Pearson Baccalaureate for the IB Diploma Standard Level Mathematics Applications and Interpretation uPDF

Námskeið Mathematics 3 Mathematics 4 -
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Pearson Baccalaureate for the IB Diploma Standard Level Mathematics Applications and Interpretation uPDF

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Rafbók til leigu í 180 daga. Útgáfa: 1

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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