Revision Tips for GCSE/IGCSE Maths Exams 4:Maths Facts (GCSE Higher Level)


Mathematical Facts to Memorise (GCSE Higher Level)

If you are taking GCSE Mathematics at Higher Level there are a few more mathematical facts that you need to know in addition to all those for Foundation level. The good news is that most of these are given to you on the formula sheet so make sure that you familiarise yourself with it and have a copy to hand when working through past papers.  The main ones you need to memorise are listed below along with a few hints on how to remember them.

Trigonometry for right-angled triangles

$ \sin \theta = \frac{opp}{hyp} $ $ \cos \theta = \frac{adj}{hyp} $ $ \tan \theta \frac{opp}{adj}$

These can be remembered by the nonsense word SOHCAHTOA or by an acronym such as “Silly Old Harriet Chased A Horse Through Our Attic.”

Arc Length and Sector Area for Circles

These are just the fraction of the circle part you want (given by the angle/360) multiplied by the full circle formula.

Arc length = $\frac {\theta}{360} \times \pi D$

Area of Sector = $\frac {\theta}{360} \times \pi r^2$


If $A$and $B$ are mutually exclusive, then the probability of $A$ or $B$ occurring is $P(A) + P(B)$, whereas if $A$ and $B$ are independent events, the probability of $A$ and $B$ occurring is $P(A) \times P(B)$

This can be memorised as A or B = add, A and B = multiply

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