It is important to know your (not only mathematical) limits – when you know what you can do and what you can’t do (yet), you know where you need to focus your efforts to improve your skills. This applies to everything in life, not just mathematics.

Have you spent time analysing your own skills in mathematics? Have you looked at the list of skills that you are expect to have (and be able to demonstrate in a test) as you complete each section of study? If you haven’t you can (and should!) read the study design document at this link.

In the early days of television, there was a programme that became very popular – an early horror/thriller called The Outer Limits:

As the intro says:

There is nothing wrong with your television set. Do not attempt to adjust the picture. We are controlling transmission. If we wish to make it louder, we will bring up the volume. If we wish to make it softer, we will tune it to a whisper. We will control the horizontal. We will control the vertical. We can roll the image, make it flutter. We can change the focus to a soft blur or sharpen it to crystal clarity. For the next hour, sit quietly and we will control all that you see and hear. We repeat: there is nothing wrong with your television set. You are about to participate in a great adventure. You are about to experience the awe and mystery which reaches from the inner mind to… The Outer Limits.

You are going on an adventure from your inner mind to the outer limits – and you will have control the vertical and the horizontal with crystal clarity – if you want to pass the calculus component of Mathematical Methods!

You have already studied an introduction to calculus last year, particularly the concept of limits and derivatives from first principles, leading to the general theory of differential of polynomials:

Calculus is central to almost all mathematics that has been developed in the last 400 years of mathematical thought – and as far as you continue into mathematics (whether that be in engineering, architecture, economics, medicine, or almost any other professional field) you will need to master this area of study. To assist you in this, I have compiled a video course to support your classroom instruction. There are three playlists – I advise you to consider carefully the time needed to view these videos (approximately an hour per playlist) and plan when you will watch which ones.

Playlist 1: Calculus – Limits and Simple Derivatives (A review of Year 11 content)

Playlist 2: Calculus – Polynomials and Compound Functions (Transition from Year 11 to Year 12)

Playlist 3: Calculus – Circular and Transcendental Functions (This year’s content)

If you are experiencing difficulty, there is an excellent resource at Calculus Help – Flash Tutorials for the Calculus-Phobe

A warning to all students – this topic is the most critical aspect of Year 12 Mathematical Methods. You must bring your best efforts or all your work to this point will be devalued. Ask questions – practice – work and you will be successful.

See you in class.

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