A Year 12 Pure Mathematics lesson on Coordinate Geometry and the Circl

A Year 12 Pure Mathematics lesson on Coordinate Geometry and the Circle, designed for students in England. It develops students’ understanding of gradients, distance, midpoint, circle equations, intersections, tangents and normals through explanations, diagrams, worked examples and interactive activities. What you get A recap of essential coordinate geometry knowledge Quick diagnostic quizzes on gradients and algebra Learning objectives and key vocabulary Distance and midpoint formulae Rules for parallel and perpendicular lines Equations of circles centred at the origin and at ((a, b)) Completing the square to identify a circle’s centre and radius Intersections between straight lines and circles Tangents and normals to circles Worked examples and misconception checks A video-based explanation Ordering and multiple-choice activities An exam-style mastery task Summary Students begin by revisiting gradients and perpendicular lines before learning how to calculate distances and midpoints. They then explore the standard and general equations of circles, including how to complete the square. The lesson progresses to finding intersections, constructing tangent equations and identifying normal lines. It concludes with interactive checks and an exam-style task that brings the techniques together.