Pearson Baccalaureate for the IB Diploma Standard LevelĀ Mathematics Applications and Interpretation
Höfundar:
Ibrahim Wazir; Bryan Landmann; Kevin Frederick; Tim Garry (Útgáfa: 1)
Kaup valmöguleikar
Mathematics Applications and Interpretation for the IB Diploma Standard Level
Nánar um bókina
- Pearson International Content
- 9781292371726
- 9780435193454
- Page Fidelity (PDF)
- 1
- Ibrahim Wazir; Bryan Landmann; Kevin Frederick; Tim Garry
- English
- 2020-07-20
- 100
- 2
- 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