Efnisyfirlit

• Contents
• Introduction
• Chapter 1: Number and algebra basics
  • 1.1: Approximations and error
    • Approximations
    • Bounds
    • Percentage error of measurements
  • 1.2: The exponent laws
    • Zero, negative and rational exponents
  • 1.3: Scientific notation – numbers in the form a * 10k
  • 1.4: Exponents and logarithms
• Chapter 2: Functions
  • 2.1: Equations and formulae
    • Equations, identities and formulae
    • Equations and graphs
    • Linear equations – equations of lines
    • Systems of linear equations
  • 2.2: Relations and functions
  • 2.3: Inverse functions
    • Pairs of inverse functions
    • The existence of an inverse function
• Chapter 3: Sequences and series
  • 3.1: Sequences
  • 3.2: Arithmetic sequences
  • 3.3: Geometric sequences
    • Compound interest
  • 3.4: Series
    • Sigma notation
    • Arithmetic series
    • Geometric series
    • Applications of series to compound interest calculations
• Chapter 4: Geometry and trigonometry 1
  • 4.1: Basic coordinate geometry
    • The distance formula
    • The midpoint of a line segment
    • Equations of lines and intersection of lines
    • Perpendicular bisectors of line segments
  • 4.2: Right-angled trigonometry
    • The primary trigonometric ratios
    • The area of a triangle
    • Applications of trigonometry
    • Exact values of trigonometric ratios
  • 4.3: Non-right-angled trigonometry
    • The sine rule
    • The cosine rule
  • 4.4: Surface area and volume
• Chapter 5: Geometry and trigonometry 2
  • 5.1: Arc length and area of a sector
    • Area of a sector
    • Length of an arc
  • 5.2: Voronoi diagrams
    • Constructing Voronoi diagrams
• Chapter 6: Modelling real-life phenomena
  • 6.1: Linear models
    • Developing and testing a linear model
    • Extending and revising models
    • Models don’t always capture reality perfectly
    • Interpreting and evaluating linear models
    • Piecewise linear models
  • 6.2: Quadratic models
  • 6.3: Cubic models
  • 6.4: Exponential models
    • Just how fast is exponential growth?
    • Developing exponential models
    • Interpreting exponential models
    • Graphical interpretation
  • 6.5: Direct and inverse variation
    • Direct variation
    • Inverse variation
  • 6.6: Trigonometric models
    • Exploration
    • Developing trigonometric models
  • 6.7: Modelling skills
    • Choosing a model
    • Testing a model
    • Interpolation versus extrapolation
• Chapter 7: Descriptive statistics
  • 7.1: Data and variables
    • Variables
    • Sampling
    • Random and non-random sampling
    • Random sampling
    • Non-random sampling
  • 7.2: Displaying distributions using graphs
  • 7.3: Measures of central tendency and spread
    • Measures of location and centre
    • Measures of variability and spread
    • Range and quartiles
• Chapter 8: Probability
  • 8.1: Randomness and probability
    • Basic definitions
    • Tree diagrams, tables and grids
  • 8.2: Probability assignments
    • Probability rules
    • Equally likely outcomes
  • 8.3: Operations with events
    • Conditional probability
    • Independence
    • Some applications
• Chapter 9: Introduction to differential calculus
  • 9.1: Limits and instantaneous rate of change
    • The idea of a limit
    • Instantaneous rate of change
  • 9.2: Derivative of a function
  • 9.3: Interpretations of the derivative
  • 9.4: Derivatives of functions of the form f (x ) = axn
    • Exploration of the power rule
• Chapter 10: Further differential calculus
  • 10.1: Maxima and minima – first derivative test
  • 10.2: Tangents and normals
  • 10.3: Optimisation
• Chapter 11: Integral calculus
  • 11.1: Anti-derivatives
  • 11.2: Definite integrals
  • 11.3: Area under a curve
  • 11.4: Approximating area under a curve
• Chapter 12: Probability distributions
  • 12.1: Random variables
    • Discrete probability distribution
    • Cumulative distribution function
    • Expected values
    • Variance and standard deviation
  • 12.2: The binomial distribution
    • The cumulative binomial distribution function
  • 12.3: Continuous distributions – the normal distribution
    • The normal distribution
    • Calculations using the normal distribution
    • The inverse normal distribution
• Chapter 13: Statistical analysis
  • 13.1: Hypothesis testing in statistics
    • The hypothesis testing procedure for the population mean
    • Using hypothesis testing for comparing means of two populations
  • 13.2: Goodness-of-fit (GOF) test and test for independence
    • Goodness-of-fit
    • Test for independence: contingency table
• Chapter 14: Bivariate analysis
  • 14.1: Scatter diagrams
    • Form
    • Direction
    • Strength
    • Unusual features
    • Estimating the line of best fit
  • 14.2: Measures of correlation
    • Pearson’s product-moment correlation coefficient (r)
    • Spearman’s rank correlation coefficient (rs)
    • Differences between Pearson’s r and Spearman’s rs
  • 14.3: Linear regression
    • Least-squares regression line (LSRL)
• Internal assessment
  • Mathematical exploration
  • Internal assessment criteria
• Theory of knowledge
  • Perspectives
    • Mathematics and number
    • Purpose: mathematics for its own sake
    • Purpose: mathematical models
    • Constructivist view of mathematics
    • Platonic view of mathematics
  • The methods and tools of mathematics
    • The language and concepts of mathematics
    • Notation
    • Algebra
    • Proof
    • Sets
    • Mappings between sets
    • Infinite sets
  • Mathematics and the knower
    • Beauty by the numbers
    • Beauty in numbers
    • Mathematics and personal intuitions
    • Mathematics and personal qualities
  • Conclusion
• Answers
• Index
• Back Cover

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