AQA A Level Further Maths: Year 1 + Year 2
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Description
Contents
Reviews
Language
English
ISBN
9781382017893
Contents
PURE
Chapter 1: Complex numbers 1
Introduction
1.1 Properties and arithmetic
1.2 Solving polynomial equations
1.3 Argand diagrams
1.4 Modulus-argument form and loci
Summary and review
Exploration
Assessment
Chapter 2: Algebra and series
Introduction
2.1 Roots of polynomials
2.2 Inequalities
2.3 Summing series and the method of differences
2.4 Proof by induction
2.5 Maclaurin series 1
Summary and review
Exploration
Assessment
Chapter 3: Curve sketching 1
Introduction
3.1 Linear rational functions
3.2 Quadratic rational functions
3.3 Polar coordinates
3.4 Parabolas, ellipses and hyperbolas
3.5 Hyperbolic functions 1
Summary and review
Exploration
Assessment
Chapter 4: Integration 1
Introduction
4.1 Mean values
4.2 Volumes of revolution
Summary and review
Exploration
Assessment
Chapter 5: Matrices 1
Introduction
5.1 Properties and arithmetic
5.2 Transformations
5.3 Systems of linear equations
Summary and review
Exploration
Assessment
Chapter 6: Vectors 1
Introduction
6.1 The vector equation of a line
6.2 The scalar product
6.3 Finding distances 1
Summary and review
Exploration
Assessment
MECHANICS
Chapter 7: Forces and energy
Introduction
7.1 Work, energy and power
7.2 Hooke’s law
7.3 Dimensional analysis
Summary and review
Exploration
Assessment
Chapter 8: Momentum
Introduction
8.1 Conservation of momentum
8.2 Collisions
8.3 Impulses
Summary and review
Exploration
Assessment
Chapter 9: Circular motion 1
Introduction
9.1 Kinematics of circular motion
9.2 Horizontal circular motion
Summary and review
Exploration
Assessment
STATISTICS
Chapter 10: Discrete and continuous random variables
Introduction
10.1 Discrete distributions and expectation
10.2 The Poisson distribution
10.3 Continuous distributions 1
Summary and review
Exploration
Assessment
Chapter 11: Hypothesis testing and contingency tables
Introduction
11.1 Hypothesis testing and errors
11.2 Contingency tables
11.3 Confidence intervals
Summary and review
Exploration
Assessment
DISCRETE
Chapter 12: Graphs and networks 1
Introduction
12.1 Graphs and networks
12.2 Traversing a graph
12.3 Minimum spanning trees and Kruskal’s algorithm
12.4 Minimum spanning trees and Prim’s algorithm
12.5 The route inspection problem
e
12.7 Network flows 1
Summary and review
Exploration
Assessment
Chapter 13: Critical path analysis 1
Introduction
13.1 Activity networks
13.2 Critical paths
Summary and review
Exploration
Assessment
Chapter 14: Linear programming and game theory 1
Introduction
14.1 Constrained optimisation
14.2 Zero-sum games
14.3 Mixed-strategy games
Summary and review
Exploration
Assessment
Chapter 15: Abstract algebra
Introduction
15.1 Binary operations
15.2 Modular arithmetic
Summary and review
Exploration
Assessment
PURE
Chapter 16: Complex numbers 2
Introduction
16.1 Exponential form
16.2 De Moivre’s theorem
16.3 Roots of unity
Summary and review
Exploration
Assessment
Chapter 17: Series
Introduction
17.1 Summing series using partial fractions
17.2 Maclaurin series 2
Summary and review
Exploration
Assessment
Chapter 18: Curve sketching 2
Introduction
18.1 Reciprocal and modulus graphs
18.2 Transformations
18.3 Hyperbolic functions 2
18.4 Rational functions with oblique asymptotes
Summary and review
Exploration
Assessment
Chapter 19: Integration 2
Introduction
19.1 Improper integrals
19.2 Inverse trigonometric functions
19.3 Hyperbolic functions
19.4 Partial fractions
19.5 Reduction formulae
19.6 Polar graphs and areas
19.7 Lengths and surface areas
Summary and review
Exploration
Assessment
Chapter 20: Differential equations
Introduction
20.1 First order equations
20.2 Second order equations
20.3 Simple harmonic motion
20.4 Damped and forced harmonic motion
20.5 Coupled equations
Summary and review
Exploration
Assessment
Chapter 21: Numerical methods
Introduction
21.1 Numerical integration
21.2 Euler’s method
Summary and review
Exploration
Assessment
Chapter 22: Matrices 2
Introduction
22.1 Determinants, inverse matrices and linear equations
22.2 Manipulating determinants
22.3 Eigenvalues and eigenvectors
Summary and review
Exploration
Assessment
Chapter 23: Vectors 2
Introduction
23.1 The vector product
23.2 The equation of a plane
23.3 Finding distances 2
Summary and review
Exploration
Assessment
MECHANICS
Chapter 24: Circular motion 2
Introduction
24.1 Kinematics of circular motion 2
24.2 The conical pendulum
24.3 Vertical circular motion
Summary and review
Exploration
Assessment
Chapter 25: Centres of mass and stability
Introduction
25.1 Moments and couples
25.2 Centre of mass for point masses and laminas
25.3 Centre of mass for laminas
25.4 Further topics with centres of mass
25.5 Equilibrium
Summary and review
Exploration
Assessment
STATISTICS
Chapter 26: Random processes
Introduction
26.1 Continuous distributions 2
26.2 Exponential distribution
Summary and review
Exploration
Assessment
Chapter 27: Hypothesis testing and the t-test
Introduction
27.1 Type II errors and power
27.2 The t-test
Summary and review
Exploration
Assessment
DISCRETE
Chapter 28: Graphs and networks 2
Introduction
28.1 Planar graphs and isomorphisms
28.2 Network flows 2
Summary and review
Exploration
Assessment
Chapter 29: Critical path analysis 2
Introduction
29.1 Gantt charts
29.2 Resourcing
Summary and review
Exploration
Assessment
Chapter 30: Linear programming and game theory 2
Introduction
30.1 Simplex algorithm
30.2 Games as linear programming problems
Summary and review
Exploration
Assessment
Chapter 31: Group theory
Introduction
31.1 Groups
31.2 Subgroups
31.3 Isomorphisms
Summary and review
Exploration
Assessment
Mathematical formulae to learn
Mathematical notation
Answers
Index
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