IB DP - AI SL

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
  5. Perpendicular gradients
• 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
  3. Quadratic 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