Students develop fluency with complex numbers (imaginary units, conjugates, roots of quadratics/cubics, Argand diagrams, loci) and begin algorithmic thinking (bubble sort, quick sort, bin‑packing, order of algorithms).
Graph theory is introduced, including modelling with graphs, special graph types, matrix representations, and core decision mathematics ideas.
Formal assessment through baseline testing ensures readiness and identifies gaps early.
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Students study matrices in depth (multiplication, determinants, inverses, solving simultaneous equations) alongside linear transformations (2D and 3D, inverses, compositions).
These ideas are linked to coordinate geometry, including parametric equations, parabolas, hyperbolas, tangents, normals and algebraic/geometric inequalities.
This term consolidates algebraic structure and geometric reasoning.
Each topic will be tested through a 50 minute assessment
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Students deepen proof techniques (induction, divisibility, matrix proofs) and apply optimisation via linear programming, including graphical methods, integer solutions and optimal points.
Vector geometry in 3D is introduced: equations of lines and planes, scalar products, intersections, angles, and perpendicular distances.
Term assessments evaluate both reasoning and application.
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Students explore volumes of revolution, including compound and modelled volumes.
Decision mathematics continues with critical path analysis (CPA): early/late times, floats, Gantt charts and resource histograms.
Vector calculus extends to vector products, areas and volumes (scalar triple product).
Differential equations (first‑ and second‑order) are introduced for modelling.
Each topic will be tested through a 50 minute assessment
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Students revisit and extend complex numbers through exponential form, De Moivre’s Theorem, nth roots, and geometric interpretations.
Polynomial theory progresses to quartics, expressions and transformations of roots.
Decision mathematics includes planarity algorithms, Floyd’s algorithm, and extensive work on the Travelling Salesman Problem.
Each topic will be tested through a 50 minute assessment
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Students study series (method of differences, Maclaurin series, series expansion of compound functions).
Hyperbolic functions and polar coordinates are introduced, including curve sketching and equations.
Mock Exam
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