IB Mathematics: Analysis and Approaches | AA SL & HL Guide

IB Mathematics: Analysis and Approaches | AA SL, AA HL, Current Assessment and the 2029 Transition

IB Mathematics: Analysis and Approaches (AA) is the Diploma Programme Mathematics route that emphasises analytical methods, algebraic structure, mathematical argument and the development of exact mathematical techniques alongside technology. It is available at Standard Level and Higher Level.

The current AA course remains the live assessment route through the November 2028 examination session. The IB has announced a revised AA course for first teaching from August 2027 and first assessment in May 2029. Current students and revised-generation students must therefore be kept on separate assessment assumptions during the transition.

In the current course, all DP Mathematics students develop five content areas: Number and algebra, Functions, Geometry and trigonometry, Statistics and probability, and Calculus. AA SL is designed around 150 recommended teaching hours; AA HL around 240 hours. Both include an individual mathematical exploration worth 20% of the final grade.

1. What makes AA distinct

AA favours students who enjoy:

• algebraic manipulation;
• functions and symbolic structure;
• proof and reasoning;
• trigonometry;
• calculus;
• exact methods;
• analytical problem solving.

Technology remains important, but AA deliberately includes a paper where calculators are not permitted.

2. AA and AI should remain separate

Analysis and Approaches and Applications and Interpretation share some DP Mathematics foundations but emphasise different mathematical habits. Course choice should reflect the student’s strengths, interests and intended university pathways.

AA should not be described as universally “harder” or “better”. The appropriate route depends on the mathematical job the student needs.

3. SL and HL are different depth routes

HL contains the SL mathematical foundation plus additional depth and complexity. A strong HL learner needs:

• faster algebraic fluency;
• stronger proof habits;
• greater calculus depth;
• more demanding function/trig work;
• ability to sustain multi-stage reasoning.

4. Current SL assessment

In the current course, AA SL external assessment consists of:

• Paper 1: 1 hour 30 minutes, no calculator, 40%;
• Paper 2: 1 hour 30 minutes, graphic display calculator required, 40%.

The mathematical exploration is 20%.

5. Current HL assessment

In the current course, AA HL external assessment consists of:

• Paper 1: 2 hours, no calculator, 30%;
• Paper 2: 2 hours, graphic display calculator required, 30%;
• Paper 3: extended-response problem solving, 20%.

The mathematical exploration is 20%.

Current HL Paper 3 belongs to the current course generation. The revised first-assessment-2029 course changes Paper 3 timing and marks; those revised details should not be projected backward onto current candidates.

6. Paper 1: no technology

Paper 1 rewards exact mathematical control. Students should be fluent with:

• fractions;
• algebra;
• functions;
• exact trig values;
• proof;
• calculus;
• probability reasoning;
• structure recognition.

7. Original Paper 1 task: algebra

Simplify:

[ rac{x^2-9}{x^2+x-6}. ]

Factor:

[ rac{(x-3)(x+3)}{(x+3)(x-2)} = rac{x-3}{x-2}, ]

with original restrictions (x e-3,2).

8. Original Paper 1 task: exact trigonometry

If:

[ sin heta=rac12 ]

and (0le hetale2pi), then:

[ heta=rac{pi}{6},rac{5pi}{6}. ]

9. Original Paper 1 task: proof

Prove the product of two consecutive integers is even.

Let the integers be (n,n+1). One of two consecutive integers is even, so their product is even.

10. Paper 2: technology required

Paper 2 requires a graphic display calculator, but students should still:

• identify the mathematical model;
• predict graph behaviour;
• estimate;
• check domain;
• interpret output;
• show necessary working.

11. GDC use should be mathematical

A GDC can:

• graph functions;
• solve equations numerically;
• perform regression;
• evaluate statistical probabilities;
• calculate definite integrals;
• explore parameters.

It cannot decide whether the model is appropriate.

12. Original Paper 2 task: intersection

Find intersections of:

[ y=e^x ]

and:

[ y=3x. ]

The GDC can locate numerical solutions, but the student should understand that intersections solve:

[ e^x=3x. ]

13. GDC window matters

A poor window can hide:

• additional roots;
• turning points;
• asymptotes;
• long-run behaviour.

Students should adjust the window based on mathematical expectations.

14. HL Paper 3

Paper 3 is an HL-only extended-response problem-solving paper. It rewards:

• persistence;
• representation choice;
• linking different syllabus ideas;
• reasoned use of technology;
• clear multi-stage communication.

It should be practised through unfamiliar problems, not memorised templates.

15. Paper 3 habit: identify structure first

Before calculating, ask:

• What is being defined?
• What is known?
• What is the target?
• Which representation may simplify the problem?
• Which earlier result can be reused?

16. Number and algebra

This domain can include:

• sequences and series;
• indices and logarithms;
• proof;
• binomial ideas;
• systems and algebraic manipulation;
• complex numbers at HL.

17. Original sequence task

Geometric sequence:

[ u_n=200(1.03)^{n-1}. ]

Ask when (u_n>300). Logs can solve the inequality.

18. Original proof-by-induction task

At HL, prove:

[ 1+2+cdots+n=rac{n(n+1)}2. ]

Use base case, hypothesis and inductive step.

19. Functions

Students should connect:

• function notation;
• domain/range;
• inverse;
• composition;
• transformations;
• graphs;
• models.

20. Original function task

Let:

[ f(x)=2x+5. ]

[ f^{-1}(x)=rac{x-5}{2}. ]

Check:

[ f(f^{-1}(x))=x. ]

21. Function transformations

If (y=f(x)), then:

[ y=f(x-3)+2 ]

translates the graph 3 right and 2 up.

22. Geometry and trigonometry

AA develops:

• trig functions;
• identities;
• equations;
• vectors;
• geometry;
• complex-number geometry at HL.

23. Original trig identity task

From:

[ sin^2x+cos^2x=1, ]

derive:

[ 1+ an^2x=sec^2x ]

by dividing by (cos^2x), where defined.

24. Original vector task

For:

[ mathbf a= egin{pmatrix} 1\2\3 end{pmatrix}, quad mathbf b= egin{pmatrix} 2\-1\4 end{pmatrix}, ]

[ mathbf acdotmathbf b=2-2+12=12. ]

The dot product connects vectors and angle relationships.

25. Statistics and probability

AA includes statistical and probability reasoning but typically with greater emphasis on analytical structure than AI.

Students should understand distributions, sampling, regression and probability models according to level.

26. Original conditional-probability task

If:

[ P(A)=0.5,quad P(B)=0.4,quad P(Acap B)=0.2, ]

then:

[ P(A|B)=0.2/0.4=0.5. ]

27. Correlation is not causation

A regression model can show association. Students should avoid causal conclusions unless the study design supports them.

28. Calculus is central to AA

Students should develop:

• limits/derivative ideas;
• differentiation;
• integration;
• applications;
• differential equations at appropriate level;
• series/approximations at HL.

29. Original derivative task

For:

[ f(x)=x^3-6x^2+9x, ]

[ f'(x)=3(x-1)(x-3). ]

Use sign to classify stationary points.

30. Original optimisation task

A rectangle has perimeter 20.

Area:

[ A=x(10-x). ]

[ A’=10-2x. ]

Maximum at (x=5).

31. Original integration task

[ int_0^2(4x-2x^2),dx = rac83. ]

The learner should interpret the area if the graph is non-negative over the interval.

32. Differential equations as models

For:

[ rac{dy}{dt}=ky, ]

solution:

[ y=Ae^{kt}. ]

This models exponential growth or decay.

33. The mathematical exploration

The exploration is compulsory at SL and HL and is 20% of the final grade.

A strong exploration should have:

• a meaningful question;
• appropriate Mathematics;
• clear communication;
• reflection;
• personal mathematical engagement;
• authentic student work.

34. The exploration should not be a research essay

The centre of gravity should be Mathematics. Background context is useful only when it supports the mathematical investigation.

35. Exploration topic should match mathematical readiness

A complicated topic with weak Mathematics is worse than a focused topic with strong mathematical development.

36. Original exploration direction: optimisation

Investigate how a container shape affects material use for fixed volume.

The student can:

• define variables;
• derive formulas;
• differentiate;
• find optimum;
• evaluate assumptions.

37. Original exploration direction: modelling

Model a cooling, population or financial process. Compare fit, assumptions and residual behaviour.

38. Exploration authenticity

The exploration must be the student’s own work. Tools can support learning, but the mathematical choices, reasoning and writing must remain authentic and consistent with school/IB rules.

39. SL preparation should build independence

SL is not “easy HL”. Students should secure:

• algebra;
• functions;
• trigonometry;
• probability/statistics;
• calculus;
• calculator and non-calculator control.

40. HL preparation should add depth and endurance

HL students need stronger:

• proof;
• complex numbers;
• advanced calculus;
• vectors;
• long multi-stage problems;
• Paper 3 persistence.

41. Paper 1 and Paper 2 should cross-check

The same mathematical object may appear in exact analytical form on Paper 1 and technology-supported form on Paper 2.

Students should not create separate knowledge systems.

42. Original paired task

Paper 1 style: solve:

[ x^2-5x+6=0. ]

Paper 2 style: graph a more complex function numerically and compare roots with algebraic expectations.

43. Error categories

44. Six-week SL cycle

Week 1: algebra/functions.

Week 2: trig/geometry.

Week 3: statistics/probability.

Week 4: calculus.

Week 5: Paper 1/2 pair.

Week 6: exploration repair and transfer.

45. Six-week HL cycle

Week 1: SL foundation diagnostic.

Week 2: advanced algebra/functions.

Week 3: advanced trig/vectors/complex.

Week 4: advanced calculus.

Week 5: Paper 1/2/3 rotation.

Week 6: IA + fresh transfer.

46. Current-to-2029 transition

The IB states that the current Mathematics courses have their final assessment in November 2028. The revised AA course begins first teaching in August 2027 and first assessment in May 2029.

This creates overlapping cohorts. Current-course students should not use revised assessment timings automatically.

47. Revised 2029 changes

The IB states that the revised course keeps the external assessment model broadly the same but reduces some content and reduces marks/items on external papers. At HL, revised Paper 3 becomes one hour. The revised exploration criteria also change to a four-criterion inquiry-process model.

These are future-generation facts, not current-course rules.

48. Resource labelling during transition

Use:

• current AA through Nov 2028;
• revised AA first assessment 2029;
• cross-generation Mathematics practice;
• historical/current past papers.

49. University route considerations

Universities can have different Mathematics expectations. Students should check current course prerequisites directly with the institutions they are considering rather than assume that one IB Mathematics route is universally accepted for every quantitative degree.

50. Parent/tutor check

• AA or AI?
• SL or HL?
• current course or 2029 revised generation?
• Which paper is weakest?
• Is the exploration mathematically strong?
• What future university requirements matter?

51. Official-source control

Use the IB DP Mathematics page, current AA guide/subject brief, and the official AA curriculum-update page. The IB currently states that the present course has final assessment in November 2028 and the revised course begins first teaching in 2027 for first assessment in 2029.

52. Final learner checklist

• I know SL or HL expectations.
• I can work without technology on Paper 1.
• I can use a GDC intelligently on Paper 2.
• I can sustain extended reasoning at HL.
• I understand the five content areas.
• My exploration is mathematics-led.
• I know which curriculum generation I am in.

53. The durable IB AA model

algebraic foundation → functions/trig → probability/statistics → calculus → technology/no-technology dual control → exploration → extended reasoning → feedback → university transition → curriculum-generation check.

IB Mathematics AA Mastery Clinic: Paper 1 Exactness, Paper 2 Technology, HL Paper 3 and Exploration Quality

The second-pass standard for IB Mathematics Analysis and Approaches is integration across four different performance demands: exact analytical Mathematics without technology, technology-supported problem solving, extended reasoning at HL, and an individual exploration that communicates genuine mathematical inquiry.

1. Build one AA spine

Keep these capabilities live across the whole course:

• algebra;
• functions;
• trigonometry;
• vectors/geometry;
• probability/statistics;
• calculus;
• proof and reasoning;
• technology judgement.

Paper labels should not become permanent knowledge boundaries.

2. Paper 1 exactness is a skill set

Regular non-technology retrieval should include:

• fractions and surds;
• algebraic factorisation;
• log laws;
• exact trig values;
• derivatives and integrals;
• proof;
• probability relationships.

3. Original Paper 1 task: surd algebra

Simplify:

[ rac{1}{sqrt3-1}. ]

Rationalise:

[ rac{sqrt3+1}{(sqrt3-1)(sqrt3+1)} = rac{sqrt3+1}{2}. ]

4. Original Paper 1 task: log equation

Solve:

[ ln(x-1)+ln(x+1)=ln8. ]

Combine:

[ ln(x^2-1)=ln8. ]

[ x^2=9. ]

Domain requires (x>1), so:

[ x=3. ]

The negative algebraic solution is rejected by the log domain.

5. Original Paper 1 task: exact trigonometry

Solve:

[ 2cos^2x-1=0 ]

on (0le xle2pi).

[ cos^2x=rac12, ]

so:

[ x=racpi4,rac{3pi}4,rac{5pi}4,rac{7pi}4. ]

6. Original Paper 1 task: calculus

For:

[ f(x)=x^4-4x^2, ]

[ f'(x)=4x^3-8x=4x(x^2-2). ]

Stationary points at:

[ x=0,pmsqrt2. ]

The learner should classify them using sign or second derivative where appropriate.

7. Paper 2 should not be “calculator Paper 1”

Paper 2 preparation should build:

• GDC graphing;
• numerical solving;
• regression/statistics;
• distribution calculations;
• definite integration;
• parameter exploration;
• interpretation.

The student still needs a mathematical prediction before using technology.

8. GDC lab: transformed function

Graph:

[ f(x)=e^{-x}(x-2). ]

Before graphing, ask:

• what happens as (x oinfty)?
• where is the obvious root?
• what does the exponential factor do?

Then use the GDC to inspect turning behaviour.

9. GDC lab: numerical root

Solve numerically:

[ x=cos x. ]

Graph (y=x) and (y=cos x), locate the intersection and verify by substitution. The learner should know this is a fixed-point equation.

10. GDC lab: statistics

Given paired data, compute regression only after plotting. Ask:

• linear association?
• outlier?
• reasonable extrapolation range?
• causation?

The regression command is the final part of the modelling decision, not the first.

11. SL mastery should preserve analytical independence

A strong SL learner should be able to solve a significant amount of course Mathematics without technology even when the GDC would make the arithmetic faster. This supports Paper 1 and strengthens Paper 2 judgement.

12. HL mastery needs deeper abstraction

A strong HL learner should additionally be comfortable with:

• complex numbers;
• proof;
• advanced sequences/series;
• advanced calculus;
• differential equations;
• more demanding vectors;
• extended unfamiliar problems.

13. Complex-number lab

Let:

[ z=1+isqrt3. ]

Modulus:

[ 2. ]

Argument:

[ pi/3. ]

So:

[ z=2(cosracpi3+isinracpi3). ]

Use polar form to compute powers efficiently.

14. Proof lab: contradiction

To prove there is no greatest real number, suppose (M) is greatest. Then (M+1) is real and greater than (M), contradiction.

The proof is short because it attacks the definition directly.

15. Series lab

A geometric series has first term (a) and ratio (r), (|r|<1). Sum to infinity:

[ S_infty=rac{a}{1-r}. ]

The condition (|r|<1) is part of the formula’s jurisdiction.

16. Calculus lab: integration by parts

At HL, evaluate:

[ int xe^x,dx=e^x(x-1)+C. ]

Differentiate to verify.

17. Differential-equation lab

Suppose:

[ rac{dy}{dt}=k(100-y). ]

This models approach to an equilibrium. The learner should interpret 100 as the limiting value and (k) as a rate parameter.

18. Paper 3 should train productive persistence

For current HL candidates, Paper 3 extended-response work should train:

• reading long prompts;
• using earlier parts;
• trying representations;
• making conjectures;
• using technology strategically;
• recovering from dead ends.

19. Paper 3 stop-loss rule

If a route stalls, do not erase everything. Ask:

• what result from an earlier part can be reused?
• can I graph?
• can I test a special case?
• can I simplify notation?
• can I change representation?

20. Original Paper 3-style exploration

Define:

[ f_a(x)=x^3-3ax. ]

Investigate how the number and location of stationary points depend on (a).

[ f_a'(x)=3(x^2-a). ]

For (a>0), two real stationary points. For (a=0), one repeated stationary point. For (a<0), none.

Then ask how the graph changes as (a) varies.

21. Paper 3-style modelling task

Suppose a population follows a logistic-like model provided in the question. Ask the learner to:

• interpret parameters;
• graph with GDC;
• find an inflection or threshold numerically;
• compare with data;
• evaluate assumptions.

22. The exploration should grow from a question

A strong IA/exploration begins with a mathematical question narrow enough to investigate deeply.

Weak:

“The Mathematics of Football.”

Stronger:

“How does launch angle affect the range of a projectile model for a football kick under stated assumptions?”

23. Exploration mathematics should drive the writing

Every paragraph should serve:

• definition;
• derivation;
• calculation;
• representation;
• interpretation;
• reflection.

Background narrative should not dominate.

24. Exploration reflection is mathematical

Useful reflection includes:

• assumption limitations;
• sensitivity to parameters;
• comparison of models;
• error/uncertainty;
• why one method is better;
• what result means.

25. Original exploration lab: optimisation

For a cylinder of fixed volume (V), express surface area in one variable and differentiate to minimise material. Then discuss whether a real container needs a lid, thickness or manufacturing constraints.

26. Original exploration lab: regression

Compare linear, quadratic and exponential models for a dataset. Use residuals and contextual plausibility rather than only an (R^2)-type fit statistic.

27. Original exploration lab: sequences/fractals

Investigate a recursive pattern, derive a recurrence or closed form, examine convergence and discuss how initial conditions affect behaviour.

28. Exploration tool use should remain transparent

If software generates a regression, derivative or graph, the student should explain why that operation is relevant and what the output means.

29. First-error atlas for AA

30. Paper-pair review

After P1 and P2 practice, compare errors:

• Which ideas fail without technology?
• Which errors arise only from GDC input?
• Which methods are inefficient?
• Which results were not interpreted?

The goal is one mathematical system across both papers.

31. HL three-paper review

After P1/P2/P3, identify:

• foundation gaps;
• technology gaps;
• extended-response persistence gaps.

Repair each with a different training method.

32. Six-week SL mastery cycle

Week 1: algebra/functions.

Week 2: trig/geometry.

Week 3: statistics/probability.

Week 4: calculus.

Week 5: P1/P2 pair.

Week 6: exploration and fresh transfer.

33. Six-week HL mastery cycle

Week 1: SL floor + proof.

Week 2: complex/vectors/advanced functions.

Week 3: advanced calculus.

Week 4: statistics/probability.

Week 5: P1/P2/P3 rotation.

Week 6: exploration + delayed transfer.

34. Current/revised generation separation

A current-course student sitting by November 2028 should prepare against the current AA guide and current paper structure. A revised-course student first assessed in 2029 should use the revised guide, including the revised HL Paper 3 timing and revised exploration criteria.

35. Do not migrate IA criteria early

The revised exploration assessment changes criteria. Current-course candidates should not be assessed as if those future criteria already govern their work.

36. Cross-generation Mathematics can still be reused

Algebra, calculus, proof, function and statistics tasks remain mathematically useful. Label them as cross-generation practice unless they replicate a specific assessment format.

37. University preparation should be evidence-led

For mathematically demanding degrees, students should check current university prerequisites. Course name alone does not guarantee acceptance. Some courses specify AA HL or particular grades.

38. Delayed retrieval

Several days after a corrected paper, use an unseen task from each major domain. If the method survives without notes, the skill is more durable.

39. SL release checklist

• Paper 1 exactness;
• Paper 2 GDC judgement;
• five content areas stable;
• exploration mathematics-led;
• fresh transfer successful;
• curriculum generation correct.

40. HL release checklist

• SL foundation stable;
• advanced content stable;
• Paper 3 persistence;
• proof visible;
• GDC auditable;
• IA mathematically reflective;
• current/revised route correct.

41. Final IB AA release standard

AA is mastered when the learner can move between exact analytical work, technology-supported work, extended reasoning and independent mathematical exploration without losing mathematical meaning.

Release principle: analyse exactly, use technology intelligently, reason deeply, investigate authentically, version the course correctly.

IB AA Final Release Lab: SL/HL Paper Evidence, Exploration and Curriculum-Generation Control

The final release stage for IB Mathematics: Analysis and Approaches should prove that the student can operate across the complete AA performance system: non-technology analytical work, GDC-supported problem solving, HL extended response where applicable, and the mathematical exploration. The student should also know whether they belong to the current course or the revised first-assessment-2029 generation.

1. Final SL Paper 1 set

Use one question from each major dependency:

• algebra;
• functions;
• trigonometry;
• probability/statistics;
• calculus.

No calculator. Exact forms should be preserved.

2. SL Paper 1 algebra task

Solve:

[ rac{x+2}{x-1}=4. ]

Domain:

[ x e1. ]

Then:

[ x+2=4x-4 ]

[ 6=3x ]

[ x=2. ]

The solution respects the domain.

3. SL Paper 1 function task

Let:

[ f(x)=x^2-4x+1. ]

Complete the square:

[ f(x)=(x-2)^2-3. ]

The minimum is (-3) at (x=2). The same representation supports graph sketching and inequality reasoning.

4. SL Paper 1 trig task

Solve:

[ sin x=rac{sqrt3}{2} ]

for (0le xle2pi).

[ x=racpi3,rac{2pi}3. ]

5. SL Paper 1 calculus task

For:

[ f(x)=2x^3-3x^2+1, ]

[ f'(x)=6x^2-6x=6x(x-1). ]

Use sign to classify stationary behaviour.

6. Final SL Paper 2 set

Use a GDC-supported set containing:

• numerical intersections;
• regression/statistics;
• distribution probability;
• definite integral;
• model interpretation.

7. SL Paper 2 graph task

Find numerical intersections of:

[ y=x^3-x ]

and:

[ y=2. ]

Use a GDC but first inspect long-run behaviour and predict how many real intersections may be plausible.

8. SL Paper 2 statistics task

Given paired data, create a scatter plot, fit a regression line, identify any outlier and explain why extrapolation far beyond the observed range may be unreliable.

9. Probability distribution task

If:

[ Xsim B(20,0.25), ]

find:

[ P(Xge1)=1-(0.75)^{20}. ]

The GDC can calculate, but the student should justify the complement and binomial model.

10. Definite integral task

Use technology to evaluate a definite integral numerically, then explain what the result means geometrically or contextually. A decimal from the calculator is not enough.

11. HL Paper 1 release

HL Paper 1 should include stronger exact analytical tasks:

• proof;
• complex numbers;
• advanced functions;
• vectors;
• series;
• advanced calculus.

12. HL complex-number task

Solve:

[ z^4=-16. ]

Write:

[ -16=16e^{i(pi+2kpi)}. ]

The four roots have modulus 2 and arguments:

[ rac{pi}{4},rac{3pi}{4},rac{5pi}{4},rac{7pi}{4}. ]

Plot on the Argand plane.

13. HL vector task

For vectors:

[ mathbf a=(1,2,2),quad mathbf b=(2,0,1), ]

[ mathbf acdotmathbf b=4. ]

Use the dot product with magnitudes to find the angle between them.

14. HL proof task

Prove by induction:

[ 1+2+cdots+n=rac{n(n+1)}2. ]

Require full proof structure and use of the inductive hypothesis.

15. HL Paper 2 release

Use GDC-supported advanced tasks that still require structure and interpretation. Examples:

• numerical root of transcendental equation;
• statistical model;
• definite integral;
• differential-equation graph;
• parameter exploration.

16. HL Paper 3 release

For current-course candidates, Paper 3 should be trained through unfamiliar extended-response problems. Do not reduce preparation to one topic. The learner should practise:

• reading definitions;
• using earlier parts;
• changing representation;
• testing conjectures;
• using GDC strategically;
• writing a coherent argument.

17. Paper 3-style task: parameter family

Consider:

[ f_a(x)=x^4-2ax^2. ]

Investigate how stationary points depend on (a).

[ f_a'(x)=4x(x^2-a). ]

For (a>0), stationary points at (0,pmsqrt a). For (a=0), only (0). For (a<0), only (0) is real.

Then analyse classification and graph shape.

18. Exploration release gate: mathematical question

The title/question should be narrow enough to support mathematical depth.

Useful:

“How does changing the parameter (r) affect the long-run behaviour of a logistic map?”

Less useful:

“Mathematics in Nature.”

19. Exploration release gate: mathematics depth

The exploration should contain actual mathematical development:

• derivations;
• models;
• graphs;
• calculations;
• comparisons;
• proof/justification where appropriate.

20. Exploration release gate: reflection

Reflection should address:

• assumptions;
• limitations;
• accuracy;
• sensitivity;
• alternative methods;
• meaning of results.

21. Exploration release gate: communication

Variables, units, graphs, tables and notation should be clear enough that another reader can reconstruct the Mathematics.

22. Exploration release gate: authenticity

The student should be able to explain every mathematical step in the exploration independently. The work must remain authentic under the school’s and IB’s academic-integrity requirements.

23. First-error atlas for SL

24. First-error atlas for HL

25. SL delayed transfer

Several days after correction, use:

• one exact algebra task;
• one GDC graph task;
• one probability/statistics task;
• one calculus task.

If the methods remain available without notes, the learning is more durable.

26. HL delayed transfer

Use:

• one proof;
• one complex/vector problem;
• one advanced calculus problem;
• one extended unfamiliar prompt.

27. Current-course release check

Students sitting by November 2028 should use the current AA course, current assessment timings and current exploration criteria. Do not import revised 2029 paper timings or exploration criteria prematurely.

28. Revised-course release check

Students first assessed in 2029 should use the revised AA course. The revised course includes changed content load, reduced external assessment marks/items, a one-hour HL Paper 3 and revised four-criterion exploration assessment.

29. Transition-resource labels

Use:

• Current AA — final assessment Nov 2028;
• Revised AA — first assessment May 2029;
• Cross-generation Mathematics practice;
• Historical/current past paper.

30. University-requirement check

Before choosing SL/HL or using AA as a prerequisite claim, verify current requirements for the student’s intended university courses. Mathematics entry requirements can differ by institution and degree.

31. Three-week SL final cycle

Week 1: Paper 1 exactness.

Week 2: Paper 2 GDC + exploration repair.

Week 3: paired simulation + delayed transfer.

32. Three-week HL final cycle

Week 1: Paper 1/2 pair.

Week 2: Paper 3 + advanced content.

Week 3: full rotation + exploration final audit.

33. Final SL release standard

SL is ready when the student can work analytically without technology, use the GDC intelligently, integrate the five content areas and produce a mathematically authentic exploration.

34. Final HL release standard

HL is ready when the student can do everything above at greater depth, sustain proof and advanced calculus, and solve unfamiliar extended-response problems productively.

Final release principle: exact Paper 1 thinking, intelligent Paper 2 technology, productive HL extended reasoning, authentic exploration and correct curriculum generation.

IB AA Standards Appendix: Final Paper, Exploration and Transition Evidence

The final AA owner should contain enough evidence for a student, parent or tutor to distinguish content familiarity from actual course readiness. Readiness requires analytical independence on Paper 1, intelligent technology on Paper 2, sustained extended response at HL, a mathematics-led exploration and correct current-versus-revised curriculum ownership.

1. SL final evidence set

Use one fresh question from each content area:

• Number and algebra;
• Functions;
• Geometry and trigonometry;
• Statistics and probability;
• Calculus.

At least half should be completed without technology.

2. HL final evidence set

Add:

• proof;
• complex numbers;
• advanced vectors;
• advanced calculus/differential equations;
• one Paper 3-style extended problem.

3. Paper 1 evidence

The learner should demonstrate:

• exact form;
• domain restrictions;
• clean algebra;
• known trig values;
• proof/justification;
• calculus without GDC dependence.

4. Paper 2 evidence

The learner should demonstrate:

• appropriate GDC use;
• graph-window judgement;
• numerical solving;
• regression/distribution tools;
• definite integration;
• interpretation and verification.

5. HL Paper 3 evidence

The learner should be able to work through an unfamiliar extended prompt, reuse earlier results, change representation when stuck and communicate a coherent mathematical argument rather than waiting for a memorised template.

6. Example extended prompt

Consider:

[ f_a(x)=x^3-3ax. ]

Ask the learner to analyse stationary points, graph shape and parameter dependence, then extend the problem by comparing areas or solving a related equation numerically. The purpose is sustained reasoning across parts.

7. Exploration question evidence

The exploration should have a specific mathematical focus and a reason for the chosen mathematics.

A reviewer should be able to answer:

• What is being investigated?
• Why are these methods appropriate?
• What mathematical result was obtained?
• How was it interpreted?
• What limitation was identified?

8. Exploration depth evidence

A strong exploration contains more than graphs or calculator output. It should show derivation, transformation, modelling, comparison or another form of mathematical development appropriate to the level.

9. Exploration reflection evidence

Useful reflection asks:

• How sensitive is the result?
• What assumptions matter most?
• Would another model be better?
• What happens at a boundary case?
• How reliable is the data?

10. Exploration authenticity evidence

The learner should be able to explain any graph, equation, code-assisted result or statistical output in their own mathematical language. An impressive result that the student cannot explain is not robust evidence of mathematical ownership.

11. Paper-to-exploration transfer

Paper skills and exploration skills should support each other:

• Paper 1 algebra supports derivations;
• Paper 2 GDC skills support model exploration;
• Paper 3 persistence supports open inquiry;
• IA reflection improves model evaluation.

12. Example model-check task

A dataset is fitted with:

[ y=Ae^{kx}. ]

Ask the learner to estimate parameters, inspect residuals, compare with a linear model and explain which model is more defensible within the data range.

13. Example calculus/model task

A rate is:

[ r(t)=5e^{-0.2t}. ]

Total accumulated quantity over an interval is the integral of the rate. Ask the learner to interpret both the instantaneous rate and the accumulated amount.

14. First-error evidence

15. Delayed-transfer evidence

Several days after paper correction, use a fresh problem from each major content family. For HL, add one unfamiliar extended-response problem. The student should rebuild methods without reopening worked solutions.

16. Current-course evidence

Students assessed through November 2028 should use the current AA assessment model and current exploration criteria.

17. Revised-course evidence

Students first assessed in 2029 should use the revised course, including its revised external-paper design and revised four-criterion exploration model. Resource labels should make the generation explicit.

18. Course-choice evidence

AA SL/HL selection should be based on:

• mathematical strengths;
• future study;
• university prerequisites;
• comfort with analytical Mathematics;
• readiness for the workload.

Do not treat HL as a status label.

19. Final SL standard

Paper 1 and Paper 2 both stable, five content areas connected, exploration mathematics-led, technology auditable, delayed transfer successful and curriculum generation correct.

20. Final HL standard

SL foundation plus advanced proof/calculus/vectors/complex Mathematics, productive Paper 3 reasoning, exploration depth, strong GDC judgement and correct current/revised ownership.

Final standard: IB AA is complete when analytical technique, technology, proof, modelling and independent exploration reinforce one another under the correct assessment generation.