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How you should approach a question of this type in an exam Say you are given two lines: L 1 and L 2 with equations and you are asked to deduce whether or not they intersect. For example: L 1: r 1 = (a 1 ,b 1...

We label each equation 3x + 4y = 5 (1) 2x – 3y = 9 (2) We now want to get rid of one of the variables (x or y). Lets get rid of x: We need (1) and (2) to have the same number of x's so we multiple (1) by 2 a...

Here we will use: cot(x) = cos(x)/sin(x) cosec 2 (x) = 1 + cot 2 (x) Chain rule : dy/dt * dt/ dx = dy/ dx Product rule : d/dx (u v) = u dv/dx + v*du/dx x = cot(y)= cos(y)/sin(y) dx/dy = -cos(y) ( cos(y) / si...

dy/dx represents the gradient of a curve. The d represents an infinitesimally small range so it is essentially as though you are doing change in y over change in x like you would for a y = mx +c graph but ov...

Say we have an equation with the product of two subjects in the form f(x) = u(x)v(x). Differentiating is simple, we would just multiply the differential * of u(x) by v(x) and add the differential of v(x) tim...