12 october, 2014 st joseph's college advanced higher revision 1 advanced higher maths revision...
TRANSCRIPT
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11 April 2023St Joseph's College
ADVANCED HIGHER REVISION 1
ADVANCED HIGHER MATHS
REVISION AND FORMULAE
UNIT 2
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11 April 2023St Joseph’s College
ADVANCED HIGHER REVISION 2
Inverse Trigonometric Functions
Unit 2 Outcome 1 FURTHER DIFFERENTIATION
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11 April 2023St Joseph’s College
ADVANCED HIGHER REVISION 3
Example 1
Unit 2 Outcome 1 FURTHER DIFFERENTIATION
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11 April 2023St Joseph’s College
ADVANCED HIGHER REVISION 4
Example 2
Unit 2 Outcome 1 FURTHER DIFFERENTIATION
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11 April 2023St Joseph’s College
ADVANCED HIGHER REVISION 5
Example 1 Implicit Differentiation
Unit 2 Outcome 1 FURTHER DIFFERENTIATION
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11 April 2023St Joseph’s College
ADVANCED HIGHER REVISION 6
Example 2 Implicit Differentiation
Unit 2 Outcome 1 FURTHER DIFFERENTIATION
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11 April 2023St Joseph’s College
ADVANCED HIGHER REVISION 7
Example Equation of Tangents
Unit 2 Outcome 1 FURTHER DIFFERENTIATION
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11 April 2023St Joseph’s College
ADVANCED HIGHER REVISION 8
Example 2 (contd) Equation of Tangents
Unit 2 Outcome 1 FURTHER DIFFERENTIATION
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11 April 2023St Joseph’s College
ADVANCED HIGHER REVISION 9
Second DerivativesExample
Unit 2 Outcome 1 FURTHER DIFFERENTIATION
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ADVANCED HIGHER REVISION 10
Example (contd) Second Derivatives
2
Unit 2 Outcome 1 FURTHER DIFFERENTIATION
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11 April 2023St Joseph's College
ADVANCED HIGHER REVISION 11
Logarithmic Differentiation
Unit 2 Outcome 1 FURTHER DIFFERENTIATION
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11 April 2023St Joseph's College
ADVANCED HIGHER REVISION 12
Example 1 Logarithmic Differentiation
Unit 2 Outcome 1 FURTHER DIFFERENTIATION
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11 April 2023St Joseph's College
ADVANCED HIGHER REVISION 13
Example 2 Logarithmic Differentiation
Unit 2 Outcome 1 FURTHER DIFFERENTIATION
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ADVANCED HIGHER REVISION 14
Logarithmic DifferentiationExample 2 (contd)
Unit 2 Outcome 1 FURTHER DIFFERENTIATION
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11 April 2023St Joseph's College
ADVANCED HIGHER REVISION 15
Parametric Differentiation
Unit 2 Outcome 1 FURTHER DIFFERENTIATION
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11 April 2023St Joseph's College
ADVANCED HIGHER REVISION 16
Equation of TangentsExample
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ADVANCED HIGHER REVISION 17
Equation of TangentsExample 1 (contd)
Unit 2 Outcome 1 FURTHER DIFFERENTIATION
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11 April 2023St Joseph's College
ADVANCED HIGHER REVISION 18
Second Derivatives
Unit 2 Outcome 1 FURTHER DIFFERENTIATION
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11 April 2023St Joseph's College
ADVANCED HIGHER REVISION 19
Stationary PointsSecond Derivatives AND
Unit 2 Outcome 1 FURTHER DIFFERENTIATION
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11 April 2023St Joseph's College
ADVANCED HIGHER REVISION 20
Example
Unit 2 Outcome 1 FURTHER DIFFERENTIATION
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11 April 2023St Joseph's College
ADVANCED HIGHER REVISION 21
Unit 2 Outcome 1 FURTHER DIFFERENTIATION
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11 April 2023St Joseph's College
ADVANCED HIGHER REVISION 22
Unit 2 Outcome 1 FURTHER DIFFERENTIATION
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ADVANCED HIGHER REVISION 23
Unit 2 Outcome 2 FURTHER INTEGRATION
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ADVANCED HIGHER REVISION 24
Example 1
Example 2
Unit 2 Outcome 2 FURTHER INTEGRATION
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ADVANCED HIGHER REVISION 25
Example 3Unit 2 Outcome 2 FURTHER INTEGRATION
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ADVANCED HIGHER REVISION 26
Example 4
Unit 2 Outcome 2 FURTHER INTEGRATION
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11 April 2023St Joseph's College
ADVANCED HIGHER REVISION 27
Partial Fractions and Long DivisionExample
Unit 2 Outcome 2 FURTHER INTEGRATION
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11 April 2023St Joseph's College
ADVANCED HIGHER REVISION 28
Integration by PartsExample 1
Unit 2 Outcome 2 FURTHER INTEGRATION
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11 April 2023St Joseph's College
ADVANCED HIGHER REVISION 29
Integration by PartsExample 2
Unit 2 Outcome 2 FURTHER INTEGRATION
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ADVANCED HIGHER REVISION 30
Example 3
Unit 2 Outcome 2 FURTHER INTEGRATION
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ADVANCED HIGHER REVISION 31
Example 3 (contd)
Unit 2 Outcome 2 FURTHER INTEGRATION
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ADVANCED HIGHER REVISION 32
Example 4
Unit 2 Outcome 2 FURTHER INTEGRATION
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ADVANCED HIGHER REVISION 33
Example 4 (contd)
Unit 2 Outcome 2 FURTHER INTEGRATION
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ADVANCED HIGHER REVISION 34
First Order- Variables SeparableExample 1
Unit 2 Outcome 2 FURTHER INTEGRATION
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ADVANCED HIGHER REVISION 35
Example 2
Unit 2 Outcome 2 FURTHER INTEGRATION
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ADVANCED HIGHER REVISION 36
Example 3
Unit 2 Outcome 2 FURTHER INTEGRATION
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ADVANCED HIGHER REVISION 37
First Order- Variables SeparableExample 3 (contd)
Unit 2 Outcome 2 FURTHER INTEGRATION
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11 April 2023St Joseph's College
ADVANCED HIGHER REVISION 38
Example 1 Particular Solutions of Differential equations
Unit 2 Outcome 2 FURTHER INTEGRATION
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11 April 2023St Joseph's College
ADVANCED HIGHER REVISION 39
Example 3
Unit 2 Outcome 2 FURTHER INTEGRATION
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11 April 2023St Joseph's College
ADVANCED HIGHER REVISION 40
Example 1 Mathematical Models
Unit 2 Outcome 2 FURTHER INTEGRATION
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11 April 2023St Joseph's College
ADVANCED HIGHER REVISION 41
Example 1(contd)
Unit 2 Outcome 2 FURTHER INTEGRATION
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11 April 2023St Joseph's College
ADVANCED HIGHER REVISION 42
Example 1(contd) Mathematical Models
Unit 2 Outcome 2 FURTHER INTEGRATION
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11 April 2023St Joseph's College
ADVANCED HIGHER REVISION 43
Unit 2 Outcome 3 COMPLEX NUMBERS
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11 April 2023St Joseph's College
ADVANCED HIGHER REVISION 44
Division of Complex Numbers
Example 1
Unit 2 Outcome 3 COMPLEX NUMBERS
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ADVANCED HIGHER REVISION 45
Example 2
[ x x2 ]
Unit 2 Outcome 3 COMPLEX NUMBERS
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ADVANCED HIGHER REVISION 46
Example 2 (contd)
Unit 2 Outcome 3 COMPLEX NUMBERS
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11 April 2023St Joseph's College
ADVANCED HIGHER REVISION 47
Modulus and ArgumentExample 3
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11 April 2023St Joseph's College
ADVANCED HIGHER REVISION 48
Modulus and Argument
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11 April 2023St Joseph's College
ADVANCED HIGHER REVISION 49
Multiplication and Division of Complex Numbers in Polar Form
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11 April 2023St Joseph's College
ADVANCED HIGHER REVISION 50
Example
Multiplication and Division of Complex Numbers in Polar Form
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Example(contd)
Multiplication and Division of Complex Numbers in Polar Form
3
2
w
z
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ADVANCED HIGHER REVISION 52
De Moivres Theorem
In general
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ADVANCED HIGHER REVISION 53
De Moivres TheoremExample 1
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ADVANCED HIGHER REVISION 54
De Moivres TheoremExample 1(contd)
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ADVANCED HIGHER REVISION 55
Roots of Complex NumbersExample 2
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Roots of Complex NumbersExample 2 (contd)
(c)
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ADVANCED HIGHER REVISION 57
Polynomial EquationsExample 3
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Polynomial EquationsExample 3(contd)
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ADVANCED HIGHER REVISION 59
Polynomial EquationsExample 4
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Polynomial EquationsExample 4(contd)
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Polynomial EquationsExample 4(contd)
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11 April 2023St Joseph's College
ADVANCED HIGHER REVISION 62
Polynomial EquationsExample 4(contd)
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11 April 2023St Joseph's College
ADVANCED HIGHER REVISION 63
Trigonometric IdentitiesExample 5
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11 April 2023St Joseph's College
ADVANCED HIGHER REVISION 64
Trigonometric IdentitiesExample 5 (contd)
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11 April 2023St Joseph's College
ADVANCED HIGHER REVISION 65
Locus in the Complex PlaneExample 6
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11 April 2023St Joseph's College
ADVANCED HIGHER REVISION 66
Locus in the Complex PlaneExample 7
x
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11 April 2023St Joseph's College
ADVANCED HIGHER REVISION 67
Standard Formulae
Unit 2 Outcome 4 SEQUENCES and SERIES
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11 April 2023St Joseph's College
ADVANCED HIGHER REVISION 68
Standard FormulaeExample 1
Unit 2 Outcome 4 SEQUENCES and SERIES
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11 April 2023St 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
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11 April 2023St Joseph's College
ADVANCED HIGHER REVISION 70
Example 2
Unit 2 Outcome 4 SEQUENCES and SERIES
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11 April 2023St Joseph's College
ADVANCED HIGHER REVISION 71
Example 3
Unit 2 Outcome 4 SEQUENCES and SERIES
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11 April 2023St Joseph's College
ADVANCED HIGHER REVISION 72
Geometric SeriesExample 3 (contd)
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ADVANCED HIGHER REVISION 73
Example 4
Unit 2 Outcome 4 SEQUENCES and SERIES