Optional Mathematics 9

1. Ordered Pairs

• 1. Algebra Introduction 4 Minutes
• 2. Ordered pairs 7 Minutes
• 3. Equality of ordered pairs 3 Minutes
• 4. Example 1 (Ordered pairs) 2 Minutes
• 5. Example 2 (Ordered pairs) 5 Minutes

2. Cartesian Product

• 1. Cartesian product 5 Minutes
• 2. Ways of representing cartesian product 7 Minutes
• 3. Example 1 (Cartesian product) 2 Minutes
• 4. Example 2 (Cartesian product) 3 Minutes
• 5. Example 3 (Cartesian product) 2 Minutes
• 6. Example 4 (Cartesian product) 4 Minutes

3. Relation

• 1. Relation 7 Minutes
• 2. Example 1 (Relations) 4 Minutes
• 3. Example 2 (Relations) 2 Minutes
• 4. Ways of representing relations 6 Minutes
• 5. Types of relation 6 Minutes
• 6. Inverse relation 2 Minutes
• 7. Example 3 (Relations) 3 Minutes
• 8. Example 4 (Relations) 1 Minutes
• 9. Example 5 (Relations) 2 Minutes
• 10. Example 6 (Relations) 4 Minutes
• 11. Example 7 (Relations) 3 Minutes

4. Function

• 1. Functions 11 Minutes
• 2. Domain, range and co-domain of a function 7 Minutes
• 3. Test of a function (Vertical line test) 9 Minutes
• 4. Example 1 (Functions) 3 Minutes
• 5. Example 2 (Functions) 5 Minutes
• 6. Representation of a Function 10 Minutes
• 7. Types of function 6 Minutes
• 8. Example 3 (Functions) 2 Minutes
• 9. Example 4 (Functions) 3 Minutes
• 10. Example 5 (Functions) 1 Minutes
• 11. Example 6 (Functions) 3 Minutes
• 12. Example 7 (Functions) 2 Minutes
• 13. Example 8 (Functions) 3 Minutes
• 14. Example 9 (Functions) 5 Minutes
• 15. Example 10 (Functions) 6 Minutes
• 16. Example 11 (Functions) 7 Minutes
• 17. Example 12 (Functions) 3 Minutes
• 18. Example 13 (Functions) 4 Minutes

5. Polynomials

• 1. Polynomials( Introduction) 13 Minutes
• 2. Example 1 (Polynomials) 4 Minutes
• 3. Example 2 (Polynomials) 4 Minutes
• 4. Example 3 (Polynomials) 9 Minutes
• 5. Addition of polynomials 3 Minutes
• 6. Properties of sum of polynomials 4 Minutes
• 7. Difference of two polynomials 4 Minutes
• 8. Example 1 (Polynomials) 6 Minutes
• 9. Example 2 (Polynomials) 2 Minutes
• 10. Example 3 (Polynomials) 7 Minutes
• 11. Example 4 (Polynomials) 13 Minutes
• 12. Multiplication of polynomials 7 Minutes
• 13. Properties of product of polynomials 5 Minutes
• 14. Example 1 (Product of polynomials) 3 Minutes
• 15. Example 2 (Product of polynomials) 3 Minutes
• 16. Division of polynomials 10 Minutes
• 17. Example 1 (Division of polynomials) 4 Minutes
• 18. Example 2 (Division of polynomials) 6 Minutes
• 19. Example 3 (Division of polynomials) 5 Minutes

6. Sequence and Series

• 1. Sequence 7 Minutes
• 2. General term of sequence 7 Minutes
• 3. General term of quadratic sequence 11 Minutes
• 4. Series 3 Minutes
• 5. Example 1 (Sequence and series) 4 Minutes
• 6. Example 2 (Sequence and series) 8 Minutes
• 7. Example 3 (Sequence and series) 10 Minutes
• 8. Example 4 (Sequence and series) 4 Minutes
• 9. Example 5 (Sequence and series) 4 Minutes
• 10. Example 6 (Sequence and series) 7 Minutes
• 11. Example 7 (Sequence and series) 3 Minutes
• 12. Sigma notation 4 Minutes
• 13. Example 1 (Sigma notation) 2 Minutes
• 14. Example 2 (Sigma notation) 2 Minutes
• 15. Example 3 (Sigma notation) 6 Minutes
• 16. Example 4 (Sigma notation) 4 Minutes

1. Limit and Continuity (Introduction) 4 Minutes

2. Power of calculus 12 Minutes

3. Concept of limit by the concept of sequence of numbers 9 Minutes

4. Example 1 (3. Concept of limit by the concept of sequence of numbers) 2 Minutes

5. Example 2 (3. Concept of limit by the concept of sequence of numbers) 4 Minutes

6. Concept of limit by the concept of sequence diagrams 11 Minutes

7. Example 1 (Concept of limit by the concept of sequence diagrams) 4 Minutes

8. Example 2 (Concept of limit by the concept of sequence diagrams) 8 Minutes

9. Concept of limit by the sum of infinite series 22 Minutes

10. Example 1 (Concept of limit by the sum of infinite series) 5 Minutes

11. Example 2 (Concept of limit by the sum of infinite series) 5 Minutes

12. Example 3 (Concept of limit by the sum of infinite series) 9 Minutes

13. Limiting value of a function 12 Minutes

14 Part 2 Limits (Demonstration) converted_1 15 Minutes

15. Example 1 (Limiting value of a function) 5 Minutes

16. Example 2 (Limiting value of a function) 6 Minutes

17. Example 3 (Limiting value of a function) 3 Minutes

18. Notational representation of limit 2 Minutes

19. Example 1 (Notational representation of limit) 2 Minutes

1. Matrix (Syllabus) 2 Minutes

2. Matrix (Introduction) 8 Minutes

3. Example 1 (Matrix) 2 Minutes

4. Example 2 (Matrix) 4 Minutes

5. Example 3 (Matrix) 5 Minutes

6. Special types of matrices 23 Minutes

7. Example 1 (Special matrices) 6 Minutes

8. Example 2 (Special matrices) 4 Minutes

9. Example 3 (Special matrices) 12 Minutes

10. Operation on matrices(Addition ) 6 Minutes

11. Subtraction and Addiive inverse 6 Minutes

12. Example 1 (Addition and subtraction of matrices) 3 Minutes

13. Example 2 (Addition and subtraction of matrices) 6 Minutes

14. Properties of matrix addition 11 Minutes

15. Transpose of Matrix 3 Minutes

16. Example 1 (Properties of matrix addition) 3 Minutes

17. Example 2 (Properties of matrix addition) 3 Minutes

18. Example 3 (Properties of matrix addition) 4 Minutes

19. Example 4 (Properties of matrix addition) 5 Minutes

20. Example 5 (Properties of matrix addition) 6 Minutes

21. Scalar multiplication of matrices 3 Minutes

22. Matrix multiplication 15 Minutes

23. Example 1 (Multiplication of matrices) 2 Minutes

24. Example 2 (Multiplication of matrices) 4 Minutes

25. Example 3 (Multiplication of matrices) 4 Minutes

26. Example 4 (Multiplication of matrices) 4 Minutes

27. Example 5 (Multiplication of matrices) 6 Minutes

28. Properties of matrix multiplication 15 Minutes

29. Example 1 (Properties of matrix multiplication) 2 Minutes

30. Example 2 (Properties of matrix multiplication) 4 Minutes

31. Example 3 (Properties of matrix multiplication) 5 Minutes

32. Example 4 (Properties of matrix multiplication) 3 Minutes

33. Example 5 (Properties of matrix multiplication) 3 Minutes

1. Section Formula

• 1. Co-ordinate geometry(Syllabus) 4 Minutes
• 2. Section formula 5 Minutes
• 3. Internal division 17 Minutes
• 4. Mid-point Formula 4 Minutes
• 5. External division 14 Minutes
• 6. Centroid Formula 13 Minutes
• 7. Example 1 (Section formula) 5 Minutes
• 8. Example 2 (Section formula) 4 Minutes
• 9. Example 3 (Section formula) 3 Minutes
• 10. Example 4 (Section formula) 4 Minutes
• 11. Example 5 (Section formula) 10 Minutes
• 12. Example 6 (Section formula) 11 Minutes
• 13. Example 7 (Section formula) 8 Minutes
• 14. Example 8 (Section formula) 8 Minutes
• 15. Example 9 (Section formula) 14 Minutes

2. Locus

• 1. Locus 14 Minutes
• 2. Example 1 (Locus) 6 Minutes
• 3. Example 2 (Locus) 5 Minutes
• 4. Example 3 (Locus) 7 Minutes
• 5. Example 4 (Locus) 7 Minutes
• 6. Example 5 (Locus) 8 Minutes
• 7. Example 6 (Locus) 7 Minutes
• 8. Example 7 (Locus) 13 Minutes
• 9. Example 8 (Locus) 6 Minutes

3. Equation of Line

• 1. Basic concepts 16 Minutes
• 2. Slope of a line joining two points 6 Minutes
• 3. Example 1 (Basic Concepts) 2 Minutes
• 4. Example 2 (Basic Concepts) 4 Minutes
• 5. Example 3 (Basic Concepts) 4 Minutes
• 6. Example 4 (Basic Concepts) 6 Minutes
• 7. Slope-intercept form of line 7 Minutes
• 8. Example 1 (Slope-intercept form) 6 Minutes
• 9. Example 2 (Slope-intercept form) 5 Minutes
• 10. Example 3 (Slope-intercept form) 6 Minutes
• 11. Double-intercept form 7 Minutes
• 12. Example 1 (Double-intercept form) 7 Minutes
• 13. Example 2 (Double-intercept form) 4 Minutes
• 14. Example 3 (Double-intercept form) 3 Minutes
• 15. Example 4 (Double-intercept form) 5 Minutes
• 16. Example 5 (Double-intercept form) 6 Minutes
• 17. Example 6 (Double-intercept form) 11 Minutes
• 18. Normal form of straight line 10 Minutes
• 19. Example 1 (Normal form) 4 Minutes
• 20. Example 2 (Normal form) 6 Minutes
• 21. Example 3 (Normal form) 5 Minutes
• 22. Example 4 (Normal form) 8 Minutes
• 23. General equation of first degree in two variables 7 Minutes
• 24. Reduction to Slope-intercept form 7 Minutes
• 25. Reduction to Double-intercept form 5 Minutes
• 26. Reduction to Normal form 10 Minutes
• 27. Example 1 (Reduction of general equation) 2 Minutes
• 28. Example 2 (Reduction of general equation) 2 Minutes
• 29. Example 3 (Reduction of general equation) 13 Minutes
• 30. Example 4 (Reduction of general equation) 7 Minutes
• 31. Example 5 (Reduction of general equation) 4 Minutes
• 32. Example 6 (Reduction of general equation) 7 Minutes
• 33. Distance between a point and a line 15 Minutes
• 34. Distance between parallel lines 11 Minutes
• 35. Example 1 (Distance between a point and a line) 3 Minutes
• 36. Example 2 (Distance between a point and a line) 8 Minutes
• 37. Example 3 (Distance between parallel lines) 3 Minutes
• 38. Example 4 (Distance between parallel lines) 4 Minutes
• 39. Point-slope form 6 Minutes
• 40. Two-point form 7 Minutes
• 41. Example 1 (Point slope form) 2 Minutes
• 42. Example 2 (Point-slope form) 4 Minutes
• 43. Example 3 (Two-point form) 3 Minutes
• 44. Example 4 (Two-point form) 4 Minutes
• 45. Example 5 (Two-point form) 4 Minutes
• 46. Example 6 (Two-point form) 6 Minutes

4. Area

• 1. Area of triangle 21 Minutes
• 2. Area of quadrilateral 8 Minutes
• 3. Example 1 (Area of triangle) 4 Minutes
• 4. Example 2 (Area of triangle) 6 Minutes
• 5. Example 3 (Area of triangle) 4 Minutes
• 6. Example 4 (Area of quadrilateral) 3 Minutes
• 7. Example 5(Area of quadrilateral) 4 Minutes
• 8. Example 6 (Area of triangle) 6 Minutes
• 9. Example 7 (Area of triangle) 10 Minutes

1. Angles

• 0. Trigonometry Syllabus Introduction 3 Minutes
• 1. Angles 6 Minutes
• 2. Sexagesimal system 7 Minutes
• 3. Centesimal system 5 Minutes
• 4. Relationship between degree and grade system 3 Minutes
• 5. Example 1 (Degree and grade system) 3 Minutes
• 6. Example 2 (Degree and grade system) 4 Minutes
• 7. Example 3 (Degree and grade system) 9 Minutes
• 8. Example 4 (Degree and grade system) 1 Minutes
• 9. Example 5 (Degree and grade system) 1 Minutes
• 10. Example 6 (Degree and grade system) 7 Minutes
• 11. Example 7 (Degree and grade system) 5 Minutes
• 12. Example 8 (Degree and grade system) 4 Minutes
• 13. Example 9 (Degree and grade system) 4 Minutes
• 14. Example 10 (Degree and grade system) 3 Minutes
• 15. Circular measure 12 Minutes
• 16. Relation among degree, grade and radian system 5 Minutes
• 17. Example 1 (Radian measure) 3 Minutes
• 18. Example 2 (Radian measure) 1 Minutes
• 19. Example 3 (Radian measure) 1 Minutes
• 20. Example 4 (Radian measure) 1 Minutes
• 21. Example 5 (Radian measure) 5 Minutes
• 22. Example 6 (Radian measure) 6 Minutes
• 23. Example 7 (Radian measure) 7 Minutes
• 24. Example 8 (Radian measure) 4 Minutes
• 25. Relation between radius, arc-length and central angle 11 Minutes
• 26. Example 1 (Relation between radius, arc-length and central angle) 4 Minutes
• 27. Example 2 (Relation between radius, arc-length and central angle) 8 Minutes
• 28. Example 3 (Relation between radius, arc-length and central angle) 10 Minutes

2. Introduction to Trigonometric Ratios

• 1. Trigonometry (Introduction) 17 Minutes
• 2. Reciprocal relations 8 Minutes
• 3. Quotient relations 9 Minutes
• 4. Pythagorean relations 11 Minutes
• 5. Operation of Trigonometric ratios 14 Minutes
• 6. Trigonometric Identities 9 Minutes
• 7. Example 1 (Trigonometric ratios) 5 Minutes
• 8. Example 2 (Trigonometric ratios) 9 Minutes
• 9. Example 3 (Trigonometric ratios) 11 Minutes
• 10. Example 4 (Trigonometric ratios) 7 Minutes
• 11. Example 5 (Trigonometric ratios) 6 Minutes
• 12. Example 6 (Trigonometric ratios) 6 Minutes
• 13. Example 7 (Trigonometric ratios) 7 Minutes
• 14. Example 8 (Trigonometric ratios) 4 Minutes
• 15. Example 9 (Trigonometric ratios) 5 Minutes
• 16. Example 10 (Trigonometric ratios) 7 Minutes

3. Conversion of trigonometric ratios

• 1. Conversion of trigonometric ratios 6 Minutes
• 2. Example 1 (Conversion of trigonometric ratios) 4 Minutes
• 3. Example 2 (Conversion of trigonometric ratios) 3 Minutes
• 4. Example 3 (Conversion of trigonometric ratios) 4 Minutes
• 5. Example 4 (Conversion of trigonometric ratios) 7 Minutes
• 6. Example 5 (Conversion of trigonometric ratios) 5 Minutes
• 7. Example 6 (Conversion of trigonometric ratios) 4 Minutes
• 8. Example 7 (Conversion of trigonometric ratios) 6 Minutes

4. Trigonometric ratios of standard angles

• 1. Trigonometric ratios of standard angles 23 Minutes
• 2. Example 1 (Trigonometric ratios of standard angles) 1 Minutes
• 3. Example 2 (Trigonometric ratios of standard angles) 4 Minutes
• 4. Example 3 (Trigonometric ratios of standard angles) 2 Minutes
• 5. Example 4 (Trigonometric ratios of standard angles) 2 Minutes
• 6. Example 5 (Trigonometric ratios of standard angles) 3 Minutes

5. Trigonometric ratios of complementary angles

• 1. Trigonometric ratios of complementary angles 8 Minutes
• 2. Example 1 (Trigonometric ratios of complementary angles) 3 Minutes
• 3. Example 2 (Trigonometric ratios of complementary angles) 4 Minutes
• 4. Example 3 1 Minutes
• 5. Example 4 3 Minutes
• 6. Example 5 (Trigonometric ratios of complementary angles) 3 Minutes
• 7. Example 6 (Trigonometric ratios of complementary angles) 2 Minutes
• 8. Example 7 (Trigonometric ratios of complementary angles) 2 Minutes
• 9. Example 8 (Trigonometric ratios of complementary angles) 3 Minutes
• 10. Example 9 (Trigonometric ratios of complementary angles) 3 Minutes

6. Trigonometric ratio of any angle

• 1. Trigonometric ratio of any angle (90±θ) and (270±θ) 24 Minutes
• 2. Trigonometric ratio of any angle (180±θ) and (360±θ) 20 Minutes
• 3. Constructing trigonometric table 21 Minutes
• 4. Example 1 (Trigonometric ratio of any angle) 8 Minutes
• 5. Example 2 (Trigonometric ratio of any angle) 5 Minutes
• 6. Example 3 (Trigonometric ratio of any angle) 6 Minutes
• 7. Example 4 (Trigonometric ratio of any angle) 3 Minutes
• 8. Example 5 (Trigonometric ratio of any angle) 3 Minutes
• 9. Example 6 (Trigonometric ratio of any angle) 4 Minutes

7. Compound angle

• 1. Compound angle 10 Minutes
• 2. Compound angle (continued) 9 Minutes
• 3. Example 1 (Compound angle) 6 Minutes
• 4. Example 2 (Compound angle) 5 Minutes
• 5. Example 3 (Compound angle) 1 Minutes
• 6. Example 4 (Compound angle) 7 Minutes
• 7. Example 5 (Compound angle) 4 Minutes
• 8. Example 6 (Compound angle) 4 Minutes
• 9. Example 7 (Compound angle) 5 Minutes
• 10. Example 8 (Compound angle) 5 Minutes
• 11. Example 9 (Compound angle) 5 Minutes
• 12 example 10(Compound angle) 7 Minutes

1. Vectors Table of content 2 Minutes

2. Introduction to vectors 16 Minutes

3. Example 1 (Vectors) 4 Minutes

4. Example 2 (Vectors) 4 Minutes

5. Example 3 (Vectors) 2 Minutes

6. Example 4 (Vectors) 4 Minutes

7. Magnitude and direction of vectors 13 Minutes

8. Some types of vectors 7 Minutes

9. Position vector 5 Minutes

10. Example 1 (Magnitue and direction of vectors) 2 Minutes

11. Example 2 (Magnitue and direction of vectors) 5 Minutes

12. Example 3 (Magnitue and direction of vectors) 5 Minutes

13. Example 4 (Magnitue and direction of vectors) 6 Minutes

14 Vector magnitude demonstration 17 Minutes

15. Operation on vectors (Addition and subtration of vectors) 17 Minutes

16. Operation on vectors (Multiplication of vectors) 2 Minutes

17. Addition of vector Demonstration 17 Minutes

18. Example 1(Operation on vectors) 3 Minutes

19. Example 2 (Operation on vectors) 2 Minutes

20. Example 3 (Operation on vectors) 2 Minutes

21. Example 4 (Operation on vectors) 3 Minutes

22. Example 5 (Operation on vectors) 4 Minutes

23. Example 6 (Operation on vectors) 2 Minutes

24. Example 7 (Operation on vectors) 4 Minutes

25. Example 8 (Operation on vectors) 4 Minutes

26. Example 9 (Operation on vectors) 5 Minutes

1. Translation

• 1. Transformation Syllabus 4 Minutes
• 2. Introduction 9 Minutes
• 3. Translation (Using graphical method) 7 Minutes
• 4. Translation (Using coordinates) 5 Minutes
• 5. Example 1 (Translation) 4 Minutes
• 6. Example 2 (Translation) 3 Minutes
• 7. Example 3 (Translation) 4 Minutes
• 8. Translation Demonstration 12 Minutes

2. Reflection

• 1. Reflection (Using graphical method) 9 Minutes
• 2. Reflection (Using cooerdinates) 16 Minutes
• 3. Example 1 (Reflection) 4 Minutes
• 4. Example 2 (Reflection) 10 Minutes
• 5. Example 3 (Reflection) 3 Minutes
• 6. Reflection Demonstration 12 Minutes

3. Rotation

• 1. Rotation (Graphical method) 9 Minutes
• 2. Rotation (Using co-ordinates) 22 Minutes
• 3. Example 1 (Rotation) 6 Minutes
• 4. Example 2 (Rotation) 9 Minutes
• 5. Rotation Demonstration 17 Minutes

4. Enlargement

• 1. Enlargement(Graphical method) 8 Minutes
• 2. Enlargement (Using co-ordinates) 6 Minutes
• 3. Example 1 (Enlargement) 4 Minutes
• 4. Example 2 (Enlargement) 5 Minutes
• 5. Example 3 (Enlargement) 3 Minutes
• 6. Enlargement demonstration 13 Minutes

1. Partition Values

• 1. Statistics Syllabus 3 Minutes
• 2. Partition values(Quartiles) 12 Minutes
• 3. Partition values(Deciles and percentiles) 4 Minutes
• 4. Example 1 (Partition values) 5 Minutes
• 5. Example 2(Partition values) 8 Minutes
• 6. Example 3 (Partition values) 2 Minutes
• 7. Example 4 (Partition values) 15 Minutes
• 8. Example 5 (Partition values) 8 Minutes

2. Dispersion

• 1. Dispersion 12 Minutes
• 2. Quartile deviation and its co-efficient 5 Minutes
• 3. Example 1 (Quartile deviation) 6 Minutes
• 4. Example 2 (Quartile deviation) 10 Minutes
• 5. Example 3 (Quartile deviation) 4 Minutes
• 6. Mean deviation and its coefficient 6 Minutes
• 7. Example 1 (Mean deviation) 8 Minutes
• 8. Example 2 (Mean deviation) 8 Minutes
• 9. Example 3 (Mean deviation) 6 Minutes
• 10. Example 4 (Mean deviation) 9 Minutes
• 11. Standard deviation and its coefficient 9 Minutes
• 12. Example 1 (Standard deviation) 8 Minutes
• 13. Example 2 (Standard deviation) 7 Minutes
• 14. Example 3 (Standard deviation) 8 Minutes
• 15 Standard Deviation Demonstration 12 Minutes