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The first thing you need to do to make this easier is to multiply out the brackets so that you can then move all the 'x' terms to one side and all the numbers to the other side. It would become: 7x=4x-32 ...

Draw a diagram breaking down 110 and 132 into their multiples (on whiteboard), e.g. 110=1110 132=1112 Circle the prime numbers, 11, and then break down the composite numbers (those that aren't pr...

a) When differentiating y, the method with each term is to 'times by the power and minus 1'. In order to apply this, we need every term to consist of a coefficient multiplied by a power of x. To start wit...

Use double angle formula to rearrange for cos2x

this gives: x/2 + 1/4sin2x + C (constant)

differentiating the equation gives dy/dx = 4x^3 - 12x^2 dy/dx = 4x^2(x - 3)

at a turning point, dy/dx = 0. Solving the equation 4x^2(x - 3) = 0 yeilds x = 0, x = 3

putting 0 and 3 back into ...