A-Level Further Maths · Further Pure
Maclaurin Series
What is it
A Maclaurin series expresses a function as an infinite sum of terms calculated from its derivatives at x = 0, providing a polynomial approximation that gets more accurate the more terms are included.
Why it matters
Maclaurin series are how calculators and computers actually calculate values like sin(x) or eˣ internally — reducing a complex function to simple arithmetic operations that a machine can compute quickly.
Exam tip
Learn the standard Maclaurin series for eˣ, sin(x), cos(x) and ln(1+x) by heart — deriving them from scratch under exam time pressure wastes valuable time that's better spent applying them to the actual question.
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