I thought it would be useful for A Level maths students if we compile a list of common mistakes and misconceptions that occur in pure, stats and mechanics. Please post anything that you can think of.
Here are two to start things off and I'll add more at some point:
- The standard trig derivatives that you've learnt e.g.
dxd(sinx)=cosx are only true if the angle (
x in this case) is measured in radians. So as a general rule it's best to always work in radians (especially if the question involves calculus) unless a question specifically mentions degrees. Of course if you haven't learnt radians yet then everything will be in degrees!
- For trig equations you should only divide the equation by a trig function if you have considered whether the function could be equal to 0. For example, if you have
sinxcosx+cosx=0 and you divide by
cosx you will get
sinx+1=0 but you will lose the solutions for when
cosx=0. Normally it's best to factorise instead of dividing, so here you would get
cosx(sinx+1)=0. This doesn't just apply to trig equations e.g.
x2+x=0⇒x+1=0 but it's common for the mistake to occur with trig equations.