Elective/Further Mathematics Volume I
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1. SETS AND OPERATION ON SETS
2. SURDS
2.1. Introduction and Rules of Surds
Video - 00:25:10 mins
2.2. Addition and Subtraction of Surds
Video - 00:26:08 mins
2.3. Multiplication of Surds
Video - 00:41:20 mins
2.4. Rationalization of Surds
Video - 2:14:00 mins
2.5. Equality of Surds
Video - 1:11:31 mins
2.6. Irrational Equation
Video - 00:34:18 mins
3. BINARY OPERATIONS
3.1. Introduction and Some Worked Example
Video - 00:52:01 mins
3.2. Closure Property of Binary Operations
Video - 00:13:53 mins
3.3. Commutative Property of Binary Operations
Video - 00:23:14 mins
3.4. Associative Property of Binary Operations
Video - 00:37:55 mins
3.5. Identity and Inverse of an Element
Video - 1:34:52 mins
4. RELATIONS AND FUNCTIONS
4.1. Introduction to functions; Finding an Image/Range of a Function
Video - 00:43:36 mins
4.2. Types of Functions
Video - 00:27:01 mins
4.3. Domain of a Function
Video - 00:26:22 mins
4.4. Range of a Function
Video - 00:40:31 mins
4.5. Range of a Quadratic Function for a Given Domain
Video - 00:11:53 mins
4.6. The Inverse of a Function
Video - 00:22:29 mins
4.7. Composite of a Function
Video - 2:09:50 mins
5. POLYNOMIAL FUNCTIONS
5.1. Introduction to Polynomial Functions
Video - 00:23:38 mins
5.2. Addition, Subtraction and Multiplication of Polynomials
Video - 00:20:40 mins
5.3. Division of Polynomials
Video - 00:17:15 mins
5.4. The Remainder Theorem
Video - 1:02:07 mins
5.5. The Factor Theorem
Video - 1:10:50 mins
5.6. Zeroes or Roots of a Polynomial Function
Video - 00:42:17 mins
5.7. Repeated Factor Theorem
Video - 00:24:25 mins
6. RATIONAL FUNCTIONS
7. INDICES
8. LOGARITHM
9. QUADRATICS
9.1. Solving of Quadratic Equations by Factorization
Video - 00:46:57 mins
9.2. Solving Quadratic Equations by Completing the Square
Video - 00:28:05 mins
9.3. Solving Quadratic Equations in Quadratic Formula
Video - 00:35:46 mins
9.4. Solving Equations in Quadratic Form
Video - 00:18:24 mins
9.5. Maximum and Minimum Values of a Quadratic Function
Video - 00:35:41 mins
9.6. Types or Nature of Roots
Video - 1:34:14 mins
9.7. Relationship Between the Roots and Coefficients of a Quadratic Equation (Part 1)
Video - 1:23:44 mins
9.8. Relationship Between the Roots and Coefficients of a Quadratic Equation (Part 2)
Video - 00:51:11 mins
10. BINOMIAL THEOREM
10.1. Introduction to Binomial Expansion and Pascal’s Triangle
Video - 1:54:03 mins
10.2. The Binomial Theorem for Positive Integral Index
Video - 2:57:03 mins
10.3. The General Term in the Binomial Expansion
Video - 3:10:37 mins
10.4. The Binomial Theorem for Fractional and Negative Indices
Video - 2:40:50 mins
10.5. Application of the Binomial Theorem to Approximation
Video - 1:58:58 mins
11. CO-ORDINATE GEOMETRY I
11.1. Distance Between Two Points
Video - 00:41:56 mins
11.2. Midpoint of Two Points
Video - 00:19:21 mins
11.3. Division of a Line Segment in a Given Ratio
Video - 00:33:08 mins
11.4. Gradient (Scope) of a Line Segment
Video - 00:27:32 mins
11.5. Equation of a Straight Line
Video - 00:40:54 mins
11.6. The Point of Intersection Between Two Lines
Video - 00:26:57 mins
11.7. Parallel and Perpendicular Lines
Video - 1:48:09 mins
11.8. The Length of the Perpendicular Distance of a point to a given line
Video - 00:30:44 mins
11.9. The Acute Angle Between Two Intersecting Lines
Video - 00:20:10 mins
12. CO-ORDINATE GEOMETRY II
12.1. Introduction and General Form of Equation of a Circle
Video - 00:46:23 mins
12.2. Equation of a Circle Given the Centre and a Point on the Circumference
Video - 00:40:08 mins
12.3. Equation of a Circle Given Three Points on the Circumference
Video - 00:38:44 mins
12.4. Equation of a Circle Given the Ends of a Diameter
Video - 00:23:07 mins
12.5. Determination of the Centre and Radius Given the Equation of a Circle.
Video - 2:19:45 mins
12.6. Tangent and Normal to a Circle
Video - 1:55:53 mins
13. SEQUENCE AND SERIES (A.P)
13.1. Sequence and the General Term
Video - 00:44:21 mins
13.2. Series and Sigma (∑) notation
Video - 00:23:57 mins
13.3. Introduction to Arithmetic Progression
Video - 1:07:01 mins
13.4. The General Term of an Arithmetic Progression
Video - 00:57:21 mins
13.5. Sum of the first ‘n’ terms of an Arithmetic Progression
Video - 1:51:42 mins
13.6. The Fundamental Equation
Video - 00:24:39 mins
14. SEQUENCE AND SERIES (G.P)
14.1. Introduction to Geometric Progression
Video - 1:31:59 mins
14.2. General term of a Geometric Progression
Video - 1:47:40 mins
14.3. Sum of a G.P
Video - 1:43:57 mins
14.4. Sum of Infinity of as G.P
Video - 2:24:55 mins
14.5. Recurrence Decimals
Video - 00:27:42 mins
14.6. Recurrence Relation
Video - 1:37:02 mins