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Differentiate the original equation (y = x^2) to find the gradient (m) of the line which is a tangent to the curve.

Dy/dx = 2x 

Therefore m = 2

Calculate the negative reciprocal (m2) ...

From reading the question, we need to use the addition formula for sin(A+B)= sinAcosB+cosAsinB. So we need to think what are two common values for sine and cosine that we know and have exact answers for t...

Equation of a circle  ->  (x-a)² + (y-b)^2 = r²     where the centre = (a,b) and the radius = r

Thus using the equation above we can conclude that the centre is (2,-5)

The objective of the question is to find an answer to x = ?, where ? is a number.

Start by 'moving' all the x's to one side of the equals sign and all the numbers to the other. This can be done by ...

Firstly, expand out the first bracket -    4x - 8 - 2(3 - 5x)    
Then the second bracket (remember a minus x a minus = a positive) -     4x - 8 - 6 + 10x

Then finally group the like terms to...