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

11 April 2023St Joseph's College

ADVANCED HIGHER REVISION 1

ADVANCED HIGHER MATHS

REVISION AND FORMULAE

UNIT 2

11 April 2023St Joseph’s College


Inverse Trigonometric Functions

Unit 2 Outcome 1 FURTHER DIFFERENTIATION



Example 1




Example 2




Example 1 Implicit Differentiation




Example 2 Implicit Differentiation




Example Equation of Tangents




Example 2 (contd) Equation of Tangents




Second DerivativesExample




Example (contd) Second Derivatives

2




Logarithmic Differentiation




Example 1 Logarithmic Differentiation




Example 2 Logarithmic Differentiation




Logarithmic DifferentiationExample 2 (contd)




Parametric Differentiation




Equation of TangentsExample



Equation of TangentsExample 1 (contd)




Second Derivatives




Stationary PointsSecond Derivatives AND




Example




Unit 2 Outcome 2 FURTHER INTEGRATION



Example 1

Example 2




Example 3Unit 2 Outcome 2 FURTHER INTEGRATION



Example 4




Partial Fractions and Long DivisionExample




Integration by PartsExample 1




Integration by PartsExample 2




Example 3




Example 3 (contd)




Example 4




Example 4 (contd)




First Order- Variables SeparableExample 1




Example 2




Example 3




First Order- Variables SeparableExample 3 (contd)




Example 1 Particular Solutions of Differential equations




Example 3




Example 1 Mathematical Models




Example 1(contd)




Example 1(contd) Mathematical Models




Unit 2 Outcome 3 COMPLEX NUMBERS



Division of Complex Numbers

Example 1




Example 2

[ x x2 ]




Example 2 (contd)




Modulus and ArgumentExample 3



Modulus and Argument



Multiplication and Division of Complex Numbers in Polar Form



Example




Example(contd)


3

2

w

z



De Moivres Theorem

In general



De Moivres TheoremExample 1



De Moivres TheoremExample 1(contd)



Roots of Complex NumbersExample 2



Roots of Complex NumbersExample 2 (contd)

(c)



Polynomial EquationsExample 3



Polynomial EquationsExample 3(contd)



Polynomial EquationsExample 4



Trigonometric IdentitiesExample 5



Trigonometric IdentitiesExample 5 (contd)



Locus in the Complex PlaneExample 6



Locus in the Complex PlaneExample 7

x



Standard Formulae

Unit 2 Outcome 4 SEQUENCES and SERIES



Standard FormulaeExample 1




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




Example 2




Example 3




Geometric SeriesExample 3 (contd)



Example 4


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

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