Analytical Geometry
Gr 12

The Grade 12 Analytical Geometry module builds on the coordinate-geometry foundations developed in earlier grades and introduces more advanced techniques for analysing geometric relationships on the Cartesian plane. This chapter strengthens algebraic precision, geometric reasoning, and problem-solving skills, all of which are essential for senior-phase mathematics.

Learners revise key concepts such as distance, midpoint, and gradient before progressing to more sophisticated applications. The lessons cover equations of straight lines, determining angles between lines, and analysing parallel and perpendicular relationships using algebraic methods. Students also explore the equation of a circle in standard form, identify its centre and radius, and solve problems involving tangents, intersections, and geometric constraints.

By the end of this module, learners will be able to apply analytical geometry techniques confidently, interpret and construct equations for geometric objects, and solve multi-step problems involving lines and circles—skills that are vital for Grade 12 examinations and for future mathematical studies in fields such as engineering, computer science, and the physical sciences.