S.6 Pure Mathematics Recess Term Assignment: Algebra, Trigonometry and Analysis

This is a recess-term assignment for Senior Six pure mathematics learners. The algebra section covers common roots of quadratic equations, solving exponential, polynomial, surd and simultaneous equations, row reduction to echelon form, and relationships between the roots of cubic equations. It also covers repeated roots, roots in arithmetic or geometric progression, the remainder and factor theorems, and proofs about ratios. Further questions deal with loci on Argand diagrams, tangents to curves, areas between curves, differentiation from first principles, particle motion, integration and small changes. A trigonometry section covers identities, compound and multiple angles, the R-form and solving equations. The paper is useful for revision during the holidays.