## Get some rhythm – Some LOGARITHM!

Posted July 8, 2013 by CyberChalky
Categories: Mathematics

Logarithms are a frustrating function – the inverse of exponential functions, they are infuriatingly irritating to deal with.  But logarithms are a critical part of applied mathematics, and have been a critical tool in the mathematical kit since the dawn of mathematics (Which was when Ugg the caveman wondered how many rocks he had).

Logarithms are what you get when you find what power you must raise ten to to get another number.

The most fascinating part of history is the role of logarithms in the development of arithmetic methods. The simplest aspect is that it is simpler (and less error prone) to add instead of multiplying, so if you find the logarithm of two different numbers, the product of those numbers is equal to the sum of the logarithms. This meant, that in the age before calculators or computers, the process of multiplication was sped up and simplified by using a table of logarithms to do all calculations.

But logarithms are more than just an outdated way of speeding up arithmetic calculations – they are an important tool in graphing. By using a logarithmic scale on one or more axes, you can produce graphs that cover a broad range of numbers by compressing the axis. The graph to the left is an example of this – in one simple picture it presents the entirety of the universe – if this were linear scale, either the small items would be invisible, or the the graph would have to be so large that it is useless.

## Ohm-o-Sapiens (evolved again!)

Posted May 4, 2013 by CyberChalky
Categories: Electricity, Physics, Year 11, Year 12

The human species is continuously evolving – from the early hominids such as Homo Robustus, through the Neanderthals, and eventually Homo Sapiens. Physics students (Genus: Ohm-o-Sapiens) are clearly a new advancement in the Human species, as shown by the ability to tolerate torment provided by Physics Teachers…

OK, enough jokes – what we are doing with this post is going beyond the prior posts on electric circuit theory, and into component analysis. We have already looked at Ohm’s Law, Kirchoff’s Laws, and Thevenin’s Law – these are all based on the simple concept of simple “ohmic components”. Such circuits are relatively simple to solve (except like ones to left, and this one) – you use the rules of parallel and serial circuit elements to simplify the problem, and solve using Ohm’s Law.

Some components are not that easy – they don’t follow the simple patterns of ohm’s law. These devices do not have a constant resistance for a variety of applied voltages – their characteristic Voltage – Current graphs show a curve, and this is something you must be able to describe, analyse and discuss.

## Join the Resistance!

Posted April 26, 2013 by CyberChalky
Categories: Electricity, Year 11, Year 12

It’s time to get into the hard stuff – It’s time to join the resistance! Don’t let the current events know watt you are thinking – charge it up and…

Ah damn – I can’t come up with a pun for voltage. I’m sure one of you can – If I groan or laugh I will swear off bad puns in class for a week. That should be enough of an incentive for all of you!

Well, this post is mainly a link to a prior post, and an updated list of videos. I will add a link to some class notes shortly, but here are the two main links you need:

See you all in class!

Posted April 21, 2013 by CyberChalky
Categories: Algebra, Mathematics, Year 11

So, we’ve gone through two and a bit chapters of Mathematical methods so far, and you are beginning to think that you’ve done the worst of it – it can’t get that much harder, can it? Really?

Well, welcome to cubics, quartics and higher order polynomials – they are the big brothers and sisters to the humble quadratic, and they’d like to have a word with you about beating up on their sibling, the poor little quadratic – something about “completing your square”

On a more serious note, if you are feeling alright about algebra so far, the next section isn’t any harder – just a few more ideas – nothing new or harder than we’ve done so far, just more. Just like when we started quadratics, the first thing we do with cubics and quartics  is to identify the common pattern, and be able to factorise them directly from recognising that pattern.

Once we can do that, we will look at how you can start to graph these functions from their intercepts – but that means we need a way of finding all the intercepts. We already knew from our studies of the Null Factor Law (NFL) that the factors of a quadratic equation can give the intercept. The Remainder theorem (right now, that irritating chorus should be going through your head) allows us to find the factors by finding values for a where f(a) = 0 for a given f(x). Combining all this knowledge gives us the ability to sketch almost any graph!

## Gravity Sucks!

Posted April 5, 2013 by CyberChalky
Categories: Kinematics, Physics, Year 12

There is an unbearable pun about gravity. The fact that it is both a pun, and unbearable explains both why I know it, and why I would choose to inflict it on you. Of course, I won’t just say it, but imply that it exists – relying on the fact that right now, every bad pun about gravity is rolling through your head, and if not your fingers are twitching to Google whatever it is I am talking about – thus my purpose is achieved with minimal effort!

Regardless, the orbital movement is the final context of motion in two dimensions, our first area of study. It is clearly an outgrowth of circular motion, but it has some interesting twists of its own. For a start, the force that maintains the circular trajectory is the force of gravity – the first of the four forces of the standard model of physics. Gravity has some difference from other forces that you have thus far encountered. As an example, both Weight force (F = mg) and Elastic force (F = -kx) only involve the object that the force is affecting. Newton’s universal law of gravitation has some similarities to the weight force, but a great many more differences.

## Avoid making ERRORS in your ERAs.

Posted April 3, 2013 by CyberChalky
Categories: Assessment, General Science, Psychology, Year 10

To get the right answer, you must know how to ask the right question(s) – and psychology is all about questions  – how to ask them, what to ask, and most importantly of all, why to ask them.

Psychology will teach you about how to think – and how to understand something about the way others think. The starting point for our studies in psychology is how to approach the study of people – their behaviours &  and how the mind is related to them – in a scientific fashion. To do this, we are working toward defining and working with variables, and forming and testing hypotheses.

This process is recorded in an report called an “Empirical Research Activity” (and “ERA”), and you have to write one – just in case you weren’t paying attention for the last 10 weeks!

## Quixotic Quadratic Queries Qause Qonfusion

Posted February 24, 2013 by CyberChalky
Categories: Algebra, Mathematics, Year 11

Welcome to Mathematical Methods – a subject which will prepare you for using mathematics to analyse the world and introduce the concept of developing theoretical models to investigate potential results of decisions. It is also a subject that will require you to work hard to master the skills and techniques so that you can use them effectively.

We have already completed the simplest work of the year, revising skills which you should be familiar with from previous years of mathematics – simple linear equations, systems of functions and basic coordinate geometry. Now, we start to go further, by investigating non-linear relationships – that means all lines that can be drawn on a graph that are not straight. The simplest of these are the quadratics – which have the shape of a smile (or a frown), just like the one in graph just above.

You will have studied this last year, and you may have become quite good at factorising and sketching quadratics – which is good. If you are not so confident, you will have time to revise, but you will have to put in additional work. We will be going a lot further with quadratics over the next month, and you will need to be prepared!