1. Paper: Edexcel IGCSE Further Pure Mathematics 4PM1/01, 100 marks, 2 hours; includes algebra, series, geometry, calculus, binomial expansions, integration, and vectors.
2. Algebraic forms and surd manipulation: rationalizing denominators, expressing in standard surd form a + b√3.
3. Geometry and area: composite area derivation involving squares and rectangles, simultaneous equations solving from known total area and component area expressions.
4. Trigonometry and triangle area: non-right-angle triangle analysis using cosine rule and area formulas; use of angle and side relationships.
5. Series and sequences: geometric series with known partial and infinite sums, derivation of individual terms, difference from infinity sum.
6. Binomial and series expansion: rewriting rational functions into standard binomial forms, power series expansion, algebraic integration of expanded form to estimate definite integrals.