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cos(2x) = 2cos²(x)-1 by the double angle formula.

Rearrange to give cos²(x) = (cos(2x)+1)/2

Integrating this gives sin(2x)/4 + 1/4x + c 

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First we rearrange the equation

y + 4x = 7     to      y = −4x + 7

So we can see that the gradient of this equation is −4.

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There are quite a few stages to this problem, so let's work through each piece of information one by one.

We know that the total number of children is 120, and 60% are Year 4s. Finding 60...