Surds II

Grade 12 · Mathematics

Semester 1 | Period 1 | Week 4

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Subject: Mathematics

Semester: 1

Period: 1

Week: 4

WEEK 4

Class: Grade 12
Age: 16 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Surds II
Focus:

  1. Conjugate of binomial surds
  2. Simplification of surds including the difference of two squares in the denominator
  3. Application to solving triangles involving trigonometric ratios (30°, 60°, 45°)
  4. Evaluation of expressions involving surds

 

SPECIFIC OBJECTIVES:

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

  1. Conjugate binomial surds using the difference of two squares.
  2. Simplify surds with denominators involving differences of squares.
  3. Relate surds to trigonometric ratios, including sine values of special angles.
  4. Apply surds to solve triangles with trigonometric ratios for 30°, 45°, and 60° angles.

 

INSTRUCTIONAL TECHNIQUES:

  • Question and answer
  • Guided demonstration
  • Discussion
  • Practice exercises
  • Real-life applications (trigonometric ratios)

 

INSTRUCTIONAL MATERIALS:

  • Whiteboard and markers
  • Flashcards illustrating trigonometric ratios and surds
  • Worksheets for conjugation and simplification exercises
  • Trigonometric ratio charts

PERIOD 5: Solving Triangles Using Trigonometric Ratios

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Explains how surds are used to solve triangles, particularly using the sine and cosine values for special angles.

Students listen attentively and understand the practical application of surds in triangle solving.

Step 2 - Solving Triangles

Demonstrates solving a right triangle with known angles of 30°, 60°, and 45° using trigonometric ratios involving surds.

Students observe and follow along, solving their own triangles based on the given information.

Step 3 - Guided Practice

Provides several examples for students to solve triangles using the known sine and cosine values for 30°, 45°, and 60°.

Students work individually and in pairs to solve triangle problems, seeking guidance as necessary.

EVALUATION (5 exercises):

  1. Solve a triangle with a 30° angle using trigonometric ratios.
  2. Find the missing side of a right triangle with a 45° angle using surds.
  3. Solve a triangle with a 60° angle.
  4. Calculate the missing angle of a triangle using trigonometric ratios.
  5. Solve a triangle with a 30° and 60° angle.

CLASSWORK (5 questions):

  1. Solve for the unknown side in a triangle with a 45° angle.
  2. Find the angle in a triangle with known sides using surds.
  3. Solve for the hypotenuse of a triangle with a 30° angle.
  4. Find the length of a side in a triangle with a 60° angle.
  5. Use surds to solve a triangle with a 45° angle.

**ASSIGNMENT (5 tasks):

**

  1. Solve for the missing side of a triangle with a 30° angle.
  2. Find the missing angle of a triangle with known sides using surds.
  3. Solve a triangle with a 60° angle using trigonometric ratios.
  4. Use surds to find the hypotenuse of a triangle with a 45° angle.
  5. Calculate the length of a side in a right triangle with a 30° angle.