Recent Posts by Ian Lucas

Last Call for Revision

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. ...

2 + 0 + 1 + 7 = 10

For many years, at the start of the year, I posted a large sheet on the noticeboard in my classroom containing a 10 x 10 grid listing the numbers from 1 to 100. I invited anyone using the room to try and complete any of the numbered squares with a calculation using all four digits of the current year, and which equated to the relevant number. The rules were simple: any mathematical operation, such as addition, multiplication and powers could ...

Great Mathematicians 3 – Ada Lovelace

What an extraordinary woman Ada Lovelace was! She was born in 1815 to the poet Lord Byron and his wife Anne Millbanke, and was Byron's only legitimate child. But her parents separated when she was only a month old and she never saw her father again. She was nonetheless inspired by him, and poetry ran like a thread through her life, in spite of her mother promoting her interest in mathematics "fearing that an interest in poetry would spoil her morals." ...

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 ...

Understanding Conditional Probability

Conditional probability appears  difficult, and I think that's because it comes with yet another probability formula seemingly designed to confuse IB students! But forget the formulae for a moment, and consider these two problems: Two dice are thrown. What is the probability that: a)   The total on the dice is both greater than 9 and a double.   b)   The total is a double given that it is greater than 9? In problem (a) we have no information, so the total could be any ...

Using the TI-84 to solve equations

By Wednesday, November 30, 2016 , , , , 0

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 ...

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