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when integrating with the limits, you substitute in the two limits into the integral and then take them away. As both will have added the constant 'c', you are taking c away from c and so cancel out, so i...

F(x+2) is simply F(x) but whenever you see an 'x' replace it with 'x+2'. So when x is say 3, F(x) is F(3) and F(x+2) is F(5). If we draw this out on a graph, we see that this has the effect of shifting th...

Finding what Emma paid for her radio £78 / 1.3 = £60 (M1) (A1)

Finding what percentage of £80 that is £60 / £80 = 0.8 or 80% (M1)

Recognising the discount is 20% ie. 1-0.8=0.2 (A1)

If the ratio is 2 : 3 then in a class of 5 there would be 2 boys and 3 girls. 

So we can say that 2/5 of the class are boys and 3/5 of the class are girls. 

And we know that to calculate 3/5...

y = 2x + 5 y = 4, therefore 2x + 5 = 4 2x = 1 x = 1/2