Lesson Plan

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Lesson Plan
Grade: Date: 25/02/2026
Subject: Additional Mathematics
Lesson Topic: Solve problems involving the intersection of a circle and a straight line, including deciding whether the line is a tangent, a chord or does not meet the circle
Learning Objective/s:
  • Describe how to set up equations for a circle and a straight line to find their points of intersection.
  • Apply the discriminant of a quadratic equation to determine whether the line is a tangent, chord, or does not meet the circle.
  • Solve the resulting quadratic to obtain the coordinates of intersection points when they exist.
  • Interpret the geometric meaning of the discriminant results in the context of circle‑line relationships.
Materials Needed:
  • Whiteboard and markers
  • Projector with slides showing circle‑line diagrams
  • Graph paper and rulers for student practice
  • Calculator (or smartphone) for discriminant calculations
  • Worksheet with practice questions
  • Geogebra or similar dynamic geometry software (optional)
 Introduction:
Begin with a quick visual of a circle intersected by a line on the board, asking students to predict how many points of contact there are. Recall the standard form of a circle equation and the concept of solving simultaneous equations. Explain that by the end of the lesson they will be able to use the discriminant to classify the line as a tangent, chord, or non‑intersecting.
Lesson Structure:
  1. Do‑now (5') – students solve a short problem finding intersection points of a given line and circle; teacher checks answers.
  2. Mini‑lecture (10') – review circle equation, line forms, and substitution method.
  3. Guided practice (12') – work through the worked example together, highlighting each step and discriminant calculation.
  4. Collaborative activity (15') – groups solve one of the practice questions, then present their discriminant reasoning.
  5. Whole‑class feedback (8') – teacher confirms solutions, clarifies misconceptions, and summarises the discriminant table.
  6. Exit ticket (5') – each student writes the nature of a new line–circle pair and the discriminant value used.
Conclusion:
Summarise that the sign of the discriminant directly tells us whether the line is a chord, tangent, or misses the circle. Ask a few students to share their exit‑ticket answers for quick verification. Assign homework: complete the remaining practice questions and create a sketch of one scenario.