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ADVANCED HIGHER MATHS

REVISION AND FORMULAE

UNIT 2

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Inverse Trigonometric Functions

Unit 2 Outcome 1 FURTHER DIFFERENTIATION

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Example 1

Unit 2 Outcome 1 FURTHER DIFFERENTIATION

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Example 2

Unit 2 Outcome 1 FURTHER DIFFERENTIATION

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Example 1 Implicit Differentiation

Unit 2 Outcome 1 FURTHER DIFFERENTIATION

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Example 2 Implicit Differentiation

Unit 2 Outcome 1 FURTHER DIFFERENTIATION

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Example Equation of Tangents

Unit 2 Outcome 1 FURTHER DIFFERENTIATION

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Example 2 (contd) Equation of Tangents

Unit 2 Outcome 1 FURTHER DIFFERENTIATION

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Second DerivativesExample

Unit 2 Outcome 1 FURTHER DIFFERENTIATION

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Example (contd) Second Derivatives

2

Unit 2 Outcome 1 FURTHER DIFFERENTIATION

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Logarithmic Differentiation

Unit 2 Outcome 1 FURTHER DIFFERENTIATION

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Example 1 Logarithmic Differentiation

Unit 2 Outcome 1 FURTHER DIFFERENTIATION

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Example 2 Logarithmic Differentiation

Unit 2 Outcome 1 FURTHER DIFFERENTIATION

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Logarithmic DifferentiationExample 2 (contd)

Unit 2 Outcome 1 FURTHER DIFFERENTIATION

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Parametric Differentiation

Unit 2 Outcome 1 FURTHER DIFFERENTIATION

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Equation of TangentsExample

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Equation of TangentsExample 1 (contd)

Unit 2 Outcome 1 FURTHER DIFFERENTIATION

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Second Derivatives

Unit 2 Outcome 1 FURTHER DIFFERENTIATION

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Stationary PointsSecond Derivatives AND

Unit 2 Outcome 1 FURTHER DIFFERENTIATION

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Example

Unit 2 Outcome 1 FURTHER DIFFERENTIATION

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Unit 2 Outcome 1 FURTHER DIFFERENTIATION

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Unit 2 Outcome 1 FURTHER DIFFERENTIATION

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Unit 2 Outcome 2 FURTHER INTEGRATION

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Example 1

Example 2

Unit 2 Outcome 2 FURTHER INTEGRATION

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Example 3Unit 2 Outcome 2 FURTHER INTEGRATION

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Example 4

Unit 2 Outcome 2 FURTHER INTEGRATION

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Partial Fractions and Long DivisionExample

Unit 2 Outcome 2 FURTHER INTEGRATION

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Integration by PartsExample 1

Unit 2 Outcome 2 FURTHER INTEGRATION

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Integration by PartsExample 2

Unit 2 Outcome 2 FURTHER INTEGRATION

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Example 3

Unit 2 Outcome 2 FURTHER INTEGRATION

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Example 3 (contd)

Unit 2 Outcome 2 FURTHER INTEGRATION

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Example 4

Unit 2 Outcome 2 FURTHER INTEGRATION

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Example 4 (contd)

Unit 2 Outcome 2 FURTHER INTEGRATION

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First Order- Variables SeparableExample 1

Unit 2 Outcome 2 FURTHER INTEGRATION

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Example 2

Unit 2 Outcome 2 FURTHER INTEGRATION

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Example 3

Unit 2 Outcome 2 FURTHER INTEGRATION

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First Order- Variables SeparableExample 3 (contd)

Unit 2 Outcome 2 FURTHER INTEGRATION

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Example 1 Particular Solutions of Differential equations

Unit 2 Outcome 2 FURTHER INTEGRATION

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Example 3

Unit 2 Outcome 2 FURTHER INTEGRATION

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Example 1 Mathematical Models

Unit 2 Outcome 2 FURTHER INTEGRATION

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Example 1(contd)

Unit 2 Outcome 2 FURTHER INTEGRATION

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Example 1(contd) Mathematical Models

Unit 2 Outcome 2 FURTHER INTEGRATION

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Unit 2 Outcome 3 COMPLEX NUMBERS

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Division of Complex Numbers

Example 1

Unit 2 Outcome 3 COMPLEX NUMBERS

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Example 2

[ x x2 ]

Unit 2 Outcome 3 COMPLEX NUMBERS

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Example 2 (contd)

Unit 2 Outcome 3 COMPLEX NUMBERS

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Modulus and ArgumentExample 3

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Modulus and Argument

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Multiplication and Division of Complex Numbers in Polar Form

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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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De Moivres Theorem

In general

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De Moivres TheoremExample 1

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De Moivres TheoremExample 1(contd)

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Roots of Complex NumbersExample 2

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Roots of Complex NumbersExample 2 (contd)

(c)

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Polynomial EquationsExample 3

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Polynomial EquationsExample 3(contd)

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Polynomial EquationsExample 4

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Polynomial EquationsExample 4(contd)

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Polynomial EquationsExample 4(contd)

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Polynomial EquationsExample 4(contd)

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Trigonometric IdentitiesExample 5

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Trigonometric IdentitiesExample 5 (contd)

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Locus in the Complex PlaneExample 6

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Locus in the Complex PlaneExample 7

x

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Standard Formulae

Unit 2 Outcome 4 SEQUENCES and SERIES

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Standard FormulaeExample 1

Unit 2 Outcome 4 SEQUENCES and SERIES

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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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Example 2

Unit 2 Outcome 4 SEQUENCES and SERIES

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Example 3

Unit 2 Outcome 4 SEQUENCES and SERIES

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Geometric SeriesExample 3 (contd)

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Example 4

Unit 2 Outcome 4 SEQUENCES and SERIES