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IB Maths AA HL scheme of work

A complete plan for IB Maths AA 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 4: Geometric Series (Sum Formula)

By the end of the lesson students can: Use Sₙ = u₁(rⁿ − 1)/(r − 1) to find the sum of a finite geometric series and solve problems for an unknown ratio or number of terms.
Syllabus reference: SL Topic 1
Quick check FA2: Arithmetic & geometric sequences and series
Misconceptions to watch for: Confusing common difference d with common ratio r; using the arithmetic sum formula for a geometric series.
Then the unit test SA1 (week 7): Unit 1 Test: Number & Algebra · Paper 1 & 2 style · mixed (non-calculator section + calculator section) · 60 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: Algebraic Manipulation, Indices & Surds · PK Refresher: Linear Equations, Inequalities & Simultaneous Equations · PK Refresher: Basic Trigonometry, Pythagoras & Coordinate Geometry · PK Refresher: Functions, Graphs & Algebraic Fractions	FA1
Unit 1 · Number & Algebra
2	Sequences 1: Arithmetic Sequences (nth term) · Sequences 2: Arithmetic Series (Sum Formula) · Sequences 3: Geometric Sequences (nth term) · Sequences 4: Geometric Series (Sum Formula)	FA2
3	Sequences 5: Sum to Infinity & Sigma Notation · Exponents 1: Laws of Exponents & Solving Exponential Equations · Logarithms 1: Introducing Logs & the Log Laws · Logarithms 2: Change of Base & Solving Log Equations	FA3
4	Counting Principles: Permutations & Combinations (ⁿPᵣ and ⁿCᵣ) · Binomial 1: Pascal's Triangle, Binomial Expansion & the General Term · Binomial 2: Extension to Negative & Fractional Indices · Proof 1: Simple Deductive Proof (LHS = RHS) & Notation	FA4
5	Proof 3: Mathematical Induction · Complex Numbers 1: Cartesian Form & Basic Operations · Radians & the Unit Circle (Primer): Radian Measure, Exact Values & Trig Ratios in All Four Quadrants · Complex Numbers 2: The Argand Diagram & Modulus-Argument (Polar) Form	FA5
6	Complex Numbers 3: Euler's Form & De Moivre's Theorem · Complex Numbers 4: nth Roots of Complex Numbers & Geometric Applications · Systems of Equations: 2×2 & 3×3 Linear Systems — Elimination, Technology & Classifying Solutions · Partial Fractions: Denominators with Two Distinct Linear Factors	FA6
	Counting Principles 2: Arrangements with Restrictions · Binomial 3: Validity & Approximations for Fractional & Negative Indices · Proof 4: Induction for Divisibility & Series · Complex Numbers 5: De Moivre's Theorem — Exact Powers
7	Financial Applications: Compound Interest, Depreciation & the TVM Solver · Proof 2: Proof by Contradiction & Counterexample · Unit 1 Revision: Exam-Style Problem Solving · Summative Assessment 1 (SA1)	SA1
Unit 2 · Functions
8	Straight Lines 1: Gradient, Midpoint & Equation of a Line · Straight Lines 2: Parallel & Perpendicular Lines · Quadratics 1: Factorising & Completing the Square · Quadratics 2: The Quadratic Formula, Discriminant & Sketching Parabolas	FA7
9	Functions 1: Function Notation, Domain & Range · Functions 2: Composite, Inverse & Self-Inverse Functions (Domain Restriction) · Transformations 1: Translations & Stretches · Transformations 2: Reflections, Combined Transformations & Odd/Even Functions	FA8
10	Rational Functions 1: Reciprocal & (ax+b)/(cx+d) Graphs, Asymptotes & Rational Equations · Rational Functions 2: (ax+b)/(cx²+dx+e) & (ax²+bx+c)/(dx+e), incl. Oblique Asymptotes · Exponential & Logarithmic Functions 1: Graphs & Modelling · Graphs of \|f(x)\|, f(\|x\|), 1/f(x), f(ax+b) & [f(x)]²	FA9
11	Polynomial Functions 1: The Factor & Remainder Theorems · Polynomial Functions 2: Sketching Graphs & Multiplicity of Roots · Polynomial Functions 3: Solving Polynomial Equations & Complex Conjugate Roots · Polynomial Functions 4: Sum & Product of Roots & Consolidation	FA10
12	Inequalities: Solving g(x) ≥ f(x) Graphically & Analytically (incl. Modulus & Rational) · Unit 2 Revision: Exam-Style Problem Solving · Unit 2 Revision: Common Misconceptions Clinic · Summative Assessment 2 (SA2)	SA2
Unit 3 · Geometry & Trigonometry
13	3D Coordinate Geometry 1: Distance & Midpoint in 3D · 3D Coordinate Geometry 2: Volume & Surface Area of Solids · Right-Angle Trig 1: SOHCAHTOA & Angles of Elevation/Depression · Right-Angle Trig 2: Pythagoras & Trig in 3D	FA11
14	Sine Rule: Finding Sides, Angles & the Ambiguous Case · Cosine Rule: Finding Sides & Angles · Area of a Triangle (½ab sin C) & Applications · Circular Measure 1: Radians & Arc Length	FA12
15	Circular Measure 2: Area of a Sector & Segment · The Unit Circle: Exact Values & Trig Ratios of Any Angle · Trig Identities 1: The Pythagorean Identity & Double Angle Formulae · Trig Equations 1: Solving sin/cos/tan Equations	FA13
16	Trig Equations 2: Quadratic-Type & Further Trig Equations · Trig Graphs 1: Sine, Cosine & Tangent Functions · Trig Graphs 2: Transformations, Reciprocal (sec, cosec, cot) & Inverse (arcsin, arccos, arctan) Functions · Vectors 1: Vector Basics, Magnitude & Unit Vectors, Vector Equation of a Line (incl. Motion r = a + tv)	FA14
	Non-Right-Angled Trigonometry: The Ambiguous Case & Bearings · Unit Circle 2: Given One Ratio, Find the Others · Trig Equations 3: Equations Using Identities · Trig Graphs 3: Reciprocal & Inverse Trig Functions
17	Vectors 2: The Scalar (Dot) Product & Angle Between Vectors · Vectors 3: The Vector (Cross) Product & Areas · Vectors 4: Vector Equations of Planes · Vectors 5: Intersecting, Parallel & Skew Lines; Intersections of Lines/Planes & Angles Between Them	FA15
	Vectors 6: Lines — Vector, Parametric & Cartesian Forms · Vectors 7: The Foot of the Perpendicular from a Point to a Line · Vectors 8: Planes — Normal Vectors & Cartesian Equations · Vectors 9: Intersections of Two & Three Planes
18	Trig Identities 2: Compound-Angle Formulae, tan 2θ, 1 + tan²θ = sec²θ & 1 + cot²θ = cosec²θ · Unit 3 Revision: Exam-Style Problem Solving · Unit 3 Revision: Common Misconceptions Clinic · Summative Assessment 3 (SA3)	SA3
Unit 4 · Statistics & Probability
19	Data Collection 1: Sampling Methods & Bias · Central Tendency 1: Mean, Median & Mode from Frequency Tables · Data Presentation: Grouped Data, Histograms, Cumulative Frequency, Quartiles, IQR, Box Plots & Outliers (1.5 × IQR) · Dispersion: Variance & Standard Deviation	FA16
20	Correlation 1: Scatter Diagrams & Pearson's r · Correlation 2: Least-Squares Regression (y on x & x on y), Predictions & Causation · Probability 1: Venn Diagrams & Basic Probability · Probability 2: Tree Diagrams, Conditional Probability & Independence	FA17
21	Discrete Random Variables 1: Probability Distributions & E(X) · Discrete Random Variables 2: Variance & the Binomial Distribution · Random Variables 3: Linear Transformations — E(aX + b), Var(aX + b) & Effect of Constant Changes on Data · Bayes' Theorem 1: Conditional Probability Revisited	FA18
22	Normal Distribution 1: The Standard Normal Curve · Normal Distribution 2: Finding Probabilities & Inverse Normal · Normal Distribution 3: Standardisation (z = (x − μ)/σ) — Finding an Unknown μ or σ · Bayes' Theorem 2: Applications & Problem Solving	FA19
23	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
24	Limits & Derivatives 1: The Idea of a Limit & Gradient of a Curve · Limits & Derivatives 2: Differentiation from First Principles · Limits & Derivatives 3: Evaluating Limits & Limit Notation · Differentiation Rules 1: The Power Rule & Sums/Differences	FA20
25	Differentiation Rules 2: The Chain Rule · Differentiation Rules 3: The Product & Quotient Rules · Differentiation Rules 4: Derivatives of Trig, Exponential & Log Functions · Applications 1: Tangents & Normals	FA21
26	Applications 2: Increasing/Decreasing Functions & Stationary Points · Applications 3: The Second Derivative, Concavity & Points of Inflection · Applications 4: Optimisation Problems · Integration 1: Reversing Differentiation (Indefinite Integrals)	FA22
27	Integration 2: Integrating Standard, Trig & Exponential Functions · Integration 3: Integration by Substitution · Integration 4: Definite Integrals, Area Under a Curve & Between Curves · Kinematics: Displacement, Velocity & Acceleration via Calculus	FA23
28	Differential Equations 1: Setting Up & Solving by Separation of Variables · Differential Equations 2: Euler's Method & Modelling Applications · Maclaurin Series: Series Expansions of Standard Functions · L'Hôpital's Rule: Evaluating Indeterminate Limits	FA24
29	Full Course Revision: Algebra, Complex Numbers & Functions · Full Course Revision: Geometry, Vectors & Statistics · 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 5 · Calculus
1	Advanced Differentiation 1: Derivatives of sec x, cosec x, cot x, aˣ & logₐ x · Advanced Differentiation 2: Derivatives of arcsin x, arccos x & arctan x · Advanced Differentiation 3: Implicit Differentiation · Advanced Differentiation 4: Related Rates of Change	FA1
2	IA Workshop 1: The Exploration — Criteria A–E, Strong Explorations & Choosing a Topic · Optimisation with Implicit & HL Functions · IA Workshop 2: Aim, Plan & the Level of Mathematics — Topic Approval · Continuity & Differentiability: Piecewise Functions & One-Sided Limits	FA2
	Implicit Differentiation 2: Tangents & Normals to Implicit Curves · Related Rates 2: Volumes, Ladders & Shadows · Inverse Trig & Exponential Derivatives in Context · Continuity & Differentiability 2: Finding Constants for a Smooth Join
3	Advanced Integration 1: Standard Integrals incl. sec²x, 1/(a² + x²) & 1/√(a² − x²) · Advanced Integration 2: Integration by Substitution — Harder Cases & Changing the Limits · Advanced Integration 3: Integration by Parts · Advanced Integration 4: Repeated Integration by Parts	FA3
4	Advanced Integration 5: Integrating Rational Functions Using Partial Fractions · Areas: The Area Between a Curve and the y-axis · Volumes of Revolution 1: Rotation About the x-axis · Volumes of Revolution 2: Rotation About the y-axis	FA4
	Advanced Integration 6: Completing the Square for Inverse Trig Integrals · Advanced Integration 7: ∫ ln x dx & Cyclic Integration by Parts · Integration Strategy: Choosing the Method · Volumes of Revolution 3: Exam-Style Problems with Exact Answers
5	Differential Equations 3: Homogeneous Equations & the Substitution y = vx · Differential Equations 4: The Integrating Factor Method · Differential Equations 5: Modelling with Differential Equations · Consolidation: Advanced Integration & Differential Equations	FA5
6	Maclaurin Series 2: Substitution, Products & Composite Functions · Maclaurin Series 3: Series from Differential Equations, Differentiation & Integration · Limits Using Maclaurin Series & L'Hôpital's Rule · Consolidation: HL Calculus Extensions	FA6
	Differential Equations 6: Choosing the Method · Differential Equations 7: Euler's Method vs the Exact Solution · Maclaurin Series 4: Approximations from Series · Limits 2: Repeated L'Hôpital & Limits from Series
7	Unit 5 Revision: HL Calculus · Unit 5 Revision: Exam-Style Problem Solving · IA Workshop 3: Writing Up — Communication & Mathematical Presentation (Criteria A & B) · Summative Assessment 1 (SA1)	SA1
Unit 4 · Statistics & Probability
8	Continuous Random Variables 1: Probability Density Functions · Continuous Random Variables 2: Mode, Median & Probabilities from a pdf · IA Workshop 4: Personal Engagement, Reflection & Use of Mathematics (Criteria C, D & E) · Continuous Random Variables 3: E(X), Var(X) & E(g(X))	FA7
9	Continuous Random Variables 4: Piecewise pdfs & Linear Transformations · Bayes' Theorem 3: Problems with Three Events · Probability Problem Solving: Counting, Distributions & Bayes Together · Consolidation: HL Statistics & Probability	FA8
	Continuous Random Variables 5: Finding Constants & Probabilities · Continuous Random Variables 6: Mean, Variance, Median & Mode · Random Variables: E(aX + b) and Var(aX + b) · Bayes' Theorem 4: Reading Tree Diagrams Backwards
Unit 1 · Number & Algebra (Revision)
10	IA Draft Deadline: Complete Draft In — Final Self-Check Against Criteria A–E · Review: Complex Numbers — Forms, De Moivre's Theorem & Roots · Review: Proof by Induction, Contradiction & Counterexample · Review: Counting Principles, the Binomial Theorem & Partial Fractions	FA9 IA-D
Unit 2 · Functions (Revision)
11	Review: Polynomials, the Factor Theorem & Sums and Products of Roots · Review: Rational Functions & Oblique Asymptotes · Review: Modulus Graphs & Inequalities · Review: Transformations, \|f(x)\|, f(\|x\|) & 1/f(x)	FA10
Unit 3 · Geometry & Trigonometry (Revision)
12	Review: Vector Lines, Skew Lines & Shortest Distances · Review: Planes, Intersections & Angles · Review: Compound-Angle Identities & Inverse Trig Functions · Review: Non-Right-Angled Trigonometry & Circular Measure	FA11
Unit 4 · Statistics & Probability (Revision)
13	IA Workshop 5: Acting on Draft Feedback & Finalising the Exploration · Review: Descriptive Statistics & Regression · Review: Discrete Random Variables & the Binomial Distribution · Review: The Normal Distribution & Standardisation	FA12
Unit 5 · Calculus (Revision)
14	Review: Differentiation incl. Implicit Differentiation · Review: Integration Techniques · Review: Kinematics & Volumes of Revolution · Review: Differential Equations & Maclaurin Series	FA13
Full Course Revision · End of Term 1
15	Full Course Revision: Paper 1 (Non-Calculator) Technique · Full Course Revision: Paper 2 (Calculator) 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 (Non-Calculator, 120 mins) · Mock Exam: Paper 2 (Calculator, 120 mins) · Mock Exam: Paper 3 (Calculator, Extended Problem Solving, 75 mins) · Post-Mock Review: Mark Schemes, Corrections & a Personal Revision Plan	SA3
Paper 3 · Extended Problem Solving
18	Paper 3 Workshop 1: Spotting, Generalising & Proving Patterns · Paper 3 Workshop 2: Extended Problems with Complex Numbers · IA Workshop 6: Final Checks — Referencing, Academic Integrity & Presentation · Paper 3 Workshop 3: Extended Problems in Calculus	FA14
19	IA Final Submission: Exploration Handed In with the Academic-Integrity Declaration · Paper 3 Workshop 4: Extended Problems in Functions & Polynomials · Paper 3 Workshop 5: Extended Problems in Probability & Statistics · Paper 3 Workshop 6: Extended Problems in Vectors & Geometry	FA15 IA-F
Unit 5 · Calculus (Targeted Revision)
20	Targeted Revision: Limits, Continuity & L'Hôpital's Rule · Targeted Revision: Implicit Differentiation & Related Rates · Targeted Revision: Integration by Parts & Substitution · Targeted Revision: Differential Equations & Euler's Method	FA16
Unit 1 · Number & Algebra (Targeted Revision)
21	Targeted Revision: Complex Roots & De Moivre's Theorem · Targeted Revision: Systems of Linear Equations · Targeted Revision: Sequences, Series & Logarithms · Targeted Revision: Counting & the Binomial Theorem	FA17
Unit 3 · Geometry & Trigonometry (Targeted Revision)
22	Targeted Revision: Vectors — Lines & the Vector Product · Targeted Revision: Planes & Intersections · Targeted Revision: Reciprocal & Inverse Trig Functions · Targeted Revision: Trigonometric Equations	FA18
Exam Practice · Paper 1 (Non-Calculator)
23	Paper 1 Practice: Section A Short-Response Questions · Paper 1 Practice: Section B Extended-Response Questions · Non-Calculator Skills: Exact Values, Surds, Fractions & Sketching · Paper 1 Practice: A Timed Section A
Exam Practice · Paper 2 (Calculator)
24	Paper 2 Practice: Section A with the GDC · Paper 2 Practice: Section B Extended-Response Questions · Command Terms & Mark Schemes: Show That, Hence, Justify & Accuracy (3 s.f.) · Paper 2 Practice: A Timed Section B
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.

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What the course covers

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