Mathematics for the IB Diploma: Analysis and approaches HL
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Description
Contents
Reviews
Language
English
ISBN
9781510461840
Cover
Title Page
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) = ax + b / cx2 + dx + e and f(x) = ax2 + bx + c / dx + e
■ 7B Solutions of g(x) ≥ f(x), both analytically and graphically
■ 7C The graphs of the functions y = |f(x)| and y = f(|x|)2
■ 7D The graphs of the functions y = 1 / f(x) y = f(ax + b) and y = [f(x)]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
Index
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