AQA A Level Further Maths: Year 1 + Year 2 (AQA A Level Maths)

Description

Please note this title is suitable for any student studying: Exam Board: AQA Level/Subject: AS and A Level Maths First teaching: September 2017 First exams: June 2018 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), each chapter starts with an Orientation box, clarifying which A Level Maths topics are being built on, and what learning objectives will be covered. Each chapter section starts with a clear and concise explanation of the maths, with an emphasis on visual presentation. Abundant worked examples show how key techniques can be used and common pitfalls to avoid. Separate exercises allow students to practise first their fluency and skills, and then the new exam-style problem-solving and modelling questions. The problem-solving is supported by Strategy boxes, which provide guidance on how best to approach these questions. Answers are given in the back of the book, while full step-by-step solutions to every single question can be found online. This Student Book provides a complete course for Further Maths and is the ideal way for a student to become a mathematician. Cover Contents About this book 1 - Complex numbers 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 2 - Algebra and series 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 3 - Curve sketching 1 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 4 - Integration 1 4.1 - Mean values 4.2 - Volumes of revolution Summary and review Exploration Assessment 5 - Matrices 1 5.1 - Properties and arithmetic 5.2 - Transformations 5.3 - Systems of linear equations Summary and review Exploration Assessment 6 - Vectors 1 6.1 - The vector equation of a line 6.2 - The scalar product 6.3 - Finding distances 1 Summary and review Exploration Assessment 7 - Forces and energy 7.1 - Work, energy and power 7.2 - Hooke's law 7.3 - Dimensional analysis Summary and review Exploration Assessment 8 - Momentum 8.1 - Conservation of momentum 8.2 - Collisions 8.3 - Impulses Summary and review Exploration Assessment 9 - Circular motion 1 9.1 - Kinematics of circular motion 9.2 - Horizontal circular motion Summary and review Exploration Assessment 10 - Discrete and continuous random variables 10.1 - Discrete-distributions and expectation 10.2 - The Poisson distribution 10.3 - Continuous distributions 1 Summary and review Exploration Assessment 11 - Hypothesis testing and contingency tables 11.1 - Hypothesis testing and errors 11.2 - Contingency tables 11.3 - Confidence intervals Summary and review Exploration Assessment 12 - Graphs and networks 1 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 12.6 - The travelling salesman problem 12.7 - Network flows 1 Summary and review Exploration Assessment 13 - Critical path analysis 1 13.1 - Activity networks 13.2 - Critical paths Summary and review Exploration Assessment 14 - Linear programming and game theory 1 14.1 - Constrained optimisation 14.2 - Zero-sum games 14.3 - Mixed-strategy games Summary and review Exploration Assessment 15 - Abstract algebra 15.1 - Binary operations 15.2 - Modular arithmetic Summary and review Exploration Assessment 16 - Complex numbers 2 16.1 - Exponential form 16.2 - De Moivre's theorem 16.3 - Roots of unity Summary and review Exploration Assessment 17 - Series 17.1 - Summing series using partial fractions 17.2 - Maclaurin series 2 Summary and review Exploration Assessment 18 - Curve sketching 2 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 19 - Integration 2 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 20 - Differential equations 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 21 - Numerical methods 21.1 - Numerical integration 21.2 - Euler's method Summary and review Exploration Assessment 22- Matrices 2 22.1 - Determinants, inverse matrices and linear equations 22.2 - Manipulating determinants 22.3 - Eigenvalues and eigenvectors Summary and review Exploration Assessment 23 - Vectors 2 23.1 - The vector product 23.2 - The equation of a plane 23.3 - Finding distances 2 Summary and review Exploration Assessment 24 - Circular motion 2 24.1 - Kinematics of circular motion 2 24.2 - The conical pendulum 24.3 - Vertical circular motion Summary and review Exploration Assessment 25 - Centres of mass and stability 25.1 - Moments and couples 25.2 - Centre of mass for point masses and laminas 25.3 - Centres of mass for laminas and solids 25.4 - Further topics with centres of mass 25.5 - Equilibrium Summary and review Exploration Assessment 26 - Random processes 26.1 - Continuous distributions 2 26.2 - Exponential distribution Summary and review Exploration Assessment 27 - Hypothesis testing and t-test 27.1 - Type II errors and power 27.2 - t-tests Summary and review Exploration Assessment 28 - Graphs and networks 2 28.1 - Planar graphs and isomorphisms 28.2 - Network flows 2 Summary and review Exploration Assessment 29 - Critical path analysis 2 29.1 - Gantt charts 29.2 - Resourcing Summary and review Exploration Assessment 30 - Linear programming and game theory 2 30.1 - Simplex algorithm 30.2 - Games as linear programming problems Summary and review Exploration Assessment 31 - Group theory 31.1 - Groups 31.2 - Subgroups 31.3 - Isomorphisms Summary and review Exploration Assessment Mathematical formulae to learn Mathematical notation Answers Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18 Chapter 19 Chapter 20 Chapter 21 Chapter 22 Chapter 23 Chapter 24 Chapter 25 Chapter 26 Chapter 27 Chapter 28 Chapter 29 Chapter 30 Chapter 31 Index End