May, 2015

Conditional probability and the normal distribution

Until fairly recently, you could throw a handkerchief over the variety of normal distribution questions you might expect to see in an EdExcel S1 exam. It would be one or more of: given a mean and a standard deviation, work out the probability that the random variable is larger or

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How do I decide whether to take things away from 1 (Normal distribution)

A student asks: I’m never sure whether I have to take the number that comes out of the normal distribution table away from 1. How do you know? It’s a familiar song: you’ve worked out your $z$-score (naturally, you remember that this means “how many standard deviations you are above

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Why are there so many equations for variance?

A student asks: Why are there so many equations for the variance? In S1, depending on the board you’re working with, you might need to know three equations for variance. For listed data, it’s: $\Var(X) = \frac{\sum x^2}{n} – \left(\frac{\sum x}{n}\right)^2$ For grouped data, it’s: $\Var(X) = \frac{\sum fx^2}{\sum f}

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A circle problem that succumbs to a circle theorem

A tweet from @GregSchwanbeck some time back asked: Does square or circle have greater perimeter? A surprisingly hard prob for HS: http://t.co/vwLIs26pcC #mathchat #math pic.twitter.com/Vpjop8yU7G — Greg Schwanbeck (@GregSchwanbeck) March 16, 2015 The setup is: one side of a square is tangent to a circle, and two corners of the

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Getting your $x$s in one basket

A reader asks: I need to solve $\frac ac \frac {NP}{N_0 + N} = mP$ for $N$, and I don’t know where to start. Help! I had a maths teacher in the early 90s who loved nothing more than making the class groan with bad jokes. If she showed up

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Minecraft circles

I have a confession to make. One that will lower me seriously in the esteem of my 10-year-old nephew: I don’t really get Minecraft. Sorry, buddy. I’ve tried it. I love that you love it — honestly, creative games are awesome for your problem-solving skills and breaking down the barriers

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A great student question

Most of the time, my goal as a tutor is to help students stop hating maths and, if I’m lucky, to grudgingly accept that there are some good bits to it. I’m not here to indoctrinate anyone into becoming a mathematician unwillingly. And then sometimes, I get asked a question

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Attack of the Mathematical Zombies: Five excuses that need a bullet to the head

“Where are they all coming from?” said the first, cocking the shotgun. “I don’t know,” said the second, “but I hope you’re a good shot.” “We haven’t covered this yet.” The first zombie lumbered into view, only instead of mindlessly saying “brains!”, it mindlessly said “We haven’t covered this yet.”

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