\$63.75

# AQA A Level Further Maths: Year 1 + Year 2

By Katie Wood, Brian Jefferson, David Bowles, Eddie Mullan, Garry Wiseman, John Rayneau, Mike Heylings, Rob Wagner, Paul Williams, Neil Tully, Shaun Procter-Green, L Bostock, Tony Beadsworth, C P Rourke, Mark Gaulter, Brian Gaulter, Robert Smedley, Ian Cook, Graham Upton, Thorning, Sadler
US\$ 63.75
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Book Description

This Student Book provides full support for AQA's new linear Further Maths specification. Covering both the compulsory content (further pure) and all the optional content (mechanics, statistics and discrete maths), it offers dedicated problem-solving exercises, along with abundant worked examples.

Table of Contents
• 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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