Pearson Baccalaureate for the IB Diploma Standard LevelĀ Mathematics Applications and Interpretation

Höfundar: Ibrahim Wazir; Bryan Landmann; Kevin Frederick; Tim Garry (Útgáfa: 1)
Pearson Baccalaureate for the IB Diploma Standard LevelĀ Mathematics Applications and Interpretation

Kaup valmöguleikar

Mathematics Applications and Interpretation for the IB Diploma Standard Level

Nánar um bókina

Útgefandi
Pearson International Content
ISBN
9781292371726
Print ISBN
9780435193454
Format
Page Fidelity (PDF)
Útgáfa
1
Höfundar
Ibrahim Wazir; Bryan Landmann; Kevin Frederick; Tim Garry
Tungumál
English
Útgefið
2020-07-20
Prent takmörkun á líftíma
100
Prent takmörkun
2
Afritunar takmörkun
2

Kaflar

  • 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