Further Mathematics - Senior Secondary 2 - Roots of Quadratic Equation II

Roots of Quadratic Equation II

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TERM: 1ST TERM

WEEK: 2
Class: Senior Secondary School 2
Age: 16 years
Duration: 40 minutes of 4 periods
Subject: Further Mathematics
Topic: Roots of Quadratic Equation II
Focus: Conditions for the given line to intersect a curve, be tangent to a curve, or not intersect a curve. Solution of problems on roots of quadratic equations.

 

SPECIFIC OBJECTIVES:

By the end of the lesson, students should be able to:

  1. Identify and understand the conditions for the quadratic equation to have equal roots, real roots, or no roots (complex roots).
  2. Solve problems based on the roots of quadratic equations.
  3. Determine when a line will intersect, be tangent to, or not intersect a curve.
  4. Apply the discriminant in solving these conditions.

 

INSTRUCTIONAL TECHNIQUES:

  • Question and answer
  • Guided demonstration
  • Discussion
  • Practice exercises
  • Real-life problem-solving
  • Visual aids (charts)

 

INSTRUCTIONAL MATERIALS:

  • Whiteboard and markers
  • Charts showing conditions for lines to intersect a curve, be tangent to a curve, or not intersect a curve
  • Graphs for visual representation of quadratic curves
  • Practice worksheets

 

PERIOD 1 & 2: Conditions for Intersection, Tangency, and Non-Intersection

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1: Introduction

Recap the previous lesson on quadratic equations and introduce the concept of intersection, tangency, and non-intersection of lines with curves.

Students listen attentively and ask questions for clarification.

Step 2: Conditions for Equal Roots

Explain the condition for equal roots (discriminant = 0). Use a visual of a curve and a line that touches the curve at exactly one point.

Students observe the explanation and take notes.

Step 3: Conditions for Real Roots

Explain the condition for real roots (discriminant > 0), where the line intersects the curve at two distinct points.

Students ask questions and discuss the condition for real roots.

Step 4: Conditions for No Real Roots

Explain the condition for no real roots (discriminant < 0), where the line does not intersect the curve, and the roots are complex.

Students listen carefully and take notes on the condition for no real roots.

Step 5: Demonstration

Use charts to show visual representations of the line intersecting, being tangent to, or not intersecting the curve.

Students examine the charts and engage in a discussion about how the discriminant affects the intersection type.

NOTE ON BOARD:

  • Equal Roots: Discriminant = 0
  • Real Roots: Discriminant > 0
  • No Real Roots (Complex Roots): Discriminant < 0
  • Visuals of the conditions (curve intersections, tangency, etc.).

 

EVALUATION (5 exercises):

           1. What is the condition for a quadratic equation to have equal roots?