I have just returned from teaching on an OSC revision course at the Anglo-American school in Moscow, and was impressed by the focus of the students there towards revision, and how well they were able to sustain that focus over a fairly gruelling week. By the time this blog is published I hope to have seen some of you at the Oxford revision courses as well; my aim, and that of all the teachers on OSC revision courses, is to ...

## Puzzle time again

Last year I posed three mathematical puzzles in a blog. This time there's just one, but don't just read it and then look at the answer - it's a really good puzzle to spend some time trying to solve; most people give up, and yet when you see the solution, it's surprisingly straightforward. And please note: there are no catches, no tricks, no sneaky wordplay; the puzzle is exactly as I present it. Four people are being chased by a dragon. ...

## Understanding logarithms

A popular topic on OSC revision courses is logarithms. I usually start by asking who knows what a logarithm is, to be met by most of the class staring at their fingernails! To fully comprehend the laws of logarithms, and how to use them, it really helps to start with a clear understanding of the basics: and as long as you can cope with indices (powers), logs follow closely behind. A logarithm is really just a power. If I asked you: ...

## Bubble sort

Suppose you want to buy a new phone accessory online. You go to a search site and it finds 100 retailers stocking the accessory, and offers to sort them by price. Or you've got a list of 1000 names on a spreadsheet which you want to sort alphabetically. Have you ever wondered how a computer carries out a sort? Such a problem can be solved using an algorithm which is simply a set of simple, unambiguous instructions which will lead to a solution. ...

## The Hailstone Sequence

Follow this rule to generate a sequence of integers: Choose any integer n as the first term of the sequence If n is even, divide it by 2 to get the next term. If n is odd, multiply it by 3, add 1, and then divide by 2 to get the next term. In other words, if uk is even, uk+1 = uk/2; if uk is odd, uk+1 = (3uk + 1)/2. For example, if u1 = 14, subsequent terms are 7, 11, 17, 26, 13, 20, 10, 5, ...

## Try these New Year Resolutions…

The five mathematical resolutions I have suggested below are, unlike some New Year Resolutions, very achievable! But you do have to stick with them if you are to get the benefit. 1. I will know my times tables up to 12 by the end of January. Does that sound a bit beneath you? It isn't - many students find themselves doing questions slower that they should - or getting wrong answers - because their recall of simple multiplications is poor. Don't ...

## Using the TI-84 to solve equations

You must have a graphic display calculator (GDC). For HL and SL exams the GDC can only be used in Paper 2, but you will require it for both papers if you are following the Studies course. But don't wait until the exams are close before practising the GDC functionality: you need to do this throughout the course so that you can use it to maximum effect in the exams. Whatever level you are taking, it is almost inevitable that you ...

## Have you ever thought about… zero?

I expect most of you are familiar with Roman numerals. For example, V represents five, I represents one, so seven is written as VII. The full set is: 1 I 5 V 10 X 50 L 100 C 500 D 1000 M The key difference between the Roman system and our number system is that the position of a number makes no difference - X represents 10 wherever it appears. So, translate LXXV11 ..... the answer is 76. (The system did change over the years so that position had some relevance. For example, instead of writing ...

## Increase your marks – avoid these common errors…

Let's face it: there will almost certainly be questions, or parts of questions, in your exam papers that you just can't do. Maybe you've forgotten the method, or the algebra is too hard, or you don't understand what is being asked, or you simply get stuck. OK, so you probably won't get 100%. But there are also lots of very common slips which lead to unnecessary marks being lost; do your very best not to fall into these numeric and ...

## Great Mathematicians 2 – Rene Descartes

Descartes was born in La Haye en Touraine, in France, in 1596. However, he spent much of his life in Holland where he found the more liberal environment conducive to his philosophical views. Although best remembered as "the father of modern philosophy", whose work is still the basis of much philosophical discourse, he was also very active as a scientist and as a mathematician. His main focus in mathematical thought was to try to combine algebra and geometry. In this he ...