Topics
This video will answer all your questions about translations. It looks at how graphs are translated using graphical means and algebra. It starts with some easy examples before heading onto more complex ones. This is a video of the Mathematical Methods Units 3 and 4 course here in Australia, but it's equally suited for any other Mathematics course in the world. I hope you enjoy its content.
This video will answer all your questions about dilations. It looks at dilations away from the x-axis and y-axis and how we can tell which is which. It looks at simple examples using an ordered-pair and then moves onto showing how we can use algebra to help us find equations of transformed functions. Finally, I take a look at how to reverse the process as this is an important skill used in exams. So much fun and learning in such a short video! Enjoy.
This video will tell you everything you need to know about Reflections in terms of transformations. This is the third in the series and builds on the work being followed for Mathematical Methods Units 3 and 4. I look at what a reflection is (and explain it in terms of the x-axis and y-axis) and then look at examples where I reflect a single point and then use algebra to help find the function for a reflection. A couple of shortcuts later and I'm done!
Do you wonder what it means to combine transformations? Me too! Well, at least I did until I created this video which builds on the work we have already been doing in Methods 3 and 4. This video takes a look at how we can now combine Translations, Dilations, and Reflections to create some awesome mappings. I use three methods to show how this works; algebra, shortcuts and sketching. All examples are well explained and relevant to the course and the VCE exam at the end of the year.
This video looks at how you can find the transformations which map one function onto another. It looks at many ways to be able to do this but favours the algebraic method. I take a look at graph sketching and just looking at the functions to try and work them out. I look at the specific language you need to use and how to ensure that you interpret the transformations in the correct way. This is part of the Mathematical Methods Units 3 and 4 course.
This video has to be one of the hardest I've ever done! 20 minutes of end footage took over an hour to record! But ... it's here and it's not bad! It takes the time to show you how to put all the knowledge we have gained so far about Dilations, Reflections and Translations and functions to sketch graphs. This takes a base graph and, through a series of intermediate sketches, builds up the graph of the final functions looking at Dilations, Reflections, and Translations. There are a number of examples and some trick questions thrown in to show how examiners like to trick people.
This video looks at how we can use the transformations we have been looking at to move power functions. This chapter on transformations of power functions with positive integer index is from the Mathematical Methods 3 and 4 course. It has a number of worked examples and all the relevant theory is explained in an interesting and informative way. You've tried the rest, now try something which is useful!
This video takes a look at how to determine the rule for a function from its graph. When a question gives you the general form of a graph, it's quite simple to find the actual equation. In many cases, all they need to give you is a couple of coordinates. There are a number of examples used where the "general form" for a function is given and some helpful information and, using simultaneous equations, you find the values of some missing pronumerals. This is part of the Methods 3 and 4 course.
This is possibly the longest video I have ever recorded! But it's probably needed as there is a lot which needs to be covered to make sure we understand not only the theory but how to apply it to the many different types of questions which can be asked with matrices and transformations. I start by looking at how we have been used to seeing transformations and then look at how we can express these same transformations with matrices. Before getting too excited, I take a look at how to multiply matrices together. This allows me to speed through the rest of the content (LOL). The video moves on to look create each of the matrices which define the transformations. I take a short time to look at how to create two of the six and leave the rest up to the reader. I finally look at how to apply the theory to a number of "standard questions" before moving on to showing how the theory can be used to answer past exam questions from VCAA Methods exams. The two exams used are 2016 and 2017. I hope the video is useful!
Select a topic
These are the videos which are available in each chapter. You will notice that some are free and some are for subscribers only. Making and hosting these videos costs a little bit of money. To help pay for the hosting fees I have no choice but to hide some of the videos and make them for subscribers only.