Search over 10,000 free study notes

One of the best ways to view dy/dx is as a fraction. When we have y=f(g(x)), we need to make a substitution u=g(x) to find dy/dx. This leaves us y=f(u) and u=g(x). Differentiating said terms leaves us wit...

The general form of factorising is that if we have ab+ac, we can rewrite this as a(b+c). We multiply each statement inside the bracket by a. So we’re effectively ripping out common terms. We are dividing ...

First, we find the form of the two fractions we're going to get. As one denominator has a power of 2, and the other a power of 1, our answer will be of the form: [(Ax+B)/(x²+1)] + [C/(x+2)]. If...

Conduction, where particles within a conductor gain energy as they heat up and vibrate more vigorously passing energy onto adjacent particles as they collide. Convection, which only occurs in fluids, as f...

First we assign, for example, that x = cost of 1 book, and y = cost of 1 apple. Then we make these into simultaneous equations, such as: 3x+2y=19 (eqn. 1) and x+5y=15 (eqn. 2). Now multiply eqn. 2 to get ...