Browsing category gcse

A student asks: upper bounds

A student asks: When you've got a value to the nearest whole number, why is the upper bound something $.5$ rather than $.4$? Doesn't $.5$ round up? So I don't have to keep writing something$.5$, let's pick a number, and say we've got 12 to the nearest whole number. $12.5$

HOW much rice?

There's a legend, so well-known that it's almost a cliche, about the wise man who invented chess. When asked by the great king what reward he wanted, he replied that he'd be satisfied by a chessboard full of rice: one grain on the first square, two on the second, four

A student asks: How do you simplify surds?

A student asks: How could I simplify a sum like $(\sqrt 3+\sqrt 2)(\sqrt 3-\sqrt 2)$? Great question! The trick is to treat it like it's an algebraic bracket, like this: $(x + y)(x - y) = x^2 + yx - xy - y^2$ But then you've got $+yx -xy$ in

Nine ways to revise for the GCSE Calculator paper

A student asks: Hi, I am struggling with trying to revise for my GCSE maths calculator mock… I was wondering if you could give a few tips on how to revise for this exam in particular. There's a commonly-held belief that the calculator paper is easier than the non-calc one,

Dealing with nasty powers

There's nearly always a question on the non-calculator GCSE paper about Nasty Powers. I'm not talking about the Evil Empire or anything, I just mean powers that aren't nice - we can all deal with positive integer powers, it's the zeros, the negatives and the fractions that get us down.

There’s More Than One Way To Do It: Direct and Inverse Proportion

$y$ is directly proportional to $x^3$, you say? And when $x = 4$, $y = 72$? Well, then. The traditional method is to say: $y = kx^3$ and substitute in what you know. $72 = 64k$ $k = \frac{72}{64} = \frac{9}{8}$ That gives $y = \frac98 x^3$. Easy enough. But

Is there a tangent rule?

There's a natural question, when you learn about the sine and cosine rules: "Is there a tan rule?" The answer to that is yes - yes, there is a tan rule. The natural follow-up is "Why don't we learn it?" Let me explain why not! Here's the tangent rule in

Is there a tangent rule?

There's a natural question, when you learn about the sine and cosine rules: "Is there a tan rule?" The answer to that is yes - yes, there is a tan rule. The natural follow-up is "Why don't we learn it?" Let me explain why not! Here's the tangent rule in

Is there a tangent rule?

There's a natural question, when you learn about the sine and cosine rules: "Is there a tan rule?" The answer to that is yes - yes, there is a tan rule. The natural follow-up is "Why don't we learn it?" Let me explain why not! Here's the tangent rule in

Two mysteries cleared up in one

Since the dawn of time, two mysteries have plagued mathematicians: a) How do you find a centre of a 90º rotation? and b) What's the 45º set square for? Imagine my surprise when I discovered that each is the answer to the other! Some facts about the centre of rotation

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