1. Paper: Edexcel IGCSE Further Pure Mathematics 4PM1/01, Jan 2023; 100 marks; topics: arithmetic and geometric series, algebra, polynomial roots, coordinate geometry, graphs and asymptotes, and intersections.
2. Sequences: use of known sums from specific terms to find first term; application of nth term and sum formulas for arithmetic progressions.
3. Coordinate geometry: perpendicular lines, vector slopes, distance and midpoint checks, tangent ratio for angle determination.
4. Rational functions: identification of horizontal and vertical asymptotes, solving for constant term from y-asymptote, finding x- and y-intercepts.
5. Polynomial algebra: using known factors and remainders to determine coefficients; solving cubic equations by factorization.
6. Simultaneous equations: equating a rational curve with a linear function, finding exact intersection point through substitution and solving quadratics.