# 12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 1 ADVANCED HIGHER MATHS REVISION AND FORMULAE UNIT 2.

## Presentation on theme: "12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 1 ADVANCED HIGHER MATHS REVISION AND FORMULAE UNIT 2."— Presentation transcript:

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 1 ADVANCED HIGHER MATHS REVISION AND FORMULAE UNIT 2

12 October, 2014 St Joseph’s College ADVANCED HIGHER REVISION 2 Inverse Trigonometric Functions Unit 2 Outcome 1 FURTHER DIFFERENTIATION

12 October, 2014 St Joseph’s College ADVANCED HIGHER REVISION 3 Example 1 Unit 2 Outcome 1 FURTHER DIFFERENTIATION

12 October, 2014 St Joseph’s College ADVANCED HIGHER REVISION 4 Example 2 Unit 2 Outcome 1 FURTHER DIFFERENTIATION

12 October, 2014 St Joseph’s College ADVANCED HIGHER REVISION 5 Example 1 Implicit Differentiation Unit 2 Outcome 1 FURTHER DIFFERENTIATION

12 October, 2014 St Joseph’s College ADVANCED HIGHER REVISION 6 Example 2 Implicit Differentiation Unit 2 Outcome 1 FURTHER DIFFERENTIATION

12 October, 2014 St Joseph’s College ADVANCED HIGHER REVISION 7 Example Equation of Tangents Unit 2 Outcome 1 FURTHER DIFFERENTIATION

12 October, 2014 St Joseph’s College ADVANCED HIGHER REVISION 8 Example 2 (contd) Equation of Tangents Unit 2 Outcome 1 FURTHER DIFFERENTIATION

12 October, 2014 St Joseph’s College ADVANCED HIGHER REVISION 9 Second Derivatives Example Unit 2 Outcome 1 FURTHER DIFFERENTIATION

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 10 Example (contd) Second Derivatives 2 Unit 2 Outcome 1 FURTHER DIFFERENTIATION

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 11 Logarithmic Differentiation Unit 2 Outcome 1 FURTHER DIFFERENTIATION

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 12 Example 1 Logarithmic Differentiation Unit 2 Outcome 1 FURTHER DIFFERENTIATION

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 13 Example 2 Logarithmic Differentiation Unit 2 Outcome 1 FURTHER DIFFERENTIATION

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 14 Logarithmic Differentiation Example 2 (contd) Unit 2 Outcome 1 FURTHER DIFFERENTIATION

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 15 Parametric Differentiation Unit 2 Outcome 1 FURTHER DIFFERENTIATION

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 16 Equation of Tangents Example

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 17 Equation of TangentsExample 1 (contd) Unit 2 Outcome 1 FURTHER DIFFERENTIATION

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 18 Second Derivatives Unit 2 Outcome 1 FURTHER DIFFERENTIATION

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 19 Stationary PointsSecond Derivatives AND Unit 2 Outcome 1 FURTHER DIFFERENTIATION

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 20 Example Unit 2 Outcome 1 FURTHER DIFFERENTIATION

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 21 Unit 2 Outcome 1 FURTHER DIFFERENTIATION

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 22 Unit 2 Outcome 1 FURTHER DIFFERENTIATION

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 23 Unit 2 Outcome 2 FURTHER INTEGRATION

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 24 Example 1 Example 2 Unit 2 Outcome 2 FURTHER INTEGRATION

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 25 Example 3 Unit 2 Outcome 2 FURTHER INTEGRATION

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 26 Example 4 Unit 2 Outcome 2 FURTHER INTEGRATION

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 27 Partial Fractions and Long Division Example Unit 2 Outcome 2 FURTHER INTEGRATION

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 28 Integration by Parts Example 1 Unit 2 Outcome 2 FURTHER INTEGRATION

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 29 Integration by Parts Example 2 Unit 2 Outcome 2 FURTHER INTEGRATION

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 30 Example 3 Unit 2 Outcome 2 FURTHER INTEGRATION

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 31 Example 3 (contd) Unit 2 Outcome 2 FURTHER INTEGRATION

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 32 Example 4 Unit 2 Outcome 2 FURTHER INTEGRATION

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 33 Example 4 (contd) Unit 2 Outcome 2 FURTHER INTEGRATION

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 34 First Order- Variables SeparableExample 1 Unit 2 Outcome 2 FURTHER INTEGRATION

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 35 Example 2 Unit 2 Outcome 2 FURTHER INTEGRATION

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 36 Example 3 Unit 2 Outcome 2 FURTHER INTEGRATION

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 37 First Order- Variables Separable Example 3 (contd) Unit 2 Outcome 2 FURTHER INTEGRATION

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 38 Example 1 Particular Solutions of Differential equations Unit 2 Outcome 2 FURTHER INTEGRATION

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 39 Example 3 Unit 2 Outcome 2 FURTHER INTEGRATION

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 40 Example 1Mathematical Models Unit 2 Outcome 2 FURTHER INTEGRATION

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 41 Example 1(contd) Unit 2 Outcome 2 FURTHER INTEGRATION

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 42 Example 1(contd)Mathematical Models Unit 2 Outcome 2 FURTHER INTEGRATION

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 43 Unit 2 Outcome 3 COMPLEX NUMBERS

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 44 Division of Complex Numbers Example 1 Unit 2 Outcome 3 COMPLEX NUMBERS

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 45 Example 2 [ x x 2 ] Unit 2 Outcome 3 COMPLEX NUMBERS

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 46 Example 2 (contd) Unit 2 Outcome 3 COMPLEX NUMBERS

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 47 Modulus and Argument Example 3

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 48 Modulus and Argument

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 49 Multiplication and Division of Complex Numbers in Polar Form

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 50 Example Multiplication and Division of Complex Numbers in Polar Form

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 51 Example(contd) Multiplication and Division of Complex Numbers in Polar Form

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 52 De Moivres Theorem In general

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 53 De Moivres Theorem Example 1

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 54 De Moivres Theorem Example 1(contd)

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 55 Roots of Complex NumbersExample 2

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 56 Roots of Complex NumbersExample 2 (contd) (c)

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 57 Polynomial EquationsExample 3

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 58 Polynomial EquationsExample 3(contd)

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 59 Polynomial EquationsExample 4

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 60 Polynomial EquationsExample 4(contd)

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 61 Polynomial EquationsExample 4(contd)

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 62 Polynomial EquationsExample 4(contd)

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 63 Trigonometric IdentitiesExample 5

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 64 Trigonometric IdentitiesExample 5 (contd)

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 65 Locus in the Complex PlaneExample 6

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 66 Locus in the Complex PlaneExample 7 x

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 67 Standard Formulae Unit 2 Outcome 4 SEQUENCES and SERIES

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 68 Standard Formulae Example 1 Unit 2 Outcome 4 SEQUENCES and SERIES

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 69 nth term of arithmetic series sum of arithmetic series to n terms nth term of geometric series sum of geometric series to n terms sum to infinity of geometric series Unit 2 Outcome 4 SEQUENCES and SERIES

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 70 Example 2 Unit 2 Outcome 4 SEQUENCES and SERIES

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 71 Example3Example3 Unit 2 Outcome 4 SEQUENCES and SERIES

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 72 Geometric SeriesExample 3 (contd)

12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 73 Example4Example4 Unit 2 Outcome 4 SEQUENCES and SERIES