Grade 12 Mathematics(Common)

Class

Biemnet Habtezghi

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Lessons

Here is the class outline:

Sequence

A. Arithmetic Sequences

B. Geometric Sequences

Sigma Notation and Partial Sums

sum of arithmetic sequence

sum of geometric progressions

Infinite Series

applications of arithmetic and geometric progressions

Binomial Series

lower bounds and upper bounds of a sequence

least upper bounds and greatest lower bounds

Monotonic Sequences

Limits of Sequences

Convergence Properties of Sequences

limits of functions

Basic Theorems of Limits

one side and two side limits

continuity of a function

continuity of a function on an interval

properties of continuous functions

The Intermediate Value Theorem And Extreme Value Theorem

exercises of applications of limits 1

Exercises on Applications of Limits 2

Average Rate of Change of Functions

Derivative as rate of change at a point

Introduction to Derivatives

The derivative as a function

Differentiable on an Interval

Derivatives of Some Functions 1

Derivatives of some Functions 2

Derivatives of Exponential and Logarithmic Functions

Derivatives of Combinations and Compositions of Functions 1

Derivatives of Combinations and Compositions of Functions 2

Derivatives of Combinations and Compositions of Functions 3

Derivatives of Combinations and Compositions of Functions 4

The Chain Rule 1

The Chain Rule 2

Higher Order Derivatives of a Function 1

Higher Order Derivatives of a Function 2

Higher Order Derivatives 3

Revision on Zeros of Functions

Maximum and minimum values of functions

Extreme-value theorem

Critical Numbers

Absolute Extrema of a Continuous Function f on [a, b]

Rolle's Theorem

Mean-Value Theorem

Increasing and Decreasing functions 1

Local Extreme Values of a Function On Its Entire Domain

CONCAVITY AND INFLECTION POINTS

Inflection Point 1

Inflection points 2

Curve sketching 1

Curve sketching 2

MINIMIZATION AND MAXIMIZATION PROBLEMS 1

MINIMIZATION AND MAXIMIZATION PROBLEMS 2

MINIMIZATION AND MAXIMIZATION PROBLEMS 3

Rate of Change 1

Rate of Change 2

Rate of Change 3

Related Rates 4

Related Rates 5

The Concept of Indefinite Integral 1

The Concept of Indefinite Integral 2

Integration of some simple functions 1

Integration of some simple functions 2

Integration of some simple functions 3

Integration of some simple functions 4

Integration of some simple functions 5

Properties of Indefinite Integrals

Integration of simple trigonometric functions

Integration by Substitution 1

Integration by Substitution 2

Integration by Substitution 3

Integration by Substitution 4

Integration by Substitution 5

Integration by Partial Fractions 1

Integration by partial fractions 2

Integration by parts 1

Integration by parts 2

Integration by parts 3

Fundamental Theorem of Calculus

Properties of the definite integral 1

Properties of the definite integral 2

Change of variable

The Area Between Two Curves 1

The Area Between Two Curves 2

The Area Between Two Curves 3

The Area Between Two Curves 4

The Area Between Two Curves 5

The Area Between Two Curves 6

The Area Between Two Curves 7

Volume of Revolution 1

Volume of Revolution 2

Volume of Revolution 3

Motion of a Particle in a straight line

Coordinates Of a Point In Space

DISTANCE BETWEEN TWO POINTS IN SPACE

MIDPOINT OF A LINE SEGMENT IN SPACE

Equation of a Sphere

VECTORS IN SPACE

The Notion of Vectors in Space

Addition and Subtraction of Vectors

Scalar Or Dot Product Of Two vectors In Space

Angle Between Two Vectors In Space

Revision On Logic

Open Statements and Quantifiers

Arguments and Validity of Arguments

Arguments and validity 2

Different Types of proofs

Principle of Mathematical Induction

Revision for Lessons 1 and 2

Revision for Lessons 3 and 4

Revision for Lessons 5 and 6

Revision for Lesson 7

Revision for Lesson 8 and 9

Revision on unit 1

Revision for lessons 10 and 11

Revision on lessons 12 and 13

Revision on lessons 14 and 15

Revision on lessons 16 and 17

Revision on lessons 18,19 and 20

Revision on lessons 21 and 22

Revision on unit 2

Revision on lessons 24 and 25

Revision on lessons 26 and 27

Revision on lessons 28 and 29

Revision on lessons 30 and 31

Revision on lessons 32 -35

Revision on lessons 36 -40

Revision on unit 3

Revision on lessons 41- 43

Revision on lessons 44-48

Revisions on Lessons 50-54

Revision on lessons 55-56

Revision on lessons 57-58

Revision on lessons 59-62

Revision on unit 4

Revision on lessons 63-66

Revision on Lessons 67-71

Revision on lessons 72-76

Revision on lessons 79-81

Revision on lessons 83-84

Revision on lessons 86-92

Revision on unit 5

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Grade 12 Mathematics(Common)

Lessons

1. unit-1: Sequences and Series

2. Types of Sequences

3. Types of Sequences

4. Sequences and Series

5. Sum of Arithmetic Progression

6. Sum of Geometric Progressions

7. Infinite Series

8. Applications of Arithmetic and Geometric progressions

9. Binomial Series

10. Lower Bounds and Upper Bounds of a Sequences

11. Least Upper Bound (lub) and Greatest Lower Bound (glb)

12. Monotonic Sequences

13. Limits of Sequences

14. Convergence properties of Sequences

15. Limits of Functions

16. Basic Theorems of Limits

17. One Side and Two Side Limits

18. Continuity of a Function

19. Continuity of a Function on an Interval

20. Properties of Continuous Functions

21. The Intermediate Value Theorem And Extreme Value Theorem

22. Exercises of Applications of Limits 1

23. Exercises on Applications of Limits 2

24. Average Rate of Change of Functions

25. Derivative as Rate of Change at a Point

26. Introduction to Derivatives

27. The derivative as a function

28. Differentiability on an Interval

29. Derivatives of Some Functions 1

30. Derivatives of some Functions 2

31. Derivatives of Exponential and Logarithmic Functions

32. Derivatives of Combinations and Compositions of Functions 1

33. Derivatives of Combinations and Compositions of Functions 2

34. Derivatives of Combinations and Compositions of Functions 3

35. Derivatives of Combinations and Compositions of Functions 4

36. The Chain Rule 1

37. The Chain Rule 2

38. Higher Order Derivatives of a Function 1

39. Higher Order Derivatives of a Function 2

40. Higher Order Derivatives 3

41. Revision on Zeros of Functions

42. Maximum and minimum values of functions

43. Extreme-value theorem

44. Critical Numbers

45. Absolute Extrema of a Continuous Function f on [a, b]

46. Rolle's Theorem

47. Mean-Value Theorem

48. Increasing and Decreasing Functions 1

49. Local Extreme Values of a Function On Its Entire Domain

50. CONCAVITY AND INFLECTION POINTS

51. Inflection Point 1

52. Inflection points 2

53. Curve sketching 1

54. Curve sketching 2

55. MINIMIZATION AND MAXIMIZATION PROBLEMS 1

56. MINIMIZATION AND MAXIMIZATION PROBLEMS 2

57. MINIMIZATION AND MAXIMIZATION PROBLEMS 3

58. Rate of Change 1

59. Rate of Change 2

60. Rate of Change 3

61. Related Rates 4

62. Related Rates 5

63. The Concept of Indefinite Integral 1

64. The Concept of Indefinite Integral 2

65. Integration of some simple functions 1

66. Integration of some simple functions 2

67. Integration of some simple functions 3

68. Integration of some simple functions 4

69. Integration of some simple functions 5

70. Properties of Indefinite Integrals

71. Integration of simple trigonometric functions

72. Integration by Substitution 1

73. Integration by Substitution 2

74. Integration by Substitution 3

75. Integration by Substitution 4

76. Integration by Substitution 5

77. Integration by Partial Fractions 1