This is the first in a new section of videos as part of the Year 12 General Maths (Units 3 and 4) course relating to Financial Mathematics. The full title of the work is ... and wait for the length of this title ... "Combining linear and geometric growth or decay to model compound interest investme…
This is the third video on the series looking at financial mathematics for the Year 12 General Maths course at Unit 3 and 4 level. Amortisation tables seem to be really important and something which can lose students a number of marks in the end of year exam and SACs so I spend some time looking at…
This video is part of the Year 12 VCE (Units 3 and 4) General Maths course and looks at part of the content required for Networks. Dijkstra's algorithm used to be something which was confusing and had the most bizarre algorithm but not any more. This video looks at how to find the shortest part pro…
This is the second video in a series of 5 which looks at Time Series for the Further Maths Units 3 and 4 course. To be able to find trends in data it makes sense to smooth the random fluctuations. This can be done in a number of ways. The first I look at is through mean smoothing. I look at both od…
So you've woken up in the night wondering what the 68-95-99.7% rule is and why we would call a distribution normal? Well, this is going to the video for you. I take a small amount of time to talk through what a normal distribution is and why we need it. I look at standard deviations and how we can …
This video is the next in the series for the Year 12 General Mathematics course looking at Matrices. This video looks at Matrix Inverse, the Determinant and Matrix Equations. I look at what the inverse of a matrix is and how you can find it using both pencil and paper methods and a CAS. As we only …
This is the final video in the Specialist Mathematics series relating to Techniques of Integration. Although this is tailored for the Year 12 VCE Units 3 and 4 Specialist Mathematics course here in Australia, it's universally taught and should be useful. I show how the integration by parts formula …
This is the first video in the Kinematics section forming part of the Year 12 VCE Units 3 and 4 Specialist Mathematics course. Looking at the ideas behind position, velocity and acceleration. I explain the difference and look at lots of worked examples. The theory is explained in an easy to underst…
This video concluded the videos relating to Differentiation forming part of the VCE Units 3 and 4 Specialist Mathematics course in Australia (but useful throughout the world!). I take a look at what Implicit differentiation is and why we would need it. I show how to do it, with a number of worked e…
This video is another in the series which looks at how to integrate using substitution. Forming part of the Year 12 VCE Specialist Mathematics (Units 3 and 4) course, it shows how to use substitution to solve some pretty complex integrals in a much simpler way. There are lots of worked examples wit…
This video is another in the series looking at Techniques for Integration as part of the Year 12 VCE (Units 3 and 4) Specialist Mathematics course. This video looks at the great topic of Partial Fractions (one I really enjoyed at school). I explain the theory using a large number of examples which …
This video is the second in the series looking at Vectors. In this I look at how we can resolve vectors into rectangular components. It forms part of the Year 12 Specialist Mathematics (VCE) Units 3 and 4 course. I take time to explain all the theory needed with a number of well explained worked ex…
This video is a return to the idea of the quotient rule but with circular functions. As the previous video was used to recap all the work for differentiation, this one is a lot shorter (YEA!). A quick example showing how the quotient rule works moves swiftly into two examples where we use the quoti…
I have spent a lot of time showing you the theory behind the normal distribution and so I think it's been a good idea to stop and solve problems with the normal distribution. This video takes a look at the most common types of problems which are encountered with the normal distribution with a step…
How much fun can be had in one video? Lots! This video takes a look at the ways you can use to find the area under a graph. Starting with the basic consideration of finding areas of triangles (for straight line graphs) it then moves on to look at how we might find areas under curves. It start…
This video shows how to use the Quotient Rule to differentiate functions. This video takes the time to look at how the quotient rule is and how it is used. We have already looked at the chain rile which shows how to split the product of terms and differentiate them. When we divide two functions we …
We have spent a lot of video time talking about sine and cosine functions - which are really important in terms of understanding for the exams and possible SAC questions. We now take a look at the tan function in terms of what it looks like, how it can be transformed and how it can be used to help …
This video takes an exciting look at what exponential functions are. It looks at the form of the functions and how to graph them. I have a detailed look at how to transform them too. This is part of the Methods 3 and 4 course over here in Australia and it's about as exciting as Mathematics can get.
We have looked at the concepts of what exponential graphs are and how we can draw them. We have looked at how we can simplify them and now it's onto the exciting stuff to see how we can solve exponentials and graphs. I open the video with a small rant about how people who do nothing more than fly …
This video is the first in a new series of videos looking at transformation of functions. This video starts relatively simply by looking at Translation of Functions. I look at what it means to translate a function (move up, down, left or right) and how you might use algebraic methods and substituti…
This video looks comprehensively at the use and need for the discriminant in solving quadratics. The discriminant is a way to find if there is one, two or zero crossing points on the x-axis. This is a way to find if there are solutions to a quadratic equation. Solutions, in Mathematics, are simp…
This is another video in the Sequences and Finance section of the Year 11 VCE General Maths course. This video takes a look at how we can create arithmetic sequences using recursion. I look back at what an arithmetic sequence is as well as how we can now use recurrence relations to write sequences.…
This is the next video in the Year 11 General Maths (Units 1 and 2) VCE course for measurement, scale and similarity. In a previous video we looked at finding areas and circumferences of circles. Now we are going to look at arc lengths and areas of sectors. This is really finding the length of a sm…
This video looks to introduce the topic area of Integration. It's hard to find the area under a curve using basic tools. I look at how we might estimate using the left endpoint, right endpoint and trapezoidal estimate methods. I look at how to use the CAS and pencil and paper methods along with the…
So, we have learned how to complete the square, but did we learn much about why we are doing it? Well, a little bit! In this video, I look at how we can solve quadratic equations by completing the square. I look at why we want to complete the square and what it means to solve an equation. In this …
Following on from the last video, this looks at the method of solving simultaneous equations by the method of elimination.
This video reviews the work from Year 9 where we use the gradient/intercepts form and intercept form to sketch straight line graphs. We look at what a relationship is, how to tell if a point lies on a line and how to sketch straight lines, including the "special lines".
Quadratic equations are used over and over again throughout all aspects of Mathematics at Years 10, 11 and 12 and it's really important to not only know how to "solve" them but what the process of solving is really telling you. In this video, part of the Year 9 course on Quadratic Equations, I take…
This video take a look at how to create stem and leaf plots and is related to the Year 9 mathematics course. There are some examples where we look at creating a single stem and leaf plot showing how to make an unsorted and sorted stem and leaf plot. I then move on to looking at how to construct and…
This video looks at the amazing properties of parallel lines and a single transversal (a line which passes through two other lines). I look at how the angles which are created can be identified and found using the FUZX rules! Which, in real Maths speak would otherwise be known as, Vertically Opposi…
This video continues the series on Algebra and looks at what it means to substitute into an expression (or equation!) and how to find the value by using BIDMAS/BODMAS. There are lots of worked examples and lots of theory to help you completely understand why you are doing this. There is also ref…
This video looks at how to do prime decomposition which means splitting a number into the product of its primes. There is also a discussion relating to expanded notation and index form
This video will introduce you to the the ideas behind experimental probability by recapping a previous video on Theoretical Probability. And exciting stuff it is too! We do experiments to prove whether things are right or wrong. And this is also true in Mathematics.
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Specialist Maths: Units 3 and 4
This is the fourth video in the series relating to Vectors as part of the Year 12 VCE (Units 3 and 4) Specialist Mathematics course. This content is important all over the world! Looking at what vector projections are and how they might come in useful for some of the more complex problems is covere…
Specialist Maths: Units 3 and 4
This is the third video in the series relating to Vectors as part of the Year 12 VCE (Units 3 and 4) Specialist Mathematics course. This content is important all over the world! Looking at what the scalar product is (or more honestly does!) I show how we can use the dot product to help us find angl…
Specialist Maths: Units 3 and 4
This video is the second in the series looking at Vectors. In this I look at how we can resolve vectors into rectangular components. It forms part of the Year 12 Specialist Mathematics (VCE) Units 3 and 4 course. I take time to explain all the theory needed with a number of well explained worked ex…