Perfect fit for IB DP Mathematics: Applications and Interpretations Standard Level. Good fit for general upper secondary mathematics courses (ages 16-18).

Contains Numbers, Linear Formulas, Functions, Geometry, Calculus, Statistics, Probability and more.

English

- Numbers
- Number sets
- Rounding and approximation
- Significant figures
- Errors
- Percentage errors

- Exponents and logarithms
- Integer exponents
- Negative exponents
- Fractional exponents
- Logarithms

- Applications
- Scientific notation
- Simple interest
- Compound interest
- Annuities and amortisation

- Formulas
- Formulas
- Dependent and independent variables
- Graphs

- Linear functions
- Linear formula
- Slope and intercept
- Composing a linear formula
- Forms of linear formulas
- Perpendicular gradients

- Linear equations
- Linear equations
- The general solution
- Intersection points
- Systems of equations

- Basics of functions
- Domain
- Functions and graphs
- The range of a function

- Operations for functions
- Arithmetic operations on functions
- Composition of functions

- Range
- Recognising graphs
- Transformations of a graph
- Symmetry of functions

- Inverse functions
- One-to-one
- Monotone functions
- The inverse of a function
- Properties of inverse functions

- Function modelling
- Introduction to modelling
- Linear models
- Quadratic models
- Cubic models
- Exponential models
- Trigonometric models

- Modelling techniques
- Direct variation
- Inverse variation
- Choosing a model
- Testing a model
- Interpolation and extrapolation

- Sequences
- Introduction to sequences
- Arithmetic sequences
- Geometric sequences
- Sigma notation and series

- Coordinate Geometry
- Pythagorean Theorem
- Distances
- Midpoints of lines

- Right-angled geometry
- Basic trigonometric relations
- Angles of elevation and depression

- Areas and volumes
- Solids with a triangular or rectangular base
- Solids with a circular base

- Further geometry
- Sine and cosine rules
- Arc length and area of a sector

- Voronoi diagrams
- Introduction to Voronoi diagrams
- Constructing Voronoi diagrams
- Using Voronoi diagrams

- Introduction to differential calculus
- The concept of a limit
- Instantaneous rate of change

- The derivative
- The difference quotient
- The difference quotient at a point
- The tangent line
- The notion of derivative
- The derivative of power functions

- Sum and product rule
- The sum rule
- The product rule

- Chain rule
- Composite functions
- The chain rule

- The derivative of standard functions
- The derivative of trigonometric functions
- The base e and the natural logarithm
- The derivative of exponential functions and logarithms

- Quotient rule
- Quotient rule

- Applications of derivatives
- Increasing and decreasing
- Extreme values
- The second derivative
- Types of increasing and decreasing
- Inflection points
- Higher order derivatives
- Tangents and normals
- Optimisation

- Antiderivatives
- The antiderivative of a function
- The antiderivative of a power function
- Rules of calculation for antiderivatives

- Areas under curves
- Definite integral
- Area
- Approximating the area under a curve

- Types of data
- Quantitative and qualitative variables
- Measurement scales

- Frequency distributions
- Absolute, relative, and cumulative frequencies
- Frequency distribution tables
- Frequency distribution graphs
- Shape of a distribution

- Measures of central tendency
- Mode
- Median
- Mean

- Quantiles
- Percentiles
- Quartiles

- Measures of dispersion
- Range, interquartile range, and the five-number summary
- Interquartile range rule for identifying outliers
- Deviation from the mean and the sum of squares
- Variance and standard deviation

- Correlation
- Visualizing the relationship between variables
- Pearson correlation coefficient
- Spearman correlation coefficient

- Regression
- The line of best fit
- Making predictions
- Interpreting the line

- Set theory
- Sets, subsets, and elements
- Random experiments
- Complement of an event
- Intersection of two events
- Union of two events

- Probability principles
- Definition of probability
- Probability of the complement
- Conditional probability
- Independence
- Probability of the intersection
- Probability of the union

- Probability distributions
- Random variables
- Probability distributions
- Expected value of a random variable
- Binomial distribution
- Normal distribution

- Sampling
- Sampling methods
- Bias in sampling

- Test for independence
- Introduction to hypothesis testing
- Formulating hypotheses
- Setting the criteria for a decision
- Computing the test statistic
- Computing the p-value and making a decision

- Goodness of fit test
- Test for a uniform distribution
- Test for other distributions

- Student’s t-test
- One-tailed and two-tailed hypotheses
- Performing a t-test