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Further Mathematics
Revision Notes
Further Pure Mathematics 2
Further Mathematics · Cambridge 9231
Further Pure Mathematics 2
6 chapters · 56 lessons
Collection
Further Pure Mathematics 1
Further Pure Mathematics 2
Further Mechanics
Further Probability & Statistics
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01
Hyperbolic functions
9 lessons · 4 topic areas
01
Definitions and graphs
2 lessons
Understanding sinh and cosh
Tanh and the reciprocal functions
02
Identities and equations
3 lessons
The basic hyperbolic identities
Addition and double-input identities
Solving hyperbolic equations
03
Inverse functions
3 lessons
Understanding inverse hyperbolic functions
Deriving logarithmic forms
Inverse sech, cosech and coth
04
Graph transformations
1 lesson
Graph transformations and mixed questions
Practise this chapter
02
Matrices 2
9 lessons · 3 topic areas
01
Eigenvalues and eigenvectors
4 lessons
Understanding eigenvectors
Finding eigenvalues and eigenvectors
Three-by-three matrices
Eigenvalues of related matrices
02
Diagonalisation and powers
3 lessons
Understanding diagonalisation
Calculating matrix powers
The Cayley–Hamilton theorem
03
Systems of equations
2 lessons
Solving three linear equations
Solutions, parameters and planes
03
Differentiation
8 lessons · 3 topic areas
01
Second derivatives
2 lessons
Implicit second derivatives
Parametric second derivatives
02
Hyperbolic and inverse derivatives
3 lessons
Hyperbolic derivatives
Inverse trigonometric derivatives
Inverse hyperbolic derivatives
03
Maclaurin series
3 lessons
Building a Maclaurin polynomial
Using known series
Series from derivative relations
Practise this chapter
04
Integration
11 lessons · 4 topic areas
01
Integration methods
4 lessons
Hyperbolic integrals
Integrals with square roots
Integrals with quadratic denominators
Parts and further substitutions
02
Reduction formulae
2 lessons
Trigonometric reduction formulae
Other reduction formulae
03
Arc length and surface area
3 lessons
Cartesian and parametric arc length
Polar arc length
Surface area of revolution
04
Sums and integrals
2 lessons
Integral bounds for sums
Limits of sums
Practise this chapter
05
Complex numbers
8 lessons · 4 topic areas
01
Complex forms and powers
2 lessons
Complex numbers as lengths and angles
De Moivre's theorem
02
Trigonometric identities
2 lessons
Multiple angles and polynomial equations
Powers of sine and cosine
03
Complex roots
2 lessons
Roots of unity
Complex roots and rational powers
04
Trigonometric sums
2 lessons
Finite trigonometric sums
Weighted and binomial sums
Practise this chapter
06
Differential equations
11 lessons · 5 topic areas
01
First-order linear equations
2 lessons
Why integrating factors work
Choosing an integrating factor
02
Homogeneous second-order equations
3 lessons
The auxiliary equation
Repeated roots
Complex roots and oscillation
03
Particular integrals
2 lessons
Complementary functions and particular integrals
When a PI trial is already in the CF
04
Substitutions
3 lessons
First-order substitutions
Substituting for the dependent variable
Changing the independent variable
05
Initial conditions and models
1 lesson
Initial conditions and models
Practise this chapter
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Further Mathematics
AS & A Level · 9231
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