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This video is the start of the new topic for Further Mathematics Units 3 and 4 relating to modelling growth and decay using recursion. This video is an introduction to the idea of sequences. It looks at the language used and sets the scene for the next video which looks at recurrence relationships.
This video continues looking at the work for the Further Mathematics Units 3 and 4 course. In the previous video, we looked at sequences and what they were and how to create them. This video looks at how we can write sequences in terms of a recurrence relation. The video takes time to explain what the terminology means and how to use it. Example questions are worked through and related back to the theory.
This video looks at modelling linear growth and decay. In previous videos, we have looked at what a sequence is and how we can describe such a sequence as a recurrence relation. It becomes clear, that the basic form of a recurrence relation can be used to describe both growth and decay. The only thing which changes is a positive and negative sign. Looking at financial mathematics we see that we can use a simple formula to find the growth and decay needed per year. I also look at flat rate depreciation and unit cost depreciation and how these can be calculated with lots of worked examples!
This video forms part of the Further Mathematics course and, more specifically, the Core section. Building on previous videos, we now look at how we can make rules for linear growth and decay which move away from the simple term-to-term methods and onto the more complication, "If I know the start term, the payments made and the number of payments, can I go straight to the answer without having to write all the terms out?". I look at a number of examples on how to create the rules and how to apply them to questions. It's an awesome video!
This video continues the series on Further Mathematics Units 3 and 4 and the core data sections of the course. Previous videos have looked at the ideas of linear growth and decay where we add the same amount on each time period. Whilst easy, this isn't representative of most things in life! Paying money into an account, we would like to get interest and interest on the interest! Hence, we need to continue a model where things grow in ways which aren't linear. This video looks at models where, to go from term-to-terms we multiply (or divide) rather than add or subtract. I hope it's useful!
This video is a part of the Further Maths Units 3 and 4 course and completes the part of the course dealing with recursion. Having spent a lot of time looking at how we can use recursion to create sequences, we're going to draw the work together and look at how we can create one formula to allow us to find any term of a geometric sequence. Lots of worked examples are included to demonstrate how awesome this one formula can be.
This video is part of the Further Maths Units 3 and 4 course and completes this section of the course. Looking at the difference between nominal and effective interest rates, there are a number of examples give of what a nominal rate is, how to convert a per annum interest rate to monthly/quarterly/weekly etc. I look at what effective interest rates are with a detailed look at how to calculate them by hand and using the CAS. This video does all it can to help you understand this fascinating and very "real world" topic.
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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.