Search over 10,000 free study notes

Test factors of -3 to find a root for the equation. For example, try 1, 1^3+3*1^2-1-3=0, so 1 is a root, and (x-1) is a factor. Now it's known that: (ax^2+bx+c)(x-1)=x^3+3x^2-x-3. By comparing coefficient...

In order to find the intercepts of this curve, we first need to factorise the quadratic equation. We need to find 2 numbers that add together to equal -5 and those two same numbers multiply together to e...

Thinking of sine and cosine as ratios of side lengths in a right angled triangle, sin(x) = o/h and cos(x) = a/h, so the sin(x)^2 + cos(x)^2 becomes (o^2 + a^2)/h^2. By Pyhtagoras, o^2 + a^2 = h^2, so we g...

Often, the compound angle formulae can seem quite offputting, especially since exam pressures can mean the random "R" at the front of an angle addition formulae appears confusing. However, findi...

First we calculate du/dx = -2x and rearrange to get dx as the subject, dx=du/(-2x). Now we change the limits of integration because we are now integrating with respect to u. So the bottom limit will be u(...