Application of Surds to Trigonometry Ratio and Trigonometry Graph SS3 Mathematics Lesson Note

SPECIFIC OBJECTIVES: At the end of the lesson, students should be able to:

1. Define surd
2.   Define rational and irrational numbers
3.   Identify rational numbers and irrational numbers
4.   State the rules of surd

 INSTRUCTIONAL RESOURCES: A chart showing rational and irrational numbers 

PRESENTATION: 

STEP 1: Identification of Prior Ideas

Mode: The entire class

Teacher’s activities: The teacher asks students to define rational and irrational numbers

Students’ activities: Students respond to the teacher’s questions as follows  

Rational numbers: are those numbers that can be expressed in the form of p/q where p≠0. It is also a fraction that will give an exact value without approximation e.g. 3/1, 2/5, 1/2, √100, etc.

Irrational numbers: are those numbers whose values have no ending.

Irrational numbers are also all the non-perfect square values e.g. √2, √3,√7, 1/3, 1/7, etc. 

STEP 2: Exploration

Mode: Entire class

Teacher’s activities: The teacher asks the student to give more examples of rational and irrational numbers 

Students’ activities: Students responses to the teacher’s questions 

STEP 3: Discussion

Mode: Entire class

Teacher’s activities: The teacher defines the term surd as follows 

SURD: Is the square root of non-rational numbers eg √5, √3,√7, etc.

RULES OF SURD:               

Rule 1:

a×b=a×b

Example:

To simplify √18

18 = 9 x 2 = 32 x 2, since 9 is the greatest perfect square factor of 18.

Therefore, √18 = √(32 x 2)

= √32 x √2

= 3 √2

Rule 2:

ab=ab

Example:

√(12 / 121) = √12 / √121

=√(22 x 3) / 11

=√22 x √3 / 11

= 2√3 / 11

Rule 3:

ba=ba×aa=baa

You can rationalise the denominator by multiplying the numerator and denominator by the denominator.

Example:

Rationalise

5/√7

Multiply the numerator and denominator by √7

5/√7 = (5/√7) x (√7/√7)

= 5√7/7

Rule 4:

ac±bc=(a±b)c

Example:

To simplify,

5√6 + 4√6

5√6 + 4√6 = (5 + 4) √6

by the rule

= 9√6

Rule 5:

ca+bn

Multiply top and bottom by a-b √n

This rule enables us to rationalise the denominator.

Example:

To Rationalise

32+2=32+2×2−22−2=6−324−2

=6−322

Rule 6:

ca−bn

This rule enables you to rationalise the denominator.

Multiply top and bottom by a + b√n

STEP 4: Application

Mode: Individual

Teacher’s activities: The teacher asks the student to simplify the following single surd to non-single surd  

1.     √20    2)    √12  3)  √18

Students’ activities: Students solve the following questions 

1. √20 = √4𝑋5          2√5 2. √12 = √4𝑋3          2√3
2. √18 = √9𝑋2          3√2

STEP 5: Evaluation

Mode: Entire class/Individual

Teacher’s activities: The teacher asks students to simplify the following questions:  

Student activities: the student solves the question accordingly  Assignment:

Simplify the following to single surd i)  

REFERENCE- 

1. Oluwafisayo .j. multipurpose mathematics
2. Bakare L, N mathematics clinic for SSCE
3. Otumudia M, A hidden facts in further mathematics