Mathematics for the IB Diploma: Analysis and approaches HL

Description

Enable students to construct, communicate and justify correct mathematical arguments with a range of activities and examples of maths in the real world. - Engage and excite students with examples and photos of maths in the real world, plus inquisitive starter activities to encourage their problem-solving skills - Build mathematical thinking with our 'Toolkit' and mathematical exploration chapter, along with our new toolkit feature of questions, investigations and activities - Develop understanding with key concepts and applications integrated throughout, along with TOK links for every topic - Prepare your students for assessment with worked examples, and extended essay support - Check understanding with review exercise midway and at the end of the coursebook Follows the new 2019 IB Guide for Mathematics: analysis and approaches Higher Level Available in the series Mathematics for the IB Diploma: Analysis and approaches SL Student Book ISBN: 9781510462359 Student eTextbook ISBN: 9781510461895 Whiteboard eTextbook ISBN: 9781510461901 Mathematics for the IB Diploma: Analysis and approaches HL Student Book ISBN: 9781510462366 Student eTextbook ISBN: 9781510461857 Whiteboard eTextbook ISBN: 9781510461864 SL & HL Teaching & Learning Resources ISBN: 9781510461918 Mathematics for the IB Diploma: Applications and interpretation SL Student Book ISBN: 9781510462380 Student eTextbook ISBN: 9781510461994 Whiteboard eTextbook ISBN: 9781510462007 Mathematics for the IB Diploma: Applications and interpretation HL Student Book ISBN: 9781510462373 Student eTextbook ISBN: 9781510461956 Whiteboard eTextbook ISBN: 9781510461963 SL and HL Teaching & Learning Resources ISBN: 9781510462014 Dynamic learning packages (include Teaching & Learning resources and Whiteboard eTextbooks) Analysis & approaches SL & HL ISBN: 9781510461925 Applications and interpretation SL and HL ISBN: 9781510462021 Analysis & approaches SL & HL and Applications and interpretation SL and HL ISBN: 9781510468474 Cover Book title Copyright Contents Introduction Chapter 1 Counting principles 1A Basic techniques 1B Problem solving Chapter 2 Algebra 2A Extension of the binomial theorem to fractional and negative indices 2B Partial fractions 2C Solutions of systems of linear equations Chapter 3 Trigonometry 3A Further trigonometric functions 3B Compound angle identities Chapter 4 Complex numbers 4A Cartesian form 4B Modulus–argument form and Euler form 4C Complex conjugate roots of quadratic and polynomial equations with real coefficients 4D Powers and roots of complex numbers 4E Trigonometric identities Chapter 5 Mathematical proof 5A Proof by induction 5B Proof by contradiction 5C Disproof by counterexample Chapter 6 Polynomials 6A Graphs and equations of polynomial functions 6B The factor and remainder theorems 6C Sum and product of roots of polynomial equations Chapter 7 Functions 7A Rational functions of the form f(x) = (Formula) 7B Solutions of g(x) ≥ f(x), both analytically and graphically 7C The graphs of the functions y= |f(x)| and y= f(|x|) 7D The graphs of the functions y= (Formula) y= f(ax + b) and y= [f(x)][sup(2)] 7E Properties of functions Chapter 8 Vectors 8A Introduction to vectors 8B Vectors and geometry 8C Scalar product and angles 8D Equation of a line in three dimensions 8E Intersection of lines 8F Vector product and areas 8G Equation of a plane 8H Angles and intersections between lines and planes Chapter 9 Probability 9A Bayes’ theorem 9B Variance of a discrete random variable 9C Continuous random variables Chapter 10 Further calculus 10A Fundamentals of calculus 10B L’Hôpital’s rule 10C Implicit differentiation 10D Related rates of change 10E Optimization 10F Calculus applied to more functions 10G Integration by substitution 10H Integration by parts 10I Further geometric interpretation of integrals Chapter 11 Series and differential equations 11A First order differential equations and Euler’s method 11B Separating variables and homogeneous differential equations 11C Integrating factors 11D Maclaurin series 11E Using Maclaurin series to solve differential equations Analysis and approaches HL: Practice Paper 1 Analysis and approaches HL: Practice Paper 2 Guidance for Paper 3 Analysis and approaches HL: Practice Paper 3 Answers Glossary A B C D E F G H I L M O P R S U Untitled Index A B C D E F G H I L M N O P Q R S T U V W X Y Z