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March 29, 2024, 10:20:33 pm

Author Topic: Basic Arithmetic and Algebra in 2U: How It Can Come Back to Bite You  (Read 5520 times)  Share 

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jamonwindeyer

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Hey everyone!

By this stage many of you reading this will be preparing for your Trial exams, It's a very exciting, terrifying, and stressful time. This guide is going to be short, and it is going relax you! This is a refresher of the basic algebra you should know, and more importantly, some of the trickier things you could have to do with it in your Trial/HSC exams. Plus some personal experience to boot. Be sure to register and post any questions, tips, comments, anything below! We want to hear from you and everyone would benefit from anything you have to contribute!

So, let's start off simple! You should know how to simplify, factorise, rearrange, manipulate things to your advantage. A big part of the 2U course is manipulating numbers to get the result you want. Most of you are fairly comfortable here, so I won't cover it, but rest assured there will be around 10-15 marks devoted to this basic stuff, so practice it a little!

What I will do is an example of converting a recurring decimal to a fraction, it can be slightly trickier:

EG:Convert to a fraction.

This process is a good example of that clever manipulation I was just talking about. It should be fairly self explanatory. We let the recurring decimal be x:



The hardest part of these is knowing what to multiply by... Easy trick guys! Just multiply by 10 once for every recurring decimals!

There are so many areas to cover, most of them fairly straightforward. But these skills prove invaluable in the weird and wonderful proofs you could be asked to do. Take this one, which is actually from a uni-level pre-calculus course, but it is an awesome thing to see:

EG: Aladdin wished to marry Princess Hannah. The Sultan requested him to perform a simple task, which was to bring him grains of rice. 1 grain on the first day, then twice as many every day after that, for 30 days. So, he brought 1 grain on the first day, two grains on the second day, four on the third day, etc.

Let S be the number of grains of rice brought by Aladdin in total over 30 days. Explain why , without using any of the standard formulae for geometric progressions.


Now, this is an easy question with the formula, but without it, you might be lost as to how to approach it. But you could be given something with no formula to use at all, what would you do then? You would relax, and look at the result, and see what we can do.

We see that the result has an index with base 2 in it. Look at the question. Each day, the amount of beans Aladdin brings can be written as an index base 2! So S is:



We don't have it quite yet, but we can  try multiplying through by 2:



This is where you separate yourself from the pack. Everything before that last term on the right, can be equated to (S-1) using line A:



Read over that a few times if you need to, and please ask a question if it seems unclear! But this is just showing you that basic algebra can form tricky little questions! This wasn't really a test of index laws, it was a test of your ability to problem solve. The best way to prep for that is practice practice practice!

The last thing I want to mention is absolute values. The one thing some my students have trouble with in the first few weeks is absolute values, especially inequalities. By far, my biggest piece of advice here is to draw a number line! They will give you a better idea of what is going on. For example, consider the generic inequality x>|a|. This is how you should be thinking of that: x is further from zero than a on a number line!

On the line below, x could be anywhere in the shaded region. This clearly shows that your inequality should have two distinct regions, one for when x>a, and the other for when x<-a (half of the image gets cut off, but you get the idea  ;D). The same works in the reverse sense also. For x<|a|, you would have a single region encompassing the middle section of the line, defined by x<a and x>-a. Essentially, for every absolute value inequality, you should be doing at least two basic inequalities, which may define one or two regions. Check your answers carefully!



This guide may seem a little pointless, but trust me, these simple algebraic skills are the foundation for everything else! They MUST be developed and refined! For my half yearly exam, I got a Band E3 instead of a Band E4 result, because of a question on simultaneous equations! Not calculus, not tricky proofs, just a simple concept I hadn't revised and it caught me off guard! Don't be that person. Go back and spend just an hour doing the challenge exercises from the earlier chapters. Can you still do them?

We get so preoccupied with trig and calculus in this course, and rightfully so, they are difficult. But one look at the HSC Exam I sat, 11 marks for for basic arithmetic skills, and that's only questions with nothing to do with anything else. Just pure algebra. It's easy marks! Don't miss out on them  ;)

Be sure to pop a question below if anything in this guide was unclear, share any study tips, any tough questions, anything at all! And remember, there are heaps of awesome notes available on a whole bunch of 2U topics, available here.
« Last Edit: March 20, 2016, 07:57:02 pm by jamonwindeyer »