AQA A Level Further Mathematics Year 2
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Description
Contents
Reviews
Language
English
ISBN
9781510442450
Cover
Title Page
Copyright
Contents
Getting the most from this book
Prior knowledge
1 Vectors 1
Review: Working with vectors
1.1 Using the scalar product to express the equation of a plane
1.2 Intersecting planes
Review: Matrices and transformations
R.1 Matrices
R.2 Using matrices to represent transformations
R.3 Invariance
2 Matrices 1
Review: Determinant and inverse of a 2 × 2 matrix
2.1 Determinant and inverse of a 3 × 3 matrix
2.2 Solving simultaneou sequations in three unknowns and its geometrical interpretation
2.3 Factorisation of determinants using row and column operations
3 Conics
Review: Conic sections
3.1 Conics and further transformations
4 Series and induction
Review: Summing series
4.1 Applying the method of differences with partial fractions
Review: Proof by induction
Practice Questions Further Mathematics 1
5 Further algebra and graphs
5.1 Graphs with oblique asymptotes
5.2 Modulus and reciprocal graphs
5.3 Equations and inequalities
6 Further calculus
6.1 Improper integrals
6.2 Calculus with inverse trigonometric functions
6.3 Partial fractions
6.4 Further integration
7 Polar coordinates
Review: Polar coordinates
7.1 Finding the area enclosed by a polar curve
8 Series and limits
8.1 Polynomial approximations and Maclaurin series
8.2 Using Maclaurin series for standard functions
8.3 Evaluating limits
Practice Questions Further Mathematics 2
9 Matrices 2
9.1 Eigenvalues and eigenvectors
9.2 Diagonalisation of matrices
Review: Complex numbers
R.1 Working with complex numbers
R.2 Representing complex numbers geometrically
10 Hyperbolic functions
10.1 Hyperbolic functions
10.2 Identities
10.3 Inverse hyperbolic functions
10.4 Calculus and hyperbolic functions
11 Further integration
Review: Volumes of revolution and mean values
11.1 General integration
11.2 Two limits
11.3 Reduction formulae
11.4 Curved lengths and surface areas
Review: Roots of polynomials
R.1 Roots and coefficients
R.2 Complex roots of polynomial equations
12 First order differential equations
12.1 Modelling rates of change
12.2 Separation of variables
12.3 Integrating factors and integration by substitution
Practice Questions Further Mathematics 3
13 Numerical methods
13.1 Numerical integration
13.2 Euler’s method
14 Complex numbers
Review: The modulus and argument of a complex number
14.1 DeMoivre's theorem
14.2 The nth roots of a complex number
14.3 Finding multiple angle identities using de Moivre's theorem
14.4 The form z = reiθ
15 Vectors 2
Review: Distance between point and line and between two lines
15.1 Lines and planes
15.2 The vector product
16 Second order differential equations
16.1 Higher order differential equations
16.2 Auxiliary equations with complex roots
16.3 Simple harmonic motion: Further calculations
16.4 Non-homogeneous differential equations
16.5 Systems of differential equations
Practice Questions Further Mathematics 4
Answers
Index
Full Worked Solutions
Back Cover
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