Recommendation: fill the identified gaps and correct the source errors before publishing self-learning lessons. Interactive lessons and quizzes are the next phase.
IB Mathematics: Analysis and Approaches Higher Level, current syllabus with final assessment in November 2028. Exam year is not yet confirmed.
What was checked and what the audit does not certify
Read native text and speaker notes across all 41 presentations; extracted equation text from WMF/EMF records; OCRed raster images with content deduplication; manually inspected key teaching sequences and selected original images. This is a syllabus-coverage and sampled correctness audit, not an independent recomputation of every exercise. OCR does not reliably preserve mathematical layout. Embedded audio/video was not played. The automated cache reports unsupported EMF/media assets; a separate reviewer decoded metafile text. Files and slide numbers refer to the originals, which were not edited.
The 35 main decks contain 1,812 slides. Four revision decks and two alternate vector decks account for the remaining 678. Repeated diagram builds also occur within main decks.
Syllabus coverage and supplements
| Status | Topic / requirement | Evidence and finding | Recommended repair |
|---|---|---|---|
| High-confidence gap | Advanced complex numbers AHL 1.12–1.14 | Unit 3b, slides 1–38 The sequence teaches Cartesian arithmetic, modulus, conjugates, powers of i and Cartesian square roots. No explicit argument, polar/Euler conversion, geometric multiplication/division, de Moivre or general nth-root lesson was found in the collection. | Add a complete advanced-complex unit using bible1.pdf Chapter 10, printed pp. 650–675, with independently checked examples. |
| Partial coverage | Operations on Maclaurin series AHL 5.19 | Unit 8d, slides 3–29; Units 6/7 revision Substitution, addition and multiplication by x are present. No explicit lesson or worked practice deriving a new series by termwise integration/differentiation was found. Products of two nontrivial series need stronger practice. | Add short lessons deriving ln(1+x) from a geometric series, differentiating a known series, and multiplying two series to a specified order. |
| Not found; supplement | Regression of x on y SL 4.10 (also required for HL) | Unit 4b, slides 38–52 The inspected regression sequence teaches y on x. Reverse regression and why one cannot simply invert the first fitted line were not found. | Add a paired worked example and prediction-direction quiz if Katy’s exam is in 2028 or earlier. Bivariate data is removed from 2029. |
| Needs verification / short supplement | Squared-function transformation AHL 2.16 | Unit 2b, all 47 slides Modulus, reciprocal and f(ax+b) transformations are covered. An explicit y=[f(x)]² lesson was not located; formula-only images limit certainty. | Add a brief transformation lesson with sign, fixed-point and shape reasoning unless an existing example is identified. |
| Foundation check | Scientific notation and straight-line basics SL 1.1 and SL 2.1 | Across the collection Dedicated scientific-notation instruction and explicit parallel/perpendicular gradient rules were not established. Some decks assume coordinate-geometry fluency. | Use an entry diagnostic; supply short prerequisite lessons when needed. |
| Self-study preparation | IA, Paper 3 and feedback Mathematical exploration and assessment skills | Unit 5e, slide 46; classroom activities throughout There are references to an IA proposal and future Paper 3 teaching. These do not form a complete independent-learning pathway. Textbook exercise references and teacher-led prompts need explanations and accessible solutions. | Add inquiry milestones, extended unfamiliar problems, calculator guidance, answer feedback and a cumulative review system. |
Substantial coverage already present
| Area | Sources | Finding |
|---|---|---|
| Number and algebra / functions | Units 1a–c, 2a–b, 3a–d, 7b | Sequences, generalized binomial expansion and validity, proof, partial fractions, inverse domains, modulus/reciprocal transformations, polynomial roots/inequalities and linear systems are substantially covered. |
| Geometry and trigonometry | Units 6a–e, 9a–b | Triangle geometry, radians, identities, inverse trig graphs, vectors, line/plane relationships, scalar/cross products and intersections are covered. |
| Statistics and probability | Units 4a–b, 11a–c | Sampling, descriptive statistics, distributions, Bayes (including three cases), continuous densities, transformed variance and inverse-normal problems are covered. |
| Calculus | Units 5a–e, 6f, 7a/c/d, 8a–d | Differentiation, implicit/related rates, inverse-trig calculus, substitution/parts, area/volumes, ODE methods, l’Hôpital and Maclaurin basics are covered. |
| False gaps resolved by image checks | 5a24–25; 8a7; 8b28; 11a40; 11b56–57 | Oblique asymptotes; area integrated with respect to y; partial-fraction integration; Bayes with three sources; piecewise continuous densities are present. Do not duplicate them as missing content. |
IB’s current course ends with November 2028 assessment. The revised course starts teaching in August 2027, with first assessment May 2029. Published changes remove financial applications and bivariate data; at HL they also remove proof by counterexample and Euler’s method. The exploration criteria also change. For 2029+, use the published brief as a provisional crosswalk and confirm the detailed guide when available. These removals do not repair the advanced-complex or series-teaching gaps.
Corrections before self-study publication
These are specific verified examples. They are not a complete error count for every problem in the collection.
| Source | Slides | Problem | Correction |
|---|---|---|---|
| AA HL - Unit 1b - Proof.pptx | 16 | Rationality proof specifies a,b∈R. | Use integers a,b, b≠0, with no common factor. |
| AA HL - Unit 3b - Expanding the System - Complex Numbers.pptx | 38 | 5050=4×1062+2. | Use 5050=4×1262+2. |
| AA HL - Unit 3c - Expanding the System - Polynomials.pptx | 31 | The long-division identity uses quotient 5x²+11x. | Correct identity: 5x²−4x+3=(5x+11)(x−3)+36. The displayed remainder 36 is already correct. |
| AA HL - Unit 3d - Expanding the System - Solving Systems.pptx | 96, 98 | A repeated original equation changes −8x to +8x. | Keep the original −8x coefficient consistent through the solution. |
| AA HL - Unit 4a - Analysing data and Quantifying Randomness.pptx | 16 | Random Sampling Methods includes quota and convenience sampling. | Use Sampling methods and distinguish random from non-random selection. |
| AA HL - Unit 4b - Bivariate Data.pptx | 27 | Lists cause-and-effect as an assumption of Pearson correlation. | Remove that assumption and explain that correlation does not establish causation. |
| AA HL - Unit 8b - ODEs.pptx | 35 | After y=vx, the text says xv′+x=F(v) and replace v with yx. | Use xv′+v=F(v), then substitute v=y/x. |
| AA HL - Unit 8d - Maclaurin Series.pptx | 13 | The final worked expansion ends x³/2. | The preceding calculation requires x³/3. |
| AA HL - Unit 8d - Maclaurin Series.pptx | 26 | The ln(1+x) sigma form begins at n=0 and lacks alternating signs. | Use Σ from n=1 to ∞ of (−1)^(n+1)x^n/n, with appropriate convergence conditions. |
| AA HL - Unit 9b - Vectors (lines and planes).pptx | 57 | The general plane-intersection algorithm always sets z=0. | Choose a valid free coordinate or solve parametrically. The particular example on slide 58 does allow z=0. |
| AA HL - Unit 11c - Binomial and Normal Distributions.pptx | 3 | Defines a binomial distribution merely as two possible outcomes. | Distinguish a binary trial from the count of successes in n independent trials with constant success probability. |
| AA HL - Unit 11c - Binomial and Normal Distributions.pptx | 23 | For Bin(8,0.6), the displayed tail probabilities are inaccurate. | P(X<2)=0.00851968; P(X>5)=0.31539456. Retain precision until the final rounding. |
| AA HL - Unit 11c - Binomial and Normal Distributions.pptx | 55 | Not on course anymore could be read as referring to z-standardisation. | Clarify that the note refers to manual normal tables. Standardisation remains required. |
Provisional weekly plan
Provisional 48 weeks at approximately 6 hours/week (288 planned hours), adjustable after the diagnostic and Katy’s school/exam timetable. This is a pacing proposal, not a guarantee that self-study hours equal IB teaching hours. Use four 60-minute learning/practice sessions, one hour of mixed retrieval/error correction, and one hour of inquiry or catch-up. Reserve the last hour in weeks 13–42 for a 30-hour exploration/inquiry strand; use it for foundations or timed practice in other weeks.
Weekly quiz: 10 current-topic questions, 5 retrieval questions from earlier weeks, and one written reasoning problem. Use new variants for retesting. Start with the diagnostic rather than assuming all prerequisites.
| Week | Focus | Source | Learning target |
|---|---|---|---|
| 1 | Foundation diagnostic | New prerequisite pack | Fractions, rearranging equations, powers, notation, calculator settings and scientific notation. |
| 2 | Coordinate and algebra foundations | New pack; existing coordinate-geometry material | Line equations, parallel/perpendicular gradients, factorisation and reading graphs. Repair diagnosed gaps. |
| 3 | Arithmetic sequences | 1a | Terms, recurrence, sigma notation and finite sums. |
| 4 | Geometric sequences | 1a | Finite/infinite series, convergence and modelling. |
| 5 | Proof | 1b | Deduction, contradiction and induction; explain each logical step. |
| 6 | Counting and binomial expansion | 1c | Permutations, combinations, binomial terms and rational-power expansion with validity. |
| 7 | Functions and inverse functions | 2a | Domain/range, composition, inverse restrictions and representations. |
| 8 | Function transformations | 2b + supplement | Translations, stretches, modulus/reciprocal and squared-function transformations. |
| 9 | Quadratics | 3a | Forms, roots, discriminant, inequalities and parameter problems. |
| 10 | Polynomials and rational graphs | 3c; 5a24–25 | Division, factor/remainder theorems, root relations, inequalities and oblique asymptotes. |
| 11 | Systems of equations | 3d | Unique, infinite and inconsistent systems; parameter reasoning. |
| 12 | Exponents and logarithms | 7b | Laws, change of base, domains and solving equations. |
| 13 | Exponential models | 7b | Interpret parameters and fit/check a model; financial applications through 2028. |
| 14 | Cartesian complex numbers | 3b | Argand diagrams, modulus, conjugates, arithmetic and polynomial roots. |
| 15 | Polar and Euler forms | NEW; bible1 §10.1–10.2 | Argument and quadrants, conversions, products/quotients and geometric interpretation. |
| 16 | de Moivre and complex roots | NEW; bible1 §10.3 | Integer/rational powers, induction proof, general nth roots and root geometry. |
| 17 | Geometry and triangles | 6a–b | 3D measures, trigonometric ratios, sine/cosine rules and bearings. |
| 18 | Radians and unit circle | 6a | Arc/sector measures, exact values, quadrants and signs. |
| 19 | Trigonometric identities | 6c | Reciprocal, compound and double-angle identities; prove rather than memorize. |
| 20 | Trigonometric graphs | 6d | Transformations, modelling, inverse-trig domains and ranges. |
| 21 | Trigonometric equations | 6e | Exact solutions, interval restrictions, algebraic and graphical approaches. |
| 22 | Descriptive statistics | 4a | Sampling, bias, data displays, centre/spread and interpretation. |
| 23 | Bivariate data | 4b + reverse-regression supplement | Correlation, both regression directions, prediction limitations. For 2029, use this slot for mixed review. |
| 24 | Probability foundations | 11a | Events, conditional probability, independence, trees and Bayes. |
| 25 | Limits and derivatives | 5a–b | Continuity, first principles and interpreting rates of change. |
| 26 | Differentiation rules | 5c; 7c | Power, product, quotient, chain, exponential and logarithmic rules. |
| 27 | Trigonometric calculus | 6f | Trig/inverse-trig derivatives and domain restrictions. |
| 28 | Curve analysis | 5d | Derivative graphs, extrema, inflection and sketching. |
| 29 | Applications of differentiation | 5e | Optimization including boundaries, implicit differentiation and related rates. |
| 30 | Integration foundations | 7a | Antiderivatives, constants, definite integrals and the fundamental theorem. |
| 31 | Integration techniques | 7d; 2a34–37; 8b28 | Substitution, partial fractions and inverse-trig forms. |
| 32 | Integration by parts | 7d | Choose factors, repeat parts and solve cyclic cases. |
| 33 | Areas, volumes and motion | 8a | Signed area, x/y integration, both axes of revolution, displacement versus distance. |
| 34 | Differential equations | 8b | Separation, homogeneous substitution and integrating factors. |
| 35 | Limits and numerical methods | 8c; 8b | l’Hôpital and limit reasoning; Euler method through 2028, or extra analytic ODE practice from 2029. |
| 36 | Maclaurin series | 8d + supplement | Construction, convergence, substitution, termwise operations and products to a required order. |
| 37 | Vector foundations | 9a | Components, magnitude, geometry and scalar product. |
| 38 | Vector lines | 9b | Line equations, angles, intersecting/skew/coincident cases and motion. |
| 39 | Cross products and planes | 9b | Areas, normals and equivalent plane equations. |
| 40 | Vector problem solving | 9b | Intersections, line-plane/plane-plane angles and distance reasoning. |
| 41 | Discrete distributions | 11b–c | Expectation, variance, transformations and binomial models. |
| 42 | Continuous distributions | 11b | Density conditions, piecewise functions, expectation, median and mode. |
| 43 | Normal distribution | 11c | Standardisation, inverse problems, unknown parameters and model checks. |
| 44 | Paper 1 skills | Curated mixed bank | Exact algebra, proof, clear working and non-calculator decisions. |
| 45 | Paper 2 skills | Curated mixed bank | Calculator fluency, numerical solutions and interpretation. |
| 46 | Paper 3 inquiry | New extended-problem sequence | Unfamiliar multi-part investigations, conjectures, generalisation and justification. |
| 47 | Mock and diagnosis | Fresh mixed questions | Complete a timed diagnostic; classify conceptual, algebraic and interpretation errors. |
| 48 | Targeted review and exploration reflection | Personal revision list | Retest weak topics with new questions, consolidate connections and complete the exploration review. |
Exploration milestones within the weekly hours
| Weeks | Milestone |
|---|---|
| 13–16 | Choose a question, define variables and scope, test feasibility. |
| 17–24 | Explore examples/data, record assumptions and evaluate methods. |
| 25–32 | Develop the mathematical argument, calculations, diagrams and checks. |
| 33–38 | Draft a coherent explanation and evaluate limitations. |
| 39–42 | Revise the exploration and reflect on the mathematical choices. |
Proposed math.pages.dev learning experience
The current ISOM2600 Week 5 implementation was inspected directly. The adaptation should preserve its explanation and navigation pattern while replacing classroom-dependent activities with independent practice.
- Home: Continue learning, this week, topic map and review mistakes.
- Use the current ISOM2600 Week 5 pattern: white slides, navy/teal hierarchy, readable text, topic navigation, one main question per slide and mobile scrolling.
- Lesson tabs: Understand, Worked example and Try it. Step controls: Back, Next, Play/Pause and Reset.
- Explain notation and prerequisites before a formula. Show a complete numerical example, then ask a check question immediately after the concept.
- Each lesson: 3–5 focused practice questions with hints and independently checked solutions. Each week: 10 current-topic questions, 5 spaced-review questions and one written reasoning problem.
- Mix numeric entry, equivalent expressions where supported, graph interpretation and multiple choice. Written proofs need a worked solution/rubric and learner review; do not label simple automated checks as full proof grading.
- Save topic/slide position, attempts and a mistake-review queue. A passed quiz should be followed by a fresh retrieval check rather than repeated identical questions.
- Use new HTML lessons and original checked questions with textbook section references. Consolidate revision and alternate decks; slide counts include repeated graphs/builds and should not determine the learning workload.
Build order: corrected curriculum map, prerequisite diagnostic and two representative lessons, then the full topic sequence with quizzes and weekly navigation. Verify mathematical answers, desktop/mobile readability, progress behaviour and the final deployment before calling the site published.
Source references
- Official current AA guide
- IB mathematics curriculum and transition
- IB AA curriculum update
- First-assessment-2029 subject brief
- bible1.pdf: Oxford Mathematics: Analysis and Approaches Higher Level (2019), 855 PDF pages. Advanced complex numbers: printed pp.650–675.
- Style source: ISOM2600 CourseSlides/student-plans/week5-l1.qmd and CourseSolutions/teaching-plan-week5/{adopted.css,lesson-ui.js,animations.js}.
All inspected PPTX files and slide counts
| Presentation | Slides |
|---|---|
| AA HL - Unit 11a - Probability.pptx | 42 |
| AA HL - Unit 11b - Probability Distributions.pptx | 64 |
| AA HL - Unit 11c - Binomial and Normal Distributions.pptx | 59 |
| AA HL - Unit 1a - Sequences + Series.pptx | 51 |
| AA HL - Unit 1b - Proof.pptx | 37 |
| AA HL - Unit 1c - Perms, Combs and Binomial.pptx | 37 |
| AA HL - Unit 2a - Functions Definitions.pptx | 111 |
| AA HL - Unit 2b - Functions Transformations.pptx | 47 |
| AA HL - Unit 3a - Expanding the System - Quadratics.pptx | 52 |
| AA HL - Unit 3b - Expanding the System - Complex Numbers.pptx | 38 |
| AA HL - Unit 3c - Expanding the System - Polynomials.pptx | 72 |
| AA HL - Unit 3d - Expanding the System - Solving Systems.pptx | 100 |
| AA HL - Unit 4a - Analysing data and Quantifying Randomness.pptx | 64 |
| AA HL - Unit 4b - Bivariate Data.pptx | 52 |
| AA HL - Unit 5a - Limits.pptx | 31 |
| AA HL - Unit 5b - The Derivative of a Function.pptx | 24 |
| AA HL - Unit 5c - Differentiation Rules.pptx | 32 |
| AA HL - Unit 5d - Graphical Representation of Derivatives.pptx | 42 |
| AA HL - Unit 5e - Applications of Differential Calculus.pptx | 46 |
| AA HL - Unit 6 - Revision.pptx | 176 |
| AA HL - Unit 6 - RevisionCompact.pptx | 154 |
| AA HL - Unit 6a - Relationships in space - Geometry and Trigonometry.pptx | 49 |
| AA HL - Unit 6b - Sine rule and Cosine rule.pptx | 14 |
| AA HL - Unit 6c - Trigonometric Identities.pptx | 35 |
| AA HL - Unit 6d - Trigonometric Graphs.pptx | 171 |
| AA HL - Unit 6e - Trigonometric Equations.pptx | 21 |
| AA HL - Unit 6f - Trigonometric Calculus.pptx | 23 |
| AA HL - Unit 7 - Revision compact.pptx | 69 |
| AA HL - Unit 7 - Revision.pptx | 129 |
| AA HL - Unit 7a - Introduction to Integration.pptx | 54 |
| AA HL - Unit 7b - Exponentials and Logs.pptx | 61 |
| AA HL - Unit 7c - Derivatives of Exp and Log.pptx | 21 |
| AA HL - Unit 7d - Integration Techniques.pptx | 39 |
| AA HL - Unit 8a - Area, Volume and Kinematics (1).pptx | 38 |
| AA HL - Unit 8b - ODEs.pptx | 81 |
| AA HL - Unit 8c - Limts Revisited.pptx | 25 |
| AA HL - Unit 8d - Maclaurin Series.pptx | 29 |
| AA HL - Unit 9a - Vectors-GD-X.pptx | 60 |
| AA HL - Unit 9a - Vectors.pptx | 60 |
| AA HL - Unit 9b - Vectors (lines and planes)-GD-X.pptx | 90 |
| AA HL - Unit 9b - Vectors (lines and planes).pptx | 90 |