Mathematics for the IB Diploma: Analysis and approaches HL

✍ Scribed by Paul Fannon, Vesna Kadelburg, Ben Woolley, Stephen Ward

• Publisher: Hodder Education
• Year: 2020
• Tongue: English
• Leaves: 490
• Edition: 1
• Category: Library

✦ Synopsis

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

✦ Table of Contents

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
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Untitled
Index
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