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IB Mathematics Analysis & Approaches SL - Textbook (NYP Due July 21, 2019)

$45.00

Publisher: Haese Mathematics ISBN-13: 9781925489569

Author: Michael Haese; Mark Humphries; Chris Sangwin; Ngoc Vo

Curriculum: IB Diploma Programme International Baccalaureate

Format: Paperback

Isbn 10: 1925489566

Language: English

Release date: 04/30/2019

Series: IB Diploma Program

Year: 2019

Description

This book has been written for the IB Diploma Programme course Mathematics: analysis and approaches SL, for first assessment in May 2021.

This book is designed to complete the course in conjunction with the Mathematics: Core topics SL textbook. It is expected that students will start using this book approximately 6-7 months into the two-year course, upon the completion of the Mathematics: Core topics SL textbook.

The Mathematics: analysis and approaches courses have a focus on algebraic rigour, and this book is written with this focus in mind. The material is presented in a clear, easy-to-follow style, free from unnecessary distractions, while effort has been made to contextualise questions so that students can relate concepts to everyday use.

Each chapter begins with an Opening Problem, offering an insight into the application of the mathematics that will be studied in the chapter. Important information and key notes are highlighted, while worked examples provide step-by-step instructions with concise and relevant explanations. Discussions, Activities, Investigations, and Research exercises are used throughout the chapters to develop understanding, problem solving, and reasoning.

Discussion topics for Theory of Knowledge are included throughout the book.

Table of Contents

Mathematics: analysis and approaches SL

1          THE BINOMIAL THEOREM           

           A          Factorial notation     

           B          Binomial expansions

           C          The binomial theorem         

2          QUADRATIC FUNCTIONS  

           A          Quadratic functions 

           B          Graphs of quadratic functions        

           C          Using the discriminant        

           D         Finding a quadratic from its graph

           E          Simultaneous equations      

           F          Problem solving with quadratics   

           G          Optimisation with quadratics         

3          FUNCTIONS  

           A          Relations and functions       

           B          Function notation     

           C          Domain and range   

           D         Composite functions

           E          Sign diagrams           

           F          Rational functions    

           G          Inverse functions     

           H         Graphs of functions 

           I           Absolute value functions     

4          TRANSFORMATIONS OF FUNCTIONS     

           A          Translations  

           B          Stretches       

           C          Reflections    

           D         Miscellaneous transformations      

5          EXPONENTIAL FUNCTIONS          

           A          Rational exponents  

           B          Algebraic expansion and factorisation      

           C          Exponential equations        

           D         Exponential functions         

           E          Growth and decay    

           F          The natural exponential     

6          LOGARITHMS          

           A          Logarithms in base 1010    

           B          Logarithms in base aa         

           C          Laws of logarithms   

           D         Natural logarithms   

           E          Logarithmic equations         

           F          The change of base rule      

           G          Solving exponential equations using logarithms  

           H         Logarithmic functions          

7          THE UNIT CIRCLE AND RADIAN MEASURE       

           A          Radian measure       

           B          Arc length and sector area  

           C          The unit circle          

           D         Multiples of \frac \pi 6

​​           

           E          The Pythagorean identity   

           F          Finding angles          

8          TRIGONOMETRIC FUNCTIONS     

           A          Periodic behaviour  

           B          The sine and cosine functions        

           C          General sine and cosine functions 

           D         Modelling periodic behaviour        

           E          The tangent function           

9          TRIGONOMETRIC EQUATIONS AND IDENTITIES         

           A          Trigonometric equations     

           B          Using trigonometric models

           C          Trigonometric identities      

           D         Double angle identities       

10       REASONING AND PROOF   

           A          Logical connectives  

           B          Proof by deduction  

           C          Proof by equivalence           

           D         Definitions    

11       INTRODUCTION TO DIFFERENTIAL CALCULUS           

           A          Rates of change        

           B          Instantaneous rates of change       

           C          Limits 

           D         The gradient of a tangent   

           E          The derivative function       

           F          Differentiation from first principles          

12       RULES OF DIFFERENTIATION     

           A          Simple rules of differentiation       

           B          The chain rule          

           C          The product rule      

           D         The quotient rule     

           E          Derivatives of exponential functions         

           F          Derivatives of logarithmic functions          

           G          Derivatives of trigonometric functions      

           H         Second derivatives   

13       PROPERTIES OF CURVES  

           A          Tangents       

           B          Normals         

           C          Increasing and decreasing  

           D         Stationary points      

           E          Shape

           F          Inflection points       

           G          Understanding functions and their derivatives   

14       APPLICATIONS OF DIFFERENTIATION  

           A          Rates of change        

           B          Optimisation 

15       INTRODUCTION TO INTEGRATION        

           A          Approximating the area under a curve     

           B          The Riemann integral          

           C          Antidifferentiation   

           D         The Fundamental Theorem of Calculus    

16       TECHNIQUES FOR INTEGRATION           

           A          Discovering integrals           

           B          Rules for integration

           C          Particular values      

           D         Integrating f(ax + b)f(ax+b)          

           E          Integration by substitution 

17       DEFINITE INTEGRALS       

           A          Definite integrals     

           B          The area under a curve      

           C          The area above a curve       

           D         The area between two functions   

18       KINEMATICS

           A          Displacement

           B          Velocity          

           C          Acceleration  

           D         Speed

19       BIVARIATE STATISTICS   

           A          Association between numerical variables 

           B          Pearson's product-moment correlation coefficient          

           C          The coefficient of determination    

           D         Line of best fit by eye          

           E          The least squares regression line  

           F          The regression line of xx against yy          

20       DISCRETE RANDOM VARIABLES 

           A          Random variables    

           B          Discrete probability distributions  

           C          Expectation   

           D         The binomial distribution   

           E          Using technology to find binomial probabilities   

           F          The mean and standard deviation of a binomial distribution    

21       THE NORMAL DISTRIBUTION     

           A          Introduction to the normal distribution    

           B          Calculating probabilities     

           C          The standard normal distribution 

           D         Quantiles

This product has been developed independently from and is not endorsed by the International Baccalaureate Organization.  International Baccalaureate, Baccalaureát International, Bachillerato Internacional and IB are registered trademarks owned by the International Baccalaureate Organization.

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