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Numerical methods are particularly useful to solve complex problems which are sometimes difficult or impossible to solve analytically. It is also a quicker way of solving the problem rather than using for...

a) The answer to this question is quite simple, it is all dependent on the pupil realising that they need to use the sine rule. This rule for this triangle is: BC/sin(BAC) = AC/sin(ABC) Once they get this...

Hiya! So the very first thing we need to do is find the determinant, which is just a fancy word to describe a matrix; for a 2x2 matrix, it's equal to "ad-bc", where: (a b c d) This will give...

As the derivative of e^x is e^x, so is the integral (plus some constant). As we wish to find the value of the integral from x = 1 to x = 2, we substitute x=2 into e^x, and from that we subtract e^x with x...

x^2+5x+10 -> (x+p)^2+q (x+5/2)^2 - (5/2)^2 + 10 (x+5/2)^2 - (25/4) +40/4 (x+5/2)^2 +15/4