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In simple differentiation, we can use the fact that if y= x^n, dy/dx is equal to nx^(n-1). In other words, multiply the x term by the power, then decrease the power by 1. Here we have 2 terms so approach ...

First, split into prime factors- 96= 2^5 * 3 and 132= 2^2 * 3 * 11 Whilst very similar to highest common factor, lowest common multiple is found by comparing the two sets of prime factors, and for each pr...

We are assuming that the sweets are selected at random. The question says that the sweets are eaten, so we are also assuming that they aren't put back into the bag. The total probability of selecting the ...

For a ball that has been thrown, it's height above the ground can be described by a quadratic equation of the time since it was thrown and gives a parabola.

The two real roots of the equation are t...

This  method will only work if your x term is divisible by 2. For example x² + 6x + 12. 

You then use the halved x term (e.g. 3x) to complete the square. The beginning of your factorisat...