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.