Recent Posts by Ian Lucas

It’s all in the detail

Mathematics, as you will know from Theory of Knowledge, is at the top of the tree of knowledge. It is self-referential - that is, its theorems do not need to be proven by reference to the real world, but instead by starting with other axioms and theorems. Of course, maths has many real-world applications, and if you are starting out on the new Applications and Interpretations course, then you will spend a lot of time solving real-word problems. Many of the ...

Need help with specific topics? Check these blogs

Over the past few years I have written blogs for IB students on a wide range of mathematics-related topics. Some of these blogs have covered specific areas of syllabus content where I know students can have difficulties. With many of you either at the start of your diploma course, of halfway through, this seems like a good moment to help you find them. Quadratic factorisation can cause some head-scratching, although if you are following the new Applications and Interpretation course you ...

The new IB Diploma Maths syllabus

All IB Diploma students have to follow a maths course at either standard or higher level. Until now, there were three choices: Maths HL, a tough(ish) course for good mathematicians; Maths SL, better for those who didn't want the standard of maths required at the higher level, but still needed, or enjoyed, a course with a reasonable level of mathematical content; and Maths Studies SL, for those, frankly, who weren't mathematically orientated, and which contained topics such as financial maths ...

Optical Illusions

There are many types of optical illusion but, in every case, the brain is being fooled by what the eyes see. In a short blog such as this I can only show a small set of examples from a limited number of categories but, if you are as fascinated by these as I am, a short web search will reveal countless more. It's also the case that some optical illusions can only be created using paper, and won't work on-screen. Illusory ...

Pythagorean Triples

We are all familiar with Pythagoras' Theorem: that if a triangle with sides of length a, b, and c is right-angled, then a2 + b2 = c2. (You can find a proof of the theorem in an earlier blog here). If the sides all have integer values, then the numbers a, b, c form a "Pythagorean triple" - the simplest of which is 3, 4, 5 since 32 + 42 = 52. Further triples can be formed by simple multiplication: thus, 6, 8, 10 ...

An Easy Mathematical Trick

Start by writing the number 1089 on a piece of paper and put it in your pocket. Now get someone to choose a three digit number where the last digit is at least 2 less than the first digit. Turn it round to form a new three digit number, then subtract it from the first one. For example, 481 − 184 = 297. Now turn the new number round to form a fourth three digit number, and add it to the third. 297 + ...

Hypothesis testing made easy

Carrying out a hypothesis test often causes confusion. Here's how it works. Some hypothesis tests start with a known fact, such as "25% of patients treated for a particular disease will suffer side effects." A drug company may then claim that "a new treatment reduces the number of patients suffering side effects." The original figure, the status quo, is known as the "null hypothesis" and given the symbol H0. The new claim is called the "alternative hypothesis" and given the symbol ...

Does division by zero = infinity?

Why should it? Well, try this: 5 ÷ 10 = 0.55 ÷ 1 = 55 ÷ 0.1 = 505 ÷ 0.01 = 5005 ÷ 0.001 = 5000 As we divide by smaller and smaller numbers the result gets ever bigger. Logically, then, as the divisor tends to (ie gets closer to) zero, so the result tends to infinity. But this is not the same as saying that division by zero actually is infinity, is it? What about drawing a graph with ...

How to revise for your Maths exam…

Last month I made some suggestions for a revision plan. Now, having decided you're going to spend a 3 hour session revising Maths, how should you set about it? Since the only thing you will be asked to do in the exam is answer Maths questions, then surely the best way to revise is ... do lots of past paper questions! And you need to have the answers, or the mark scheme, to hand. But it's what you learn from answering ...

Taking your IB Diploma? Here’s a revision plan…

I don't want to be too prescriptive about how you should revise – everyone's different, everyone remembers stuff in different ways – but you should definitely prepare a revision plan. If you don't, then it will be a matter of luck whether or not you'll be ready in time for the exams. Most of you will have at least some holiday time before the exams, and it's imperative you make the most of it – you're on your own, and it's ...

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