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IB Maths AI HL scheme of work

A complete plan for IB Maths AI HL: 64 weeks, 256 lessons, with a quick check most weeks and a test at the end of each unit. Here is the whole plan at a glance and one lesson in full.

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A sample lesson, in full

Week 2 · Lesson 4 · Unit 1 · Number & Algebra

Sequences 1: Arithmetic Sequences (nth term)

By the end of the lesson students can: Recognise an arithmetic sequence from its common difference and use uₙ = u₁ + (n − 1)d to find terms in real contexts.
Syllabus reference: SL Topic 1
Quick check FA2: Standard form, rounding/bounds, percentage error & introducing arithmetic sequences
Misconceptions to watch for: Writing a number in standard form with a coefficient outside 1 ≤ a < 10; giving an error interval as an inequality the wrong way round; dividing by the approximate value instead of the exact value when calculating percentage error; confusing the common difference d with the term value itself.
Then the unit test SA1 (week 7): Unit 1 Test: Number & Algebra · Paper 1 style · calculator allowed · 50 mins
In the full plan, every lesson also has: The starter for the week, practice and homework on the topic in one click, and a tick to mark it taught for your class.

The course at a glance

FA = a short formative check in that week; SA = an end-of-unit test.

Year 1 (DP1)

32 weeks · 128 lessons · 24 quick checks (FA) · 5 unit tests (SA)

Week	Lessons	Checks
Unit 0 · Prior Knowledge Bridge
1	PK Diagnostic: Number Skills, Fractions & Percentages · PK Refresher: Algebraic Manipulation & Linear Equations · PK Refresher: Basic Trigonometry, Pythagoras & Coordinate Geometry · PK Refresher: GDC & Spreadsheet Skills for Applications & Interpretation	FA1
Unit 1 · Number & Algebra
2	Standard Form: Operations & Applications in Science and Finance · Approximation 1: Rounding, Decimal Places & Significant Figures · Approximation 2: Upper & Lower Bounds, Error Intervals & Percentage Error · Sequences 1: Arithmetic Sequences (nth term)	FA2
3	Sequences 2: Arithmetic Series (Sum Formula) · Sequences 3: Geometric Sequences (nth term) · Sequences 4: Geometric Series, Sum to Infinity & Applications · Financial Maths 1: Simple & Compound Interest with the GDC Finance App	FA3
4	Financial Maths 2: Depreciation & Inflation · Financial Maths 3: Loan Amortization & Annuities · Systems of Equations 1: 2×2 Linear Systems & Polynomial Equations with Technology · Systems of Equations 2: Three Linear Equations in Three Unknowns	FA4
5	Systems of Equations 3: Solving with Technology & Real-World Applications · Complex Numbers 1: Imaginary Unit i, Cartesian Form Arithmetic & Complex Roots of Quadratics · Complex Numbers 2: The Argand Diagram, Modulus & Argument (Introducing Radian Measure) · Complex Numbers 3: Polar & Euler Form — Conversions, Products, Quotients & Powers	FA5
6	Matrices 1: Notation, Addition & Scalar Multiplication · Matrices 2: Matrix Multiplication & the Identity Matrix · Matrices 3: Determinants, Inverses & Solving Systems with Technology · Matrices 4: Eigenvalues, Eigenvectors & Markov Chains	FA6
7	Unit 1 Revision: Number & Algebra · Unit 1 Revision: Exam-Style Problem Solving · Unit 1 Revision: Common Misconceptions Clinic · Summative Assessment 1 (SA1)	SA1
Unit 2 · Functions
8	Straight Lines 1: Gradient, Intercepts & Equation of a Line · Straight Lines 2: Parallel, Perpendicular Lines & Linear Models · Straight Lines 3: Piecewise Linear Functions & Regression Lines · Quadratics 1: Graphing & Key Features (Vertex, Roots, Axis of Symmetry)	FA7
9	Quadratics 2: Quadratic Models & Technology Regression · Polynomials & Power Models: Cubic Graphs, Direct/Inverse Variation (axⁿ) · Function Features: Domain, Range & Asymptotes with Technology · Transformations 1: Translations f(x)+a, f(x+a)	FA8
	Piecewise Models: Linear Pieces & Continuity in Context · Quadratics 3: Quadratic Models — Projectiles & Optimisation · Power Models 2: Direct & Inverse Variation from Data · Function Features 2: Asymptotes, Intercepts & Domain in Context
10	Transformations 2: Stretches af(x), f(ax) & Reflections · Composite & Inverse Functions: (f∘g)(x), f⁻¹(x) & Domain Restriction · Exponential Models 1: Growth & Decay · Exponential Models 2: The Natural Exponential Function eˣ & Continuous Growth	FA9
11	Logarithmic Models 1: Laws of Logarithms & Solving Exponential/Log Equations · Logarithmic Models 2: Linearizing Data with Log-Log & Semi-Log Scales · Logistic Models 1: The Logistic Function & Its Parameters (L, k, x₀) · Logistic Models 2: Applications to Population Growth & Spread of Disease	FA10
	Transformations 3: Composite Transformations · Exponential Models 3: Solving for Time & Comparing Models · Logarithmic Models 3: Linearising y = axᵇ and y = abˣ · Logistic Models 3: Fitting & Interpreting the Carrying Capacity
12	Unit 2 Revision: Functions · Unit 2 Revision: Exam-Style Problem Solving · Unit 2 Revision: Common Misconceptions Clinic · Summative Assessment 2 (SA2)	SA2
Unit 3 · Geometry & Trigonometry
13	3D Geometry 1: Distance & Midpoint in Three Dimensions · Circles: Arc Length & Sector Area in Degrees · 3D Geometry 2: Volume & Surface Area of 3D Solids · Right-Angle Trig 1: SOHCAHTOA, Angles of Elevation & Depression	FA11
14	Right-Angle Trig 2: Pythagoras in 3D & the Angle Between a Line and a Plane · Sine Rule: Finding Sides, Angles & the Ambiguous Case · Cosine Rule: Finding Sides & Angles · Area of a Triangle (½ab sin C), Bearings & Problem Solving	FA12
15	Vectors 1: Position Vectors in 2D & 3D · Vectors 2: Magnitude, Unit Vectors & Vector Operations · Vectors 3: The Scalar (Dot) Product & Angle Between Vectors · Vectors 4: Vector Equation of a Line	FA13
16	Vectors 5: Applications — Constant Velocity Problems & Closest Approach · Voronoi Diagrams 1: Perpendicular Bisectors & Constructing Cells · Voronoi Diagrams 2: Nearest-Neighbour Interpolation & Adding a Site · Voronoi Diagrams 3: Applications — Toxic Waste Dump & Site Planning Problems	FA14
17	Radians: Radian Measure & Degree Conversion, Arc Length & Sector Area in Radians · Trigonometry: The Unit Circle, Pythagorean Identity & Solving Trig Equations Graphically · Sinusoidal Models: Amplitude, Period, Phase Shift & Principal Axis in Context · Matrix Transformations: Reflections, Rotations, Stretches, Enlargements & the Determinant	FA15
18	Unit 3 Revision: Geometry & Trigonometry · Unit 3 Revision: Exam-Style Problem Solving · Unit 3 Revision: Common Misconceptions Clinic · Summative Assessment 3 (SA3)	SA3
Unit 4 · Statistics & Probability
19	Statistics 1: Populations, Samples, Sampling Techniques & Types of Data · Central Tendency & Spread: Mean, Median, Mode, Variance & Standard Deviation with the GDC · Data Presentation: Histograms, Cumulative Frequency Graphs, Quartiles, Box Plots & Outliers · Correlation 1: Scatter Diagrams & Pearson's Correlation Coefficient	FA16
20	Correlation 2: Line of Best Fit & Linear Regression (y on x and x on y) · Correlation 3: Spearman's Rank Correlation & Choosing Pearson vs Spearman · Probability 1: Venn Diagrams, Set Notation & Basic Probability · Probability 2: Tree Diagrams & Combined Events	FA17
21	Probability 3: Conditional Probability & Independence · Discrete Random Variables 1: Probability Distributions & E(X) · The Binomial Distribution 1: Modelling & Calculating Probabilities · The Binomial Distribution 2: Mean, Variance & Applications with the GDC	FA18
22	The Poisson Distribution 1: Modelling Random Events in Time or Space · The Poisson Distribution 2: Calculating Probabilities with the GDC · The Normal Distribution 1: The Standard Normal Curve & Standardisation · The Normal Distribution 2: Finding Probabilities & Inverse Normal	FA19
23	Normal & Poisson: Applications & Choosing the Correct Distribution · Chi-Squared 1: Contingency Tables & Expected Frequencies · Chi-Squared 2: The Chi-Squared Test for Independence · Chi-Squared 3: The χ² Goodness-of-Fit Test	FA20
	Spearman's Rank 2: Calculating & Interpreting with Technology · The Binomial Distribution 3: Cumulative Probabilities & Expected Values · The Poisson Distribution 3: Choosing Poisson or Binomial · χ² Tests: Degrees of Freedom, Expected Frequencies & Conclusions
24	Unit 4 Revision: Statistics & Probability · Unit 4 Revision: Exam-Style Problem Solving · Unit 4 Revision: Common Misconceptions Clinic · Summative Assessment 4 (SA4)	SA4
Unit 5 · Calculus
25	Rates of Change: Average vs Instantaneous Rate & the Derivative as a Gradient Function · Differentiation 1: The Power Rule for Polynomials · Tangents & Normals: Equations of Tangents/Normals & Increasing/Decreasing Functions · Differentiation 2: Derivatives of eˣ, ln x, sin x, cos x & tan x	FA21
26	Differentiation 3: The Product Rule & Quotient Rule · Differentiation 4: The Chain Rule & Second Derivatives · Optimisation 1: Stationary Points, Local Maxima & Minima · Optimisation 2: Optimisation Problems in Context	FA22
27	Integration 1: Reversing Differentiation (Indefinite Integrals) · Integration 2: Integrating eˣ, 1/x & Trigonometric Functions · Integration 3: Definite Integrals & Area Under a Curve · The Trapezium Rule: Numerical Integration & Estimating Area	FA23
28	Differential Equations 1: Setting Up dy/dx from Rates of Change · Differential Equations 2: Solving by Separation of Variables · Slope Fields: Sketching & Interpreting Slope Fields · Euler's Method: Numerical Solutions of Differential Equations	FA24
29	Full Course Revision: Number, Algebra & Functions · Full Course Revision: Geometry, Statistics & Calculus · Full Course Revision: Exam Technique & Common Errors · Summative Assessment 5 (SA5): End-of-Year 1 Mock Exam	SA5

Year 2 (DP2): show the plan

Year 2 (DP2)

32 weeks · 128 lessons · 18 quick checks (FA) · 6 unit tests (SA)

Week	Lessons	Checks
Unit 3 · Geometry & Trigonometry (Graph Theory)
1	Graph Theory 1: Vertices, Edges, Degree, Simple & Complete Graphs · Graph Theory 2: Directed & Weighted Graphs, Subgraphs & Trees · Graph Theory 3: Adjacency Matrices & Counting Walks · Graph Theory 4: Eulerian & Hamiltonian Trails and Circuits	FA1
2	IA Workshop 1: The Exploration — Criteria A–E, Strong Explorations & Choosing a Topic · Graph Theory 5: Minimum Spanning Trees — Kruskal's & Prim's Algorithms · IA Workshop 2: Aim, Plan & the Level of Mathematics — Topic Approval · Graph Theory 6: The Chinese Postman Problem	FA2
3	Graph Theory 7: The Travelling Salesman Problem — Upper Bounds (Nearest Neighbour) · Graph Theory 8: Lower Bounds — the Deleted-Vertex Algorithm · Graph Theory 9: Transition Matrices for Graphs & Long-Run Behaviour · Vectors 6: The Vector (Cross) Product, Components & Areas	FA3
	Graph Theory 10: Walks of Length k with Adjacency Matrix Powers · Graph Theory 11: Kruskal's & Prim's Algorithms — Exam Practice · Graph Theory 12: Chinese Postman with Four Odd Vertices · Graph Theory 13: Travelling Salesman — Tables of Least Distances
Unit 1 · Number & Algebra (Matrices)
4	Matrices 5: Eigenvalues & Eigenvectors of 2 × 2 Matrices · Matrices 6: Diagonalisation & Powers of a 2 × 2 Matrix · Markov Chains 1: Transition Diagrams & Transition Matrices · Markov Chains 2: Steady States & Long-Term Behaviour	FA4
Unit 4 · Statistics & Probability
5	Data Design: Reliability & Validity of Data Collection · Non-Linear Regression: Least-Squares Models, SSres & R² · Random Variables: Linear Transformations & Unbiased Estimates of μ and σ² · Linear Combinations of Independent Random Variables	FA5
6	The Central Limit Theorem & the Distribution of the Sample Mean · Confidence Intervals for a Mean (z and t) · Poisson Revisited: Sums of Independent Poisson Variables · Consolidation: Estimation & Sampling Distributions	FA6
	Non-Linear Regression 2: Comparing Models with R² & SSres · Linear Combinations 2: Sums of Normal Variables · Central Limit Theorem 2: Probabilities About the Sample Mean · Confidence Intervals 2: Interpreting & Choosing z or t
7	Unit 4 Revision: Sampling Distributions & Estimation · Unit 4 Revision: Graph Theory & Matrices Exam-Style Problems · IA Workshop 3: Writing Up — Communication & Mathematical Presentation (Criteria A & B) · Summative Assessment 1 (SA1)	SA1
8	Hypothesis Testing 1: Tests for a Population Mean (z and t) · Hypothesis Testing 2: The Two-Sample t-Test · IA Workshop 4: Personal Engagement, Reflection & Use of Mathematics (Criteria C, D & E) · Hypothesis Testing 3: Tests for a Binomial Proportion & a Poisson Mean	FA7
9	Hypothesis Testing 4: Testing Correlation (H₀: ρ = 0) · Hypothesis Testing 5: Critical Regions & Type I and Type II Errors · Chi-Squared 4: Goodness of Fit to a Distribution Model · Consolidation: Choosing & Interpreting Statistical Tests	FA8
	Hypothesis Testing 6: One-Tailed & Two-Tailed Tests for a Mean · Hypothesis Testing 7: Testing for Correlation (ρ = 0) · Hypothesis Testing 8: Type I & II Error Probabilities · Chi-Squared 5: Goodness of Fit to Binomial, Poisson & Normal Models
Unit 5 · Calculus
10	IA Draft Deadline: Complete Draft In — Final Self-Check Against Criteria A–E · Related Rates of Change · Integration by Inspection & Substitution · Volumes of Revolution About the x- and y-axes	FA9 IA-D
11	Kinematics 1: Displacement, Velocity & Acceleration with Calculus · Kinematics 2: Distance Travelled & Motion in Context · Area Between a Curve and the y-axis · Consolidation: Applications of Integration	FA10
12	Coupled Differential Equations 1: Setting Up & Interpreting Coupled Linear Systems · Coupled Differential Equations 2: Euler's Method for Coupled Systems · Phase Portraits 1: Solving Coupled Systems with Eigenvalues & Eigenvectors · Phase Portraits 2: Sketching Trajectories & Classifying Equilibrium Points	FA11
	Volumes of Revolution 2: Exam-Style Problems with Technology · Kinematics 3: Distance Travelled & Changes of Direction · Coupled Differential Equations 3: Equilibrium Points & Long-Term Behaviour · Phase Portraits 3: Real, Complex & Imaginary Eigenvalues
13	IA Workshop 5: Acting on Draft Feedback & Finalising the Exploration · Second-Order Differential Equations as Coupled Systems & with Euler's Method · Differential Equations in Context: Population, Predator–Prey & Combat Models · Consolidation: HL Calculus	FA12
Unit 2 · Functions (Revision)
14	Review: Logistic & Advanced Models · Review: Linearising Data with Logarithms · Review: Composite, Inverse & Transformed Functions · Review: Complex Numbers & Euler Form	FA13
Full Course Revision · End of Term 1
15	Full Course Revision: Paper 1 (Calculator, Short Response) Technique · Full Course Revision: Paper 2 (Calculator, Extended Response) Technique & GDC Efficiency · Full Course Revision: Mixed Past-Paper Questions · Summative Assessment 2 (SA2): End-of-Term Test	SA2
Mock Examinations · Preparation
16	Pre-Mock Revision: Number, Algebra & Functions · Pre-Mock Revision: Geometry & Trigonometry · Pre-Mock Revision: Statistics & Probability · Pre-Mock Revision: Calculus & Paper 3 Problem Solving
Mock Examinations
17	Mock Exam: Paper 1 (Calculator, Short Response, 120 mins) · Mock Exam: Paper 2 (Calculator, Extended Response, 120 mins) · Mock Exam: Paper 3 (Calculator, Extended Problem Solving, 75 mins) · Post-Mock Review: Mark Schemes, Corrections & a Personal Revision Plan	SA3
Unit 4 · Statistics & Probability (Targeted Revision)
18	Targeted Revision: Hypothesis Tests · Targeted Revision: Confidence Intervals & the Central Limit Theorem · IA Workshop 6: Final Checks — Referencing, Academic Integrity & Presentation · Targeted Revision: Markov Chains	FA14
Unit 3 · Geometry & Trigonometry (Targeted Revision)
19	IA Final Submission: Exploration Handed In with the Academic-Integrity Declaration · Targeted Revision: Graph Theory Algorithms · Targeted Revision: Vectors & Kinematics · Targeted Revision: Voronoi Diagrams & the Scalar Product	FA15 IA-F
Unit 5 · Calculus (Targeted Revision)
20	Targeted Revision: Differentiation & Related Rates · Targeted Revision: Integration & Volumes · Targeted Revision: Slope Fields & Euler's Method · Targeted Revision: Phase Portraits	FA16
Unit 1 · Number & Algebra (Targeted Revision)
21	Targeted Revision: Matrices, Eigenvalues & Eigenvectors · Targeted Revision: Complex Numbers · Targeted Revision: Financial Mathematics · Targeted Revision: Logarithms & Infinite Geometric Series	FA17
Paper 3 · Extended Investigation
22	Paper 3 Workshop 1: Modelling Investigations — Functions & Regression · Paper 3 Workshop 2: Statistics & Probability Investigations · Paper 3 Workshop 3: Networks & Matrices Investigations · Paper 3 Workshop 4: Calculus & Differential Equations Investigations	FA18
Exam Practice · Paper 1 (Calculator, Short Response)
23	Paper 1 Practice: Short-Response Questions by Topic · Paper 1 Practice: Mixed Short-Response Questions · GDC Skills: Solvers, Graphs, Statistics & Finance Apps Under Time Pressure · Paper 1 Practice: A Timed Half Paper
Exam Practice · Paper 2 (Calculator, Extended Response)
24	Paper 2 Practice: Extended-Response Questions with the GDC · Paper 2 Practice: Interpreting & Communicating Results in Context · Command Terms & Mark Schemes: Show That, Hence, Justify & Accuracy (3 s.f.) · Paper 2 Practice: A Timed Half Paper
Exam Practice · Timed Papers
25	Summative Assessment 4 (SA4): Timed Paper 1 · Summative Assessment 4 (SA4): Timed Paper 2 · Summative Assessment 4 (SA4): Timed Paper 3 · SA4 Review: Corrections & Final Revision Priorities	SA4
Final Revision · Weak-Topic Clinics
26	Weak-Topic Clinic: Number, Algebra & Functions · Weak-Topic Clinic: Geometry & Trigonometry · Weak-Topic Clinic: Statistics & Probability · Weak-Topic Clinic: Calculus
Final Revision · Past Papers
27	Past-Paper Walk-Through: Paper 1 · Past-Paper Walk-Through: Paper 2 · Past-Paper Walk-Through: Paper 3 · Past-Paper Practice: Questions Students Choose
Final Revision · Exam Readiness
28	Exam Readiness: Formula Booklet Fluency & What Is Not in It · Exam Readiness: Time Management, Marks per Minute & Checking · Exam Readiness: Last Questions & Personal Revision Plans · Exam Leave Begins: Revision Timetable Check-In

The full plan: every lesson with its objective, starters, practice and homework links, your own order and dates, and a tick to mark each lesson taught.

Get the full editable scheme of work — free for teachers

What the course covers

Every syllabus point in plain English, with practice for each: IB Maths AI HL syllabus checklist.