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Suppose you have 2 functions: f(x) = 3x², g(x) = log₃(x). These are arbitrary, any functions would work. Evaluate f(g(x)): let y = log₃(x) ( = g(x) ), then f(g(x)) = f(...

The most important thing to remember when differentiating implicitly is that y is a function of x. Rewriting y as y(x) often makes it much clearer. For example, evaluate d/dx (y²): using the...

First, we need to find the value of t when x = 6p°C. We are told that after t minutes the temperature, x, will be 60°C; so we can insert 60 into the equation for x: 

60 = 15 + 70e^(-t/40)...

Ah yes, the question which haunted my years of study, particularly during GCSE and A Levels.

At this stage, many exams are ‘open book’ - that is, you can take either a blank or highlighte...

In chemistry if a substance is oxidised it loses electrons in a reaction.

If a substance is reduced it gains electrons in a reaction.

A reaction that has both oxidation and ...