Week 8 – SS1 Third Term Further Mathematics Notes

WEEK 8
Topic:         Straight line
Sub-topic:
     Angle between lines
Duration:     80 minutes
Learning Objectives: By the end of the lesson, students should be able to calculate the angle between two lines.
Reference Materials: New Further Mathematics Project 2 by M. R Tuttuh Adegun
Previous Knowledge: Students can draw the graph of a linear equation (straight-line graph).
Instructional Materials: Graph board and graph book.
Content:                    ANGLE BETWEEN TWO LINES
The acute angle between lines of gradient m₁ and m₂
        
Example:    Find the acute angle between the lines x + 4y = 12 and y – 2x + 6 =0.
                        Solution
        The gradients are -1/4 and 2
         = |4.5| =77.47^o
GRADIENT INTERCEPT FORM
        The gradient intercept form of the equation of a line is y = mx + c
Example:    Determine the equation of the line whose gradient is -2 and y-intercept is 3..
                        Solution
    Let the equation of the line be y = mx + c, where m = -2 and c = 3
Hence, the equation of the line is y = -2x + 3
Presentation:
Step I: Teacher revises the last topic with the students and does necessary corrections.
Step II: Teacher introduces the new topic to the students and explains by giving illustrative examples.
Step III: Teacher welcomes and answers questions from the students.
Step IV: Teacher gives notes to the students and ensures they copy correctly.
Step V: Teacher evaluates the students on topic discussed.
Evaluation:
    1.    Determine the equation of the line whose gradient is 3 and y-intercept is -4.
        2.    Find the acute angle between the lines 2y = 3x – 8 and 5y = x + 7.
Conclusion: Teacher summarizes the topic, marks the students’ notes, does correction and allows the students to copy.
Assignment:     1.    Determine the equation of the line whose gradient is 3¼ and y-intercept is -6.
        2.    Find the acute angle between the lines 2y = – 5x + 8 and y = 3x – 7.

 PERIOD 3
Topic:         Equation of a straight line
Sub-topic:     Gradient and one point form and two point form
Duration:     40 minutes
Learning Objectives: By the end of the lesson, students should be able to determine the equation of a line in different forms.
Reference Materials: i. New Further Mathematics for SSS 2 Project 2.
Previous Knowledge: Students can calculate angle between two lines.
Instructional Materials: Graph book.
Content:                GRADIENT AND ONE POINT FORM
    Equation of a line through (x, y) with gradient m is y – y₁ = m(x – x₁)
Example:    A straight line has a gradient of -3/2 and passes through the point (1, 4). Find its equation and its intercept on the y-axis
Solution
    In this case (x, y) = (1, 4) and m = – 3/2
So the equation is
            y – 4 = – (x – 1)

• 2y – 8 = -3(x – 1)
• 2y + 3x =11
  

    So y = – ; Hence the intercept on y-axis is 5½     

 GRADIENT AND TWO POINT FORM
    Equation of a line through the two points (x₁, y₁) and (x₂, y₂)is =
Example:    Find the equation of a line AB which passes through the points (1, -1) and (-2, -13)
                            Solution
     = ;
                Therefore y + 1 = 4x – 4

• y = 4x – 5.

  Thus the gradient of AB is 4.

Evaluation:
Find the equation of a line AB which passes through the points (-2, -3) and (-2, -13)
Conclusion: Teacher summarizes the topic, marks the students’ notes, does correction and allows the students to copy.
Assignment:
Find the equation of a line AB which passes through the points (-1, 2) and (3, 0)
Assignment:
New General Mathematics for SSS 2, by M.F Macrae et al. Page 190, Exercise 16d, no 2a, 2c