1. Paper: Edexcel IGCSE Further Pure Mathematics 4PM1/01, 100 marks, 2 hours; topics: integration, quadratic inequalities, series convergence, coordinate geometry, polynomial roots.
2. Integration: definite integral of trigonometric function, exact value in simplified form.
3. Algebraic manipulation: completing the square, inequality solution from transformed quadratic, rational root factor theorem, remainder theorem application.
4. Geometric and arithmetic series: term ratio and sum to infinity, solving for unknown terms, convergence condition.
5. Graphical solution: linear inequality systems, region shading, optimization of expressions over defined region.
6. Polynomial algebra: finding coefficients using factor and remainder conditions, solving cubic equations via factorization.