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• Dedication
• Contents
• Introduction
• Chapter 1: Prior Learning Topics
• 1.1: Numbers
• Classifying numbers
• Order of operations
• Number theory
• Ratios, percentages and proportions
• 1.2: Fractions
• Simplifying fractions
• Multiplying fractions
• Dividing fractions
• Adding and subtracting fractions
• 1.3: Algebra
• Expanding and factorizing
• Rearranging formulae
• Evaluating expressions
• Solving linear equations in one variable
• 1.4: Algebra extended
• Rewriting linear equations in two variables
• Solving a system of linear equations in two variables
• Order relations
• Intervals on a real number line
• 1.5: Geometry
• Basic concepts
• Perimeter and areas of two-dimensional shapes
• Plotting on the x-, y-coordinate plane
• Midpoint of a line segment
• Right triangles and Pythagoras’ theorem
• Distance between two points
• 1.6: Financial mathematics
• World currencies
• Currency conversion
• 1.7: Statistics
• Data collection
• Bar charts
• Pie charts
• Pictograms
• Chapter 2: Number and Algebra
• 2.1: Organization of numbers
• Rational numbers
• Real numbers
• 2.2: Numbers in calculations
• Estimation
• 2.3: Standard form
• 2.4: International units of measure
• 2.5: Currency conversions
• Commission
• 2.6: Simultaneous equations
• Elimination
• Substitution
• Using your GDC
• 2.7: Quadratic equations
• Solving by factorizing when a = 1
• Solving by factorizing when a = 2
• Solving using the quadratic formula
• Solving using the GDC
• Chapter 3: Geometry
• 3.1: The equation of a line
• 3.2: The gradient of a line
• 3.3: The intercepts of a line
• 3.4: Intersection of two lines
• 3.5: Parallel and perpendicular lines
• Chapter 4: Mathematical Models
• 4.1: Relations and functions
• 4.2: Domain and range
• Finding domain algebraically
• Finding domain and range graphically
• 4.3: Function notations
• 4.4: Linear functions
• Producing a table of values
• Finding functional values
• Finding x- and y-intercepts
• Using one ordered pair and the gradient
• General form of a linear function
• Graphing linear functions
• Writing linear functions
• 4.5: Linear model
• 4.6: Quadratic functions
• Point-plotting using a table of values
• Plotting the x- and y-intercepts and the vertex
• The axis of symmetry
• Graphing quadratic functions using translations
• Graphing quadratic functions that are stretched
• Solving quadratic equations using accurately drawn graphs
• 4.7: Quadratic models
• 4.8: Exponential functions
• Exponential expressions
• Exponential functions
• Graphing exponential functions
• The ‘Guess and Check’ method and logarithms
• 4.9: Exponential models
• Chapter 5: More Mathematical Models
• 5.1: Higher order polynomial functions
• Third degree polynomial functions
• Fourth degree polynomial functions and beyond
• 5.2: Rectangular hyperbolic functions
• Graphing the rectangular hyperbola
• 5.3: Unfamiliar functions
• Graphing unfamiliar functions
• 5.4: Solving equations involving combinations of unfamiliar functions
• Further methods for solving equations
• Chapter 6: More Geometry
• 6.1: Advanced right-angled trigonometry
• The sine, cosine, and tangent of an angle
• 6.2: Further right-angled trigonometry
• 6.3: The sine rule
• 6.4: The cosine rule
• 6.5: The area of a triangle
• 6.6: The geometry of three-dimensional solids
• 6.7: Application of three-dimensional geometry
• Chapter 7: Sequences and Series
• 7.1: Arithmetic sequences
• 7.2: Arithmetic series
• Sigma notation
• 7.3: Geometric sequences
• 7.4: Geometric series
• 7.5: Compound interest
• 7.6: Financial maths on the calculator
• 7.7: Inflation and depreciation
• Chapter 8: Sets
• 8.1: Introduction to set theory
• 8.2: Subsets and complements of sets
• 8.3: The union and intersection of sets
• 8.4: Introduction to Venn diagrams
• 8.5: Applications of Venn diagrams
• 8.6: Venn diagrams involving three sets
• Chapter 9: Logic
• 9.1: Introduction to symbolic logic
• 9.2: Implication and equivalence
• 9.3: Negation and conjunction
• 9.4: Disjunction and exclusive disjunction
• 9.5: Truth tables
• 9.6: Inverse, converse, contrapositive
• 9.7: Logical equivalence, tautologies, and contradictions
• Chapter 10: Probability
• 10.1: Diagrams for experiments
• 10.2: Classical probability
• 10.3: Mutually exclusive events
• 10.4: Combined events
• 10.5: Independent even
• 10.6: Dependent events
• 10.7: Conditional probability
• 10.8: The probability of ‘at least one’
• 10.9: Summarization of the laws of probability
• 10.10: Connecting independent and mutually exclusive events
• Chapter 11: Descriptive Statistics
• 11.1: Classification of data
• 11.2: Discrete data
• 11.3: Continuous data
• Constructing a frequency distribution table
• 11.4: Measures of central tendency
• 11.5: Graphs of continuous data
• 11.6: Box-and-whisker diagram
• 11.7: Measures of dispersion
• Notations for standard deviation: sx vs σx
• Chapter 12: Statistical Applications
• 12.1: The normal distribution
• Properties of the normal distribution.
• The inverse normal distribution
• 12.2: Line of best fit (the regression line)
• Positive or negative correlation
• Strength of the correlation and r values
• Linear regression
• Using your GDC to check your work
• Additional notes tying together the concepts and techniques
• Examples of scatter plot visuals
• A summary
• Drawing a regression line by eye
• 12.3: Hypothesis testing
• Two specific examples of hypothesis testing
• 12.4: The chi-square hypothesis test
• Chi-square using a GDC
• 12.5: The chi-square test – manual working
• One final example for x 2
• Chapter 13: Calculus
• 13.1: The definition of the derivative
• Returning to Example 13.1
• 13.2: The power rule
• 13.3: Gradients of curves and equations of tangents and normals
• 13.4: Increasing and decreasing functions
• 13.5: Applications of calculus
• Chapter 14: Review Questions
• Chapter 15: Practice Papers
• Preparing for your IB exams
• First practice exam
• Second practice exam
• Solutions to first practice exam
• Solutions to second practice exam
• Chapter 16: The Project
• Time management during the project
• The assessment criteria
• Sample project ideas
• Project checklist
• Sample IB project – Relationship between temperature and precipitation
• Chapter 17: Theory of Knowledge
• Answers
• Index
• Back Cover