Conquer
The
Academy
Welcome
back
Skip to content
Conquer
YOUR A LEVELS
Subjects
Resources
Revision Notes
Practice Questions
Topical Questions
Past Papers
Competitive
Study space
Log in
Create free account
Study space
Subjects
Competitive
Revision Notes
Practice Questions
Topical Questions
Past Papers
Browse all practice
Log in
Create free account
Search resources
Further Mathematics
Revision Notes
Further Pure Mathematics 2
Further Mathematics · Cambridge 9231
Further Pure Mathematics 2
6 chapters · 56 lessons
Paper
Further Pure Mathematics 1
Further Pure Mathematics 2
Further Probability & Statistics
Expand all
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