# Oxford IB Diploma Programme: Mathematics Standard Level Course Companion

With unrivalled guidance straight from the IB, over 700 pages of practice and the most comprehensive and correct syllabus coverage, this course book will set your learners up to excel. The only resource developed directly with the IB, it fully captures the IB ethos, connecting mathematical applications and practice with inquiry.

Full syllabus coverage - the truest match to the IB syllabus, written with the IB to exactly match IB specifications

Complete worked solutions - a full set of online worked solutions take learners through problems step-by-step inow updatedr

Up-to-date GDC support - take the confusion out of GDC use and help students focus on the theory

Definitive assessment preparation - exam-style papers and questions will build confidence

Extensive practice - over 700 pages of practice cements comprehension

The Exploration - supported by a full chapter, to guide you through this new component

Real world approach - connect mathematics with human behaviour, language and more

- Front Cover
- A note on academic honesty
- About the book
- Contents
- What's on the CD?
- What's on the website?
- 1 Functions
- 1.1 Introducing functions
- 1.2 The domain and range of a relationon a Cartesian plane
- 1.3 Function notation
- 1.4 Composite functions
- 1.5 Inverse functions
- 1.6 Transforming functions

- 2 Quadratic functions and equations
- 2.1 Solving quadratic equations
- 2.2 The quadratic formula
- 2.3 Roots of quadratic equations
- 2.4 Graphs of quadratic functions
- 2.5 applications of quadratics

- 3 Probability
- 3.1 Definitions
- 3.2 Venn diagrams
- 3.3 Sample space diagrams and the product rule
- 3.4 Conditional probability
- 3.5 Probability tree diagrams

- 4 Exponential and logarithmic functions
- 4.1 Exponents
- 4.2 Solving exponential equations
- 4.3 Exponential functions
- 4.4 Properties of logarithms
- 4.5 Logarithmic functions
- 4.6 Laws of logarithms
- 4.7 Exponential and logarithmic equations
- 4.8 Applications of exponential and logarithmic functions

- 5 Rationalfunctions
- 5.1 Reciprocals
- 5.2 The reciprocal function
- 5.3 Rational functions

- 6 Patterns, sequences and series
- 6.1 Patterns and sequences
- 6.2 Arithmetic sequences
- 6.3 Geometric sequences
- 6.4 Sigma (Σ) notation and series
- 6.5 Arithmetic series
- 6.6 Geometric series
- 6.7 Convergent series and sums to infinity
- 6.8 Applications of geometric and arithmetic patterns
- 6.9 Pascal’s triangle and the binomial expansion

- 7 Limits and derivatives
- 7.1 Limits and convergence
- 7.2 The tangent line andderivative of xn
- 7.3 More rules for derivatives
- 7.4 The chain rule and higher order derivatives
- 7.5 Rates of change and motion in a line
- 7.6 The derivative and graphing
- 7.7 More on extrema and optimization problems

- 8 Descriptive statistics
- 8.1 Univariate analysis
- 8.2 Presenting data
- 8.3 Measures of central tendency
- 8.4 Measures of dispersion
- 8.5 Cumulative frequency
- 8.6 Variance and standard deviation

- 9 Integration
- 9.1 Antiderivatives and the indefinite integral
- 9.2 More on indefinite integrals
- 9.3 Area and definite integrals
- 9.4 Fundamental Theorem of Calculus
- 9.5 Area between two curves
- 9.6 Volume of revolution
- 9.7 Definite integrals with linear motion and other problems

- 10 Bivariate analysis
- 10.1 Scatter diagrams
- 10.2 the line of best fit
- 10.3 Least squares regression
- 10.4 Measuring correlation

- 11 Trigonometry
- 11.1 Right-angled triangle trigonometry
- 11.2 Applications of right-angled triangle trigonometry
- 11.3 Using the coordinate axes in trigonometry
- 11.4 The sine rule
- 11.5 The cosine rule
- 11.6 Area of a triangle
- 11.7 Radians, arcs and sectors

- 12 Vectors
- 12.1 Vectors: basic concepts
- 12.2 Addition and subtraction of vectors
- 12.3 Scalar product
- 12.4 Vector equation of a line
- 12.5 applications of vectors

- 13 Circular functions
- 13.1 Using the unit circle
- 13.2 Solving equations using the unit circle
- 13.3 Trigonometric identities
- 13.4 Graphing circular functions
- 13.5 Translations and stretches of trigonometric functions
- 13.6 Combined transformations with sine and cosine functions
- 13.7 Modeling with sine and cosine functions

- 14 Calculus with trigonometric functions
- 14.1 Derivatives of trigonometric functions
- 14.2 More practice with derivatives
- 14.3 Integral of sine and cosine
- 14.4 Revisiting linear motion
- 15 Probability distributions
- 15.1 Random variables
- 15.2 The binomial distribution
- 15.3 The normal distribution
- 16 Exploration
- 16.1 About the exploration
- 16.2 Internal assessment criteria
- 16.3 How the exploration is marked
- 16.4 Academic honesty
- 16.5 Record keeping
- 16.6 Choosing a topic
- 16.7 Getting started

- 17 Using a graphic display calculator
- 1 Functions
- 2 Differential calculus
- 3 Integral calculus
- 4 Vectors
- 5 Statistics and probability

- 18 Prior learning
- 1 Number
- 2 Algebra
- 3 Geometry
- 4 statistics

- 19 Practice paper 1
- Practice paper 2
- Answers
- Subject index
- Back Cover