Efnisyfirlit

• 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

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