# IB DP - AI SL

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.

Available languages:
English

## Course content

### Chapter 1: Numbers

• Numbers
1. Number sets
2. Rounding and approximation
3. Significant figures
4. Errors
5. Percentage errors

### Chapter 2: Exponential Calculations

• Exponents and logarithms
1. Integer exponents
2. Negative exponents
3. Fractional exponents
4. Logarithms
• Applications
1. Scientific notation
2. Simple interest
3. Compound interest
4. Annuities and amortisation

### Chapter 3: Linear formulas

• Formulas
1. Formulas
2. Dependent and independent variables
3. Graphs
• Linear functions
1. Linear formula
2. Slope and intercept
3. Composing a linear formula
4. Forms of linear formulas
• Linear equations
1. Linear equations
2. The general solution
3. Intersection points
4. Systems of equations

### Chapter 4: Functions

• Basics of functions
1. Domain
2. Functions and graphs
3. The range of a function
• Operations for functions
1. Arithmetic operations on functions
2. Composition of functions
• Range
1. Recognising graphs
2. Transformations of a graph
3. Symmetry of functions
• Inverse functions
1. One-to-one
2. Monotone functions
3. The inverse of a function
4. Properties of inverse functions

### Chapter 5: Function modelling

• Function modelling
1. Introduction to modelling
2. Linear models
4. Cubic models
5. Exponential models
6. Trigonometric models
• Modelling techniques
1. Direct variation
2. Inverse variation
3. Choosing a model
4. Testing a model
5. Interpolation and extrapolation

### Chapter 6: Sequences

• Sequences
1. Introduction to sequences
2. Arithmetic sequences
3. Geometric sequences
4. Sigma notation and series

### Chapter 7: Geometry

• Coordinate Geometry
1. Pythagorean Theorem
2. Distances
3. Midpoints of lines
• Right-angled geometry
1. Basic trigonometric relations
2. Angles of elevation and depression
• Areas and volumes
1. Solids with a triangular or rectangular base
2. Solids with a circular base
• Further geometry
1. Sine and cosine rules
2. Arc length and area of a sector
• Voronoi diagrams
1. Introduction to Voronoi diagrams
2. Constructing Voronoi diagrams
3. Using Voronoi diagrams

### Chapter 8: Differentiation

• Introduction to differential calculus
1. The concept of a limit
2. Instantaneous rate of change
• The derivative
1. The difference quotient
2. The difference quotient at a point
3. The tangent line
4. The notion of derivative
5. The derivative of power functions
• Sum and product rule
1. The sum rule
2. The product rule
• Chain rule
1. Composite functions
2. The chain rule
• The derivative of standard functions
1. The derivative of trigonometric functions
2. The base e and the natural logarithm
3. The derivative of exponential functions and logarithms
• Quotient rule
1. Quotient rule
• Applications of derivatives
1. Increasing and decreasing
2. Extreme values
3. The second derivative
4. Types of increasing and decreasing
5. Inflection points
6. Higher order derivatives
7. Tangents and normals
8. Optimisation

### Chapter 9: Integration

• Antiderivatives
1. The antiderivative of a function
2. The antiderivative of a power function
3. Rules of calculation for antiderivatives
• Areas under curves
1. Definite integral
2. Area
3. Approximating the area under a curve

### Chapter 10: Descriptive Statistics

• Types of data
1. Quantitative and qualitative variables
2. Measurement scales
• Frequency distributions
1. Absolute, relative, and cumulative frequencies
2. Frequency distribution tables
3. Frequency distribution graphs
4. Shape of a distribution
• Measures of central tendency
1. Mode
2. Median
3. Mean
• Quantiles
1. Percentiles
2. Quartiles
• Measures of dispersion
1. Range, interquartile range, and the five-number summary
2. Interquartile range rule for identifying outliers
3. Deviation from the mean and the sum of squares
4. Variance and standard deviation

### Chapter 11: Relationships between variables

• Correlation
1. Visualizing the relationship between variables
2. Pearson correlation coefficient
3. Spearman correlation coefficient
• Regression
1. The line of best fit
2. Making predictions
3. Interpreting the line

### Chapter 12: Probability

• Set theory
1. Sets, subsets, and elements
2. Random experiments
3. Complement of an event
4. Intersection of two events
5. Union of two events
• Probability principles
1. Definition of probability
2. Probability of the complement
3. Conditional probability
4. Independence
5. Probability of the intersection
6. Probability of the union
• Probability distributions
1. Random variables
2. Probability distributions
3. Expected value of a random variable
4. Binomial distribution
5. Normal distribution

### Chapter 13: Hypothesis testing

• Sampling
1. Sampling methods
2. Bias in sampling
• Test for independence
1. Introduction to hypothesis testing
2. Formulating hypotheses
3. Setting the criteria for a decision
4. Computing the test statistic
5. Computing the p-value and making a decision
• Goodness of fit test
1. Test for a uniform distribution
2. Test for other distributions
• Student’s t-test
1. One-tailed and two-tailed hypotheses
2. Performing a t-test