Course map

Topic 1: Number and algebra

Number, sequences and finance
SL and HL: SL1.1; SL1.2; SL1.3; SL1.4; SL1.5; SL1.6; SL1.7; SL1.8
- Work in standard form, round sensibly and find bounds and percentage error
- Use arithmetic and geometric sequences and series in context
- Solve compound interest, depreciation, loan and annuity problems with the GDC's finance solver
- Solve systems of linear equations and polynomial equations with technology
Lesson Practice
HL: logarithms, complex numbers and matrices
HL only: AHL1.9; AHL1.10; AHL1.11; AHL1.12; AHL1.13; AHL1.14; AHL1.15
- Use the laws of logarithms and rational exponents, and sum an infinite geometric series
- Calculate with complex numbers in Cartesian, polar and exponential form, including phase shifts
- Use matrix algebra, inverses and determinants to solve problems
- Find eigenvalues and eigenvectors and use diagonalization to find powers of a matrix
Lesson Practice

Topic 2: Functions

Functions and models
SL and HL: SL2.1; SL2.2; SL2.3; SL2.4; SL2.5; SL2.6
- Find and use equations of straight lines and the language of functions, including inverses
- Use the GDC to find key features of graphs and intersections
- Fit and use linear, quadratic, exponential, power, cubic and sinusoidal models
- Follow the modelling process: choose, fit, test, reflect and refine
Lesson Practice
HL: composites, transformations and further models
HL only: AHL2.7; AHL2.8; AHL2.9; AHL2.10
- Form composite and inverse functions in context
- Transform graphs by translations, stretches and reflections
- Model with exponential, logistic, logarithmic and sinusoidal functions
- Use logarithmic scales and linearize data with log-log and semi-log graphs
Lesson Practice

Topic 3: Geometry and trigonometry

Geometry and trigonometry
SL and HL: SL3.1; SL3.2; SL3.3; SL3.4; SL3.5; SL3.6
- Find distances, midpoints, volumes and surface areas in three dimensions
- Use right-angled trigonometry, the sine and cosine rules and the area of a triangle
- Solve problems with bearings, angles of elevation, arcs and sectors
- Construct perpendicular bisectors and use Voronoi diagrams
Lesson Practice
HL: radians, matrix transformations and vectors
HL only: AHL3.7; AHL3.8; AHL3.9; AHL3.10; AHL3.11; AHL3.12; AHL3.13
- Use radians, the unit circle and trigonometric identities and equations
- Describe and compose matrix transformations of the plane
- Use vectors, vector lines and kinematics in two and three dimensions
- Use the scalar and vector products for angles, areas and components
Lesson Practice
HL: graph theory
HL only: AHL3.14; AHL3.15; AHL3.16
- Use the language of graphs: degree, connectedness, simple, complete, weighted and directed graphs
- Use adjacency matrices to count walks
- Find minimum spanning trees with Kruskal's and Prim's algorithms
- Solve route inspection (Chinese postman) and travelling salesman problems
Lesson Practice

Topic 4: Statistics and probability

Data, correlation and hypothesis tests
SL and HL: SL4.1; SL4.2; SL4.3; SL4.4; SL4.10; SL4.11
- Sample and summarize data; find outliers and present data
- Find and interpret Pearson's and Spearman's correlation coefficients and the regression line
- Carry out and interpret chi-squared tests and t-tests with technology
Lesson Practice
Probability and distributions
SL and HL: SL4.5; SL4.6; SL4.7; SL4.8; SL4.9
- Find probabilities with Venn diagrams, tree diagrams and tables
- Use discrete random variables and expected value
- Use the binomial and normal distributions with the GDC
Lesson Practice
HL: further statistics and Markov chains
HL only: AHL4.12; AHL4.13; AHL4.14; AHL4.15; AHL4.16; AHL4.17; AHL4.18; AHL4.19
- Judge data collection and fit non-linear regression models
- Combine random variables and use the central limit theorem and confidence intervals
- Use the Poisson distribution and tests for a mean or proportion, with type I and II errors
- Use transition matrices and steady states of Markov chains
Lesson Practice

Topic 5: Calculus

Calculus
SL and HL: SL5.1; SL5.2; SL5.3; SL5.4; SL5.5; SL5.6; SL5.7; SL5.8
- Interpret derivatives as rates of change and find where functions increase or decrease
- Differentiate polynomials and find tangents, normals and stationary points
- Solve optimization problems in context
- Integrate polynomials, find areas, and estimate areas with the trapezoidal rule
Lesson Practice
HL: further differentiation, integration and kinematics
HL only: AHL5.9; AHL5.10; AHL5.11; AHL5.12; AHL5.13
- Differentiate standard functions with the chain, product and quotient rules
- Use the second derivative for concavity and points of inflexion
- Integrate standard functions and find areas and volumes of revolution
- Solve kinematics problems with displacement, velocity and acceleration
Lesson Practice
HL: differential equations
HL only: AHL5.14; AHL5.15; AHL5.16; AHL5.17; AHL5.18
- Set up differential equations from a context and solve them by separating variables
- Read slope fields and approximate solutions with Euler's method
- Analyse coupled systems with eigenvalues and phase portraits
- Solve second order equations numerically by writing them as coupled systems
Lesson Practice

The papers, technology and the exploration

The papers, technology and the exploration
SL and HL: TK1; TK2
- Know the papers at each level, their marks and times, and that technology is required in every paper
- Use the IB's accuracy rule (exact or three significant figures) and the command terms
- Know what the exploration asks and how criteria A to E reward it
Lesson Practice

IB Diploma Programme Mathematics: applications and interpretation, SL and HL. The exploration is your own written investigation, so it is described in a lesson rather than practised here.