Pearson International A Level Further Mathematics: FP2 Further Pure Mathematics 2

FP2 is an externally assessed modular unit used within Pearson Edexcel International A Level Further Mathematics. The current Mathematics, Further Mathematics and Pure Mathematics specification is Issue 3. This note follows the official FP2 order and keeps qualification cash-in choices separate from the mathematical content: your centre must still confirm that the unit combination is eligible for the award you intend to claim.

Official unit scope

1. Inequalities, series and recurrence relations.
2. Further complex numbers, de Moivre's theorem and roots.
3. First- and second-order differential equations.
4. Maclaurin series and approximation.
5. Polar coordinates and areas.

The specification assumes prerequisite knowledge stated for the unit, so later-unit questions may combine earlier methods without re-teaching them. Treat the list above as an integrated toolkit. A question can begin in one topic and finish in another, such as using algebra to form a model, calculus to optimise it and a graph to interpret the result.

Core reasoning and methods

• When solving a recurrence, distinguish a closed form from a limiting value and check the conditions for convergence.
• Use de Moivre's theorem to move between powers and multiple angles, while retaining all roots over a full turn.
• For a differential equation, classify order and form before choosing complementary-function and particular-integral methods.

Write mathematical arguments so another reader can reproduce every transition. Define symbols that are introduced, preserve exact values until a decimal is requested, and place restrictions beside the step that creates them. Calculator use can support arithmetic, graph exploration and checking, but it does not replace a proof, derivation or required chain of working.

When a model is used, state the simplifying assumptions and interpret the answer in the original setting. A mathematically valid root may be inadmissible because it lies outside a time interval, represents a negative length, violates a probability range or conflicts with a geometric domain. The final check is therefore both algebraic and contextual.

Worked example

For z^3 = 8, write 8 as 8(cos 0 + i sin 0). The cube roots have modulus 2 and arguments 0, 2pi/3 and 4pi/3. Hence the roots are 2, -1 + square root 3 i, and -1 - square root 3 i. Listing only the principal root loses two solutions. The three points form an equilateral triangle centred at the origin, which is a useful geometric check. Cubing each root returns modulus 8 and an argument equivalent to zero modulo 2pi, confirming completeness.