact area beneath a graph and between two graphs
- Calculate the average value of a function for a specified domain
- Apply the concepts on antidifferentiation on worded problems (including rate of change problems and motion graphs)

Requirements

- Be able to sketch the graphs of the basic functions, including linear, quadratic, cubic, hyperbola, truncus, square root, exponential, logarithmic, sine, cosine and tangent graphs.
- Be able to solve equations algebraically, including polynomial, exponential, logarithmic and trigonometric equations.
- Be familiar with the formulae to calculate the area of basic 2D shapes (e.g. triangle), and the volume and total surface area of basic 3D shapes (e.g. sphere). If unsure, please refer to the formula sheet on the VCAA website: http://www.vcaa.vic.edu.au/.
- NOTE: The course requirements for unit 1/2 students may not be as extensive. For instance, they are generally only required to sketch the graphs of polynomial functions, and solve polynomial equations. However, they should be familiar with the formulae for the areas and volumes.

Description

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.

Who is the target audience?

- This course mainly caters for students doing the Australian VCE subject, Mathematical Methods unit 1/2 and 3/4.
- However, students from other countries or Australian states at a level equivalent to year 11 and 12 in Australia may also find this course useful.
- This course will clearly outline the content from unit 1/2 and unit 3/4, although sometimes there is a slight overlap between the two. For unit 1/2 students, you can also watch the unit 3/4 content to get a head start for the future; while for unit 3/4 students, you can also watch the unit 1/2 content if you need some revision on the previously learnt material.

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