Week 1 and 2 – SS3 Second Term Mathematics Notes

SECOND TERM E-LEARNING NOTE

 SUBJECT: MATHEMATICS                                        CLASS: SS 3

 SCHEME OF WORK

 WEEK        TOPIC

1. Calculation on interest on bonds and debentures using logarithm table and problems on taxes and value added tax.
2. Coordinate Geometry of straight line: Cartesian coordinate graphs, distance between two points, midpoint of the line joining two points.
3. Coordinate Geometry of straight lines: Gradient and Intercepts of a line, angle between two intersecting straight lines and application.
4. Differentiation of algebraic functions: meaning of differentiation, differentiation from first principle and standard derivatives of some basic functions.
5. Differentiation of algebraic functions: Basic rules of differentiation such as sum and difference, product rule, quotient rule and maximal and minimum application.
6. Integration and evaluation of simple algebraic functions: Definition, method of integration: substitution, partial fraction and integration by parts, area under the curve and use of Simpson’s rule.

1. – 12. Revision and mock examination.

    

REFERENCE TEXT

• New General Mathematics for SS book 3 by J.B Channon
• Essential Mathematics for SS book 3
• Mathematics Exam Focus
• Waec and Jamb past Questions

 
 WEEK ONE

• Calculation on interest on bonds and debentures using logarithm table
• Problems on taxes and value added tax.

 WEEK TWO

• Coordinate Geometry of straight line: Cartesian coordinate graphs
• distance between two points
• midpoint of the line joining two points
• Coordinate Geometry of Straight line:
• Cartesian coordinate graph:

   Distance between two lines:
  In the figure below, the coordinates of the points A and B are (x₁, y₁) and (x₂, y₂), respectively. Let the length of AB be l.
  y
  B(x₂, y₂)

   l
  y₂ – y₁

    A(x₁, y₁) x₂ – x₂ C
  X
  Using Pythagoras theorem:
  AB² = AC² + BC²
  l² =(x₂ – x₁)² + (y₂ – y₁)²
  l = √(x₂ – x₁)² + (y₂ – y₁)²
  
   Example:
  Find the distance between the each pair of points: a. (3, 4) and (1, 2) b. (3, – 3) and (- 2, 5)
  Solution:
  Using l =√(x₂ – x₁)² + (y₂ – y₁)²

1. l = √(3 – 1)² + (4 – 2)²

   l = √2² + 2²
   l = √8 = 2√2 units

    

2. l = √(3 – (-2)² + (-3 – 5)²

   = √5² + (-8)²
   = √25 + 64 = √89 = 9.43 units

 Evaluation: Find the distance between the points in each of the following pairs leaving your answers in surd form: 1. (-2, – 5) and (3, – 6) 2. (- 3, 4) and (- 1, 2)

 Mid-point of a line:
The mid-point of the line joining two points:

 y
B(x₂, y₂)

  y₂ – y
M(x, y) D
x₂ –x
y – y₁

  A(x₁, y₁) x – x₁ N C
X
Triangle MAN and BMD are congruent, so AM = MD and BD = MN
x – x₁ = x₂ – x y – y₁ = y₂ – y
x + x = x₂ + x₁ y + y = y₂ + y₁
2x = x₂ + x₁ 2y = y₂ + y₁
x= x₂ + x₁ y = y₂ + y₁
2 2
Hence, the mid-point of a straight line joining two is x₂ + x₁ ,y₂ + y₁
2 2
Example: Find the coordinates of the mid-point of the line joining the following pairs of points.

1. (3, 4) and (1, 2) b. (2, 5) and ( – 3, 6)

   Solution:

Mid-point = x₂ + x₁ ,y₂ + y₁
2 2

1. Mid-point = 1 + 3 , 4 + 2 = (2, 3)

   2 2

2. Mid-point = – 3 + 2 , 6+ 5 = – 1 , 11

2 2 2 2
Evaluation: Find the coordinates of the mid-point of the line joining the following pairs of points.

1. (- 2 , – 5) and (3, – 6) b. (3, 4) and ( – 1, – 2)

 General Evaluation

1. Find the distance between the points in each of the following pairs leaving your answers in surd form: 1. (7, 2) and (1, 6)
2. What is the value of r if the distance between the points (4, 2) and (1, r) is 3 units?
3. Find the coordinates of the mid-point (-3, -2) and (-7, – 4)

 Reading Assignment: NGM for SS 3 Chapter 9 page 77 – 78,
    
Weekend Assignment:

1. Find the value of α² + β² if α + β = 2 and the distance between the points (1, α) and (β, 1) is 3 units.
2. The vertices of the triangle ABC are A (7, 7), B (- 4, 3) and C (2, – 5). Calculate the length of the longest side of triangle ABC.
3. Using the information in ‘2’ above, calculate the line AM, where M is the mid-point of the side opposite A.