Online Tutoring Index : 12th Grade Math : Calculus

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Our 12th Calculus Grade Online Tutoring program is designed to help you get the desired grade by mastering the subject.

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This is a representative list of topics covered in our Grade 12 Math - Calculus program. However all our programs will be customized for the individual student.

1. Limits- operations on functions
   
   
2. Limits of sums
   
   
3. Limits of products
   
   
4. Limits of quotients
   
   
5. Limits of composition of functions
   
   
6. Continuity of a function
   
   
7. Intermediate value, extreme value theorem
   
   
8. Intermediate value theorem
   
   
9. Extreme value theorem
   
   
10. Derivatives, differentiability
    
    
11. Derivative of a function at a point
    
    
12. Differentiability
    
    
13. Derivatives of higher orders
    
    
14. Derivatives of functions
    
    
15. Derivatives of algebraic functions
    
    
16. Derivatives of trigonometric functions
    
    
17. Derivatives of inverse trigonometric functions
    
    
18. Derivatives of exponential functions
    
    
19. Derivatives of logarithmic functions
    
    
20. Chain rule
    
    
21. Rolle
    
    
22. Mean value theorem
    
    
23. Maxima, minima, inflection points, intervals
    
    
24. Maxima
    
    
25. Minima
    
    
26. Inflection points
    
    
27. Intervals
    
    
28. Newton's method (approximating the zeros of a function)
    
    
29. Differentiation to solve problems
    
    
30. Differentiation to solve optimization problems
    
    
31. Differentiation to solve rate problems
    
    
32. Definite/indefinite integrals
    
    
33. Definite integrals
    
    
34. Indefinite integrals
    
    
35. Riemann sums
    
    
36. Fundamental theorem of calculus
    
    
37. Definite integrals problems
    
    
38. Definite integrals in problems involving area
    
    
39. Definite integrals in problems involving velocity
    
    
40. Definite integrals in problems involving acceleration
    
    
41. Definite integrals in problems involving volume of a solid
    
    
42. Definite integrals in problems involving area of a surface of revolution
    
    
43. Definite integrals in problems involving length of a curve
    
    
44. Definite integrals in problems involving work
    
    
45. Techniques of integration
    
    
46. Techniques of integration – substitution
    
    
47. Techniques of integration - integration by parts
    
    
48. Techniques of integration - trigonometric substitution
    
    
49. Inverse trigonometric functions
    
    
50. Integrals of functions
    
    
51. Integrals of rational functions
    
    
52. Integrals of trigonometric functions
    
    
53. Simpson's rule, Newton's method
    
    
54. Simpson's rule
    
    
55. Newton's method
    
    
56. Improper integrals (limits of definite integrals)
    
    
57. Tests for convergence/divergence of sequences/series
    
    
58. Convergence and divergence of sequences of real numbers
    
    
59. Convergence and divergence of series of real numbers
    
    
60. Comparison test
    
    
61. Ratio test
    
    
62. Alternate series test
    
    
63. Power series, Taylor series/polynomials
    
    
64. Power series
    
    
65. Taylor series
    
    
66. Taylor polynomials
    
    
67. Elementary differential equations
    
    
68. Solutions of selected elementary differential equations
    
    
69. Applications of elementary differential equations - growth-and-decay problems

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