1. Paper: Edexcel IGCSE Further Pure Mathematics 4PM1/02R, June 2023, 2-hour, 100 marks, 11 structured questions across core mathematical fields.
2. Algebra and inequalities: quadratic discriminants for distinct real roots, simultaneous inequalities solving, rational expressions.
3. Calculus and optimization: perimeter minimization using differentiation, second derivative test confirmation, motion analysis with integration.
4. Trigonometry and geometry: sector area and perimeter with radians, vector magnitude, direction, and unit vector construction.
5. Roots and transformations: manipulation of roots for quadratic equations, generating new equations with transformed roots, vector midpoint applications.
6. Series and function analysis: binomial expansion, solving for constants in rational functions, logarithmic equations, and inverse function plotting.