- The core difference between AI and AA: computer rules
- Assessment structure for HL and SL
- five subject areas
- The most important analysis: which ones are SL and which ones are unique to HL
- Six must-have features of GDC
- Three significant figures and step writing
- IA: Five principles and the advantages of AI topic selection
- Paper 3 (HL Proprietary)
- Basis for judging subject selection
- Course schedule and fees
1. The core difference between AI and AA: computer rules
The current IB Diploma Mathematics will be taught for the first time in September 2019 and the first exam will be held in 2021. It is divided into two subjects:Mathematics: Applications and Interpretation (AI) and Mathematics: Analysis and Approaches (AA), each subject has HL and SL.
The most critical difference: All AI test papers can use graphics computers (GDC), while AA Paper 1 does not allow the use of computers.
This one determines the different abilities required for the two subjects—but in a direction that goes counter-intuitively to many people. Have a computer Doesn't mean easier: When calculation itself is no longer an obstacle, the focus of assessment shifts to judge Top - Faced with a set of data, which model should be used? Which check should be used? What does the result mean? These cannot be answered by computers.
| Compare items | AI (Applications and Interpretation) | AA (Analysis and Approaches) |
|---|---|---|
| calculator | All exam papers available at GDC | Paper 1 is not allowed to be used |
| core orientation | Statistics, modelling and technology application; emphasis on interpretation and application of results | Analytical skills in algebraic deduction, functions and calculus; emphasis on rigor in argumentation |
| Statistical weight | Higher, it is one of the focuses of the course | lower |
| Calculus Depth | partial application | Deeper, more theoretical |
| main difficulty | Model and test selection judgment, GDC function proficiency, situational interpretation of results | Pure hand calculation fluency and complete demonstration of proof questions |
| Common study directions | Business, Social Sciences, Psychology, Design, Business Analysis | Engineering, Physics, Mathematics, Actuarial Science, Quantitative Economics |
| Details | this page | IB Mathematics AA page |
The names of the five subject areas of the two subjects are the same, but the depth and focus are different. AI goes deeper in Statistics and Probability, and AA goes deeper in Functions and Calculus. Therefore, changing subjects (such as SL AI to SL AA) is usually not just a matter of "catching up a little bit" - it requires the system to make up for the foundation of Algebra and Calculus, and to re-establish the habit of not relying on computers.
- IB Math AA
- IB/GCE course page
- Edexcel IAL Mathematics
- Overview of course topics
- TOLL
- Book a Trial Lesson
2. Evaluation structure of HL and SL
| components | SL | HL |
|---|---|---|
| Recommended teaching hours | 150 hours | 240 hours |
| Paper 1 (GDC available) | 1 hour and 30 minutes, accounting for 40% | 2 hours, accounting for 30% |
| Paper 2 (GDC available) | 1 hour and 30 minutes, accounting for 40% | 2 hours, accounting for 30% |
| Paper 3 (GDC available) | Not available | Open-ended puzzle solving, accounting for 20% |
| Internal Assessment (IA) | Mathematical Exploration, accounting for 20% | Mathematical Exploration, accounting for 20% |
| total | 100% | 100% |
The exam duration for Paper 3 has been adjusted- Data from different years are shown as 1 hour or 1 hour and 15 minutes. You should refer to the official Subject Guide (Subject Guide) for your exam year and the information provided by the school. Its proportion (20%) and properties (open extended solution puzzles, GDC can be used) are consistent.
Strategic Implications of Structure
- SL students: Paper 1 and Paper 2 each account for 40%, both can use computers, so GDC proficiency directly affects 80% of the score.
- HL students: Paper 3 accounts for 20% The number of questions is very small and the weight of each question is extremely high - this is the most easily underestimated aspect.
- IA 20% for both-Same as HL single test paper. The course features of AI (application and modelling) make the topic selection of IA more natural than that of AA, which is a practical advantage for AI students.
3. Five subject areas
AI courses are divided into five subject areas. The category name is the same as AA, but the content and focus are different.
| category | Main content orientation |
|---|---|
| Number and Algebra (Numbers and Algebra) |
Sequences and series and their applications in financial situations (compound interest, annuities, depreciation), exponents and logarithms, approximations and errors, unit conversion and scientific notation |
| Functions (function) |
With function modelling as the core - the selection and application of linear, quadratic, exponential, logarithmic, cubic, sine, logistic and other models; interpretation of images and the meaning of parameters |
| Geometry and Trigonometry (Geometry and Trigonometry) |
Solid geometry and volume surface area, trigonometric ratios and sine and cosine formulas, coordinate geometry,Voronoi diagram (Including nearest facilities and location issues) |
| Statistics and Probability (Statistics and Probability) |
The focus of the undergraduate course: sampling and data presentation, concentration and discrete trends, correlation coefficients and regression, probability, discrete and continuous distributions (including binomial and normal),Chi-square test Hypothesis testing such as t-test |
| Calculus (Calculus) |
The concept and meaning of derivatives, derivation and applications (variability, extreme values, optimization), integrals and areas, using calculus to deal with practical situations |
The above is a category-level overview. For specific details and depth requirements, please refer to the official subject guide for your exam year. The IB curriculum guide is updated regularly, and detailed processing requirements (such as whether a certain test requires hand calculations, whether a certain model requires derivation) often determine the actual focus of review. The Subject Guide provided by the school is the most reliable basis. Official information can be found at Mathematics course page of the IB official website Check.
4. The most important analysis: which ones are SL and which ones are unique to HL
This is the most common temperature error range for AI, and the direction is particularly detrimental to SL students. There is a lot of information online Voronoi diagram and Chi-square test Listed as exclusive to AI HL - actually both SL scope.
The consequence of treating SL content as HL content is: SL students think they don’t need to learn it, and as a result are completely unprepared when they encounter it in the exam. This is much more serious than studying a little more.
| content | Is SL required? | Common misunderstandings |
|---|---|---|
| Voronoi diagram (Including nearest facilities and location issues) | need (Geometry and Trigonometry) | Often mistakenly listed as HL exclusive |
| Chi-square test (chi-squared test) | need (Belongs to Statistics and Probability) | Often mistakenly listed as HL exclusive |
| Correlation coefficient and linear regression | need | — |
| Binomial distribution and normal distribution | need | — |
| financial mathematics (Compound interest, annuity, depreciation) | need | — |
| graph theory (Vertices, edges, adjacency matrices, shortest paths, minimum spanning trees) | unnecessary--HL exclusive | — |
| Matrix operations (Including applications of eigenvalues and eigenvectors) | unnecessary--HL exclusive | — |
| Markov chain and steady state | unnecessary--HL exclusive | — |
| plural (Including applications in AC circuits and other situations) | unnecessary--HL exclusive | — |
| Numerical methods for differential equations (Slope field, Euler method) | unnecessary--HL exclusive | — |
| Advanced applications of vectors | unnecessary--HL exclusive | — |
Check method: The official subject guide is SL and AHL(Additional Higher Level) indicates each learning content - anything marked AHL is unique to HL. This is the only reliable way to judge, and it is itemized, requiring no speculation. If your review materials do not have this marking, their accuracy is questionable.
Three distinctive areas of HL
- Graph theory and networks: Vertices and edges, adjacency matrix, shortest path and minimum spanning tree algorithms. Applied to logistics routes, network design, and critical path analysis. This is the most identifying thing about AI HL that AA has none of.
- Markov chain: State transition matrix and long-term steady state. Applied to weather models, customer turnover, and system reliability. It also uses the matrix operations of HL and is the union of the two HL fields.
- Numerical methods for differential equations: Slope field and Euler method. Unlike AA HL - AI focuses on numerical processing and image understanding rather than analytical solutions.
5. Six essential functions of GDC
Since all test papers are computer-based, GDC proficiency directly affects results. The following six functions must be able to be operated without thinking.
| Function | use | Common question types |
|---|---|---|
| Equation Solving | Find solutions to equations and zeros of functions | The time or number of times a specific value is evaluated in the model |
| Image and intersection | Draw function graphs, find intersection points, extreme values, and intersection points with axes | Model comparison, optimization, image interpretation |
| statistical computing | Univariate and bivariate statistics, mean, standard deviation, quartiles | Data description and comparison |
| regression analysis | Linear and nonlinear regression, correlation coefficient | Find the most suitable model from data - the iconic question type of AI |
| probability distribution | Forward and backward calculations of binomial distribution and normal distribution | Probability evaluation, infer critical value from probability |
| hypothesis test | Calculation of chi-square test, t-test, etc. | Determine whether the correlation or difference is significant |
Regression analysis: the most representative question type of AI
Why it matters"Finding the most suitable model from a set of data" is almost a hallmark of AI. It tests three things at the same time: whether you can use GDC to calculate the regression equation and correlation coefficient;judge Which model should be used (linear, exponential, logarithmic, quadratic, etc.), and whether Interpretation The meaning of the parameters in the situation.
The most likely position to lose points- Wrong model selection: Only look at the absolute value of the correlation coefficient without looking at the actual trend of the data and the rationality of the situation.
- Just give equations without interpretation: The question usually asks what a certain parameter represents, which is an independent score.
- Over extrapolation: Use the model to predict situations well beyond the range of the data without pointing out the limitations of doing so.
First draw a scatter plot to see the trend, and then decide on the model type; after solving the equation, return to the situation to check whether the parameters are reasonable; when answering, clearly write down the meaning of the model and parameters used.
Hypothesis test: Writing is equally important as calculation
The complete work is guaranteed to include- Write out the null and alternative hypotheses clearly (using words to describe what they mean in the situation, not just symbols).
- Write the name of the test used and the necessary parameters (e.g. degrees of freedom).
- Write the test statistic and p-value.
- compared with the significance level and make Back to the conclusion of the situation— Instead of just writing "rejection of the null hypothesis", explain what this means in the context of the question.
Step one and step four. The computer can give you the p-value, but it won't write the hypothesis and conclusion for you - which often account for half of the score on the question.
Computer model: must be confirmed with the school
IB has clear regulations on the computers that can be used, generally requiring image computers and Must not have Computer Algebra System (CAS) capabilities. Common approved models include Texas Instruments’ TI-84 Plus CE series and TI-Nspire CX II (Non-CAS version), and Casio’s fx-CG50 series.
Two things must be noted: 1. The CAS and non-CAS versions of the same series have similar appearances but different regulations - TI-Nspire CX II and TI-Nspire CX II CAS are different models. 2. The approved list and regulations will be updated. You must confirm the current regulations with the school before purchasing, and do not rely on old information online.
Computer check before exam
- Model meets current regulations confirmed by the school and is a non-CAS version
- The battery has been replaced with a new one and a backup battery has been prepared
- The memory has been cleaned according to the school's instructions (some cases need to be cleared)
- The display digits have been set according to the requirement of three significant digits.
- The angle mode is set correctly (radians or degrees, as required by the question)
- Six essential functions can be operated without thinking
6. Writing with three significant figures and steps
Accuracy requirements
Unless otherwise specified in the question, IB generally requires answers Accurate to three significant figures. This is particularly important for AI students because all test papers are computer-readable and the answers are mostly decimals.
| in principle | practice | reason |
|---|---|---|
| Intermediate values retain full precision | Use the computer's memory function to save it. Do not write down the rounded value by hand before entering it. | Rounding will accumulate errors, and the final answer may exceed the acceptable range. |
| Only round to the final answer | When answering, write the complete value and then write the rounded answer. | Show that you know the difference |
| First look at the specific requirements of the topic | Questions may require specifying the number of decimal places or the nearest integer | If you do not meet the requirements, you will lose answer points. |
Even if you have a computer, you still need to write the steps
Just writing the final answer without the process may result in losing most of the points. Marking is by method - this is the same as for AA or DSE Paper 1, the computer does not change the marking logic.
Correct approach: Write down the method or model used, the values substituted, and the results. Statistics questions should state the test or distribution used and its parameters; modelling questions should state the form of the model and the meaning of the parameters.
The general principles of step-by-step writing (write the formula first and then substitute it in, each step on its own line, and the answers are clearly marked) are consistent with other courses, see Writing format for derivation and proof.
7. IA: Five Criteria and Advantages of AI Topic Selection
Internal assessment Mathematical Exploration accounts for the final grade 20%, general recommendations for length 12 to 20 pages. Grading rubric is the same as AA.
| criteria | allotment | Assessment focus |
|---|---|---|
| Criterion A: Presentation | 4 points | Coherence, organization and simplicity |
| Criterion B: Mathematical Communication | 4 points | Correctness and consistency of mathematical symbols, terminology and expressions |
| Criterion C: Personal Engagement | 3 points | Substantial evidence of personal investment |
| Criterion D: Reflection | 3 points | critical judgment about mathematics itself |
| Criterion E: Use of Mathematics | 6 points | Relevance, proportionality to course level, correctness and understanding of mathematics |
| total | 20 points | The sum of the scores for the five criteria |
AI students have a structural advantage in IA. The course itself is about application and modelling, so "using real data for statistical analysis or modelling", the most natural form of IA, is exactly in line with the course content. AA students, on the other hand, more often need to put in the effort to find a topic that has mathematical depth without falling into pure theory.
But this advantage also comes with a pitfall – see below.
IA pitfalls for AI students: Insufficient mathematical depth
Criterion E requires mathematics to be "appropriate to the level of the course." The most common points lost by AI students are: collecting a large amount of data and making beautiful charts, but the mathematical processing only stops at calculating averages, drawing scatter plots and doing linear regression - this is too shallow for SL, and is even more obvious for HL.
HL Tips Students Should Use HL– For example, graph theory, Markov chains, matrices, numerical methods of complex numbers or differential equations. If the entire IA uses only SL-level methods, the score for this item will be limited, no matter how complete the data processing is.
Four Directions to Improve Mathematics Depth
- Compare multiple models: Not just do one regression, but try multiple models and use criteria to compare which one is more suitable - this naturally brings out the reflection of Criterion D.
- Add hypothesis testing: Not just describing the data, but testing whether a correlation or difference is significant.
- Featured content with HL (HL students): Frame the problem in a form that can be processed using graph theory, Markov chains, or matrices.
- Add error and sensitivity analysis: Explore how a change in an assumption affects the results—this improves both Criterion D and E.
Topic selection direction (only direction, you must find your own personal entry point)
The following is possible direction Instead of ready-made questions - directly using common online questions will directly affect Criterion C (Personal Engagement):
- Use self-collected data for modelling and testing: The key is "self-collection", which also supports Criterion C.
- Compare the performance of two models on the same data: This structure naturally supports reflection.
- Applying financial mathematics to real-world decisions: AI’s compound interest and annuity content can be used to compare different options.
- Use Voronoi diagrams to deal with site selection or service coverage problems: Both SL and HL are available, and consideration of actual distance can be added as a reflection.
- Use graph theory to solve route or network problems (HL): Logistics, transportation, network design.
- Simulate state transition using Markov chain (HL): The need for reasonable sources of transition probabilities is reflective material in itself.
Practical points for each standard
- Criterion A (4 points): The highest level requirement streamline— Lengthy data appendices and repeated calculations will result in deductions, not bonuses.
- Criterion B (4 points): All variables are defined before use; symbols are consistent; charts have titles and axis labels. AI IA usually has many diagrams, and it is easy to lose points in this category due to incomplete diagram markings.
- Criterion C (3 points): The comment is that you are in the process of exploring what was actually done (Collect data by yourself, design and verify by yourself), rather than a final paragraph of thoughts.
- Criterion D (3 points): Specifically indicate which hypothesis affects the results and the direction of the influence. General sentences such as "There could be more data" will not score points.
- Criterion E (6 points): The highest score, and there are level requirements for HL.
The specific level description of the guidelines should be based on official documents. The complete description of each level is clearly stated in the IA guide provided by the school or the official subject guide, and should be compared item by item when writing. In terms of guidance: teachers and tutors can give opinions on the direction of topic selection, appropriateness of methods and writing structure, but they are not allowed to ghostwrite - IA must be the student's own work.
time schedule
- Diploma first year second semester: Topic selection and data availability verification. The most common failure of IA in AI is Data cannot be obtained or Insufficient data quality, this step must be confirmed first.
- first year summer vacation: Complete data collection and main analysis.
- First semester of second year: Complete the first draft and self-evaluate each of the five criteria, specifically checking whether the mathematical depth of Criterion E is sufficient.
- before submission: Handles Criterion B (consistency of diagram labels and symbols) and Criterion A (removal of redundancy).
8. Paper 3 (HL exclusive)
Paper 3 is only available for HL and counts towards the final grade. 20%, the form is open extended solution puzzle, GDC can be used.
Paper 3 accounts for 20% but has very few questions. (usually two questions), which means that the weight of a single question is extremely high. And what it tests is not topic memory, but Ability to apply learned tools in unfamiliar situations: The questions are usually guided from the shallower to the deeper, and the results of the previous section are the premise of the later section.
For AI HL students, Paper 3 often appears in extended data or modelling situations, and may be combined with HL features such as graph theory and Markov chains. Therefore, it cannot cope with the type of questions by heart.
Coping methods
- The questions in the previous paragraph must be checked: Because the latter part depends on it. Spend 30 seconds checking the first question and you may save the entire question.
- Training to infer paths based on known conditions: When you can’t see the direction, list what you have on hand and what you can figure out instead of waiting for inspiration.
- Don’t give up just because you don’t understand the whole question: The design of segmented guidance means that the front segment can usually be done.
- Practice previous Paper 3 individually: Its style is obviously different from Paper 1 and 2.
9. Basis for judgment in subject selection
| Ability characteristics | How to observe | point to |
|---|---|---|
| Situational judgment and model selection | Faced with a set of data, can you determine which analysis method to use? | strong → AI |
| contextual interpretation of results | After calculating the number, can you tell what it represents in the context of the question? | strong → AI |
| Use of technological tools | Are you good at using computers or software to process data and images? | strong → AI |
| Pure hand calculation fluency | Speed and accuracy when doing algebraic simplification and derivation without a computer | strong → AA (Paper 1 does not have a computer) |
| Abstract deduction and argumentation | Can you write a complete proof? Is there any way to approach the "proof" question? | strong → AA HL |
Regarding university requirements: IB Mathematics requirements vary among universities and departments and are subject to annual adjustment. Generally speaking, AA HL is more required or preferred in engineering, physics, mathematics and other directions, while AI is more accepted in business and social science directions; however, specific subject and score requirements You must directly check the admission requirements published by the target department for that year..
We do not list specific university requirements comparison tables because this type of information changes frequently, and an outdated comparison table will directly affect a decision that will last two years.
a practical principle of judgment
like The direction of further education is still undecided, AA is generally widely accepted, especially in departments that require a foundation in mathematics. But if you have decided not to study engineering, physics, mathematics, etc., and your strengths lie in data interpretation and application, AI is a more suitable choice - choosing a subject in which you can get high scores is usually more beneficial than struggling to cope with one subject.
Transferring from other courses to AI
- Upgrading from MYP or local courses to AI: The most common gaps were lack of experience in GDC operations and English expression of statistical terminology. In the Pre-IB stage, students can first become familiar with computers.
- From AA to AI: The algebra foundation is usually enough, and the main things that need to be supplemented are the judgment of statistical methods and GDC proficiency.
- From DSE to AI: DSE’s M1 has a statistical basis and can be connected, but IB’s IA (accounting for 20%) and answering language are new requirements. Range comparison see DSE course page and M1 M2 comparison.
10. Course Arrangements and Fees
IB students have very different subject and level mixes - the same class may have AI HL, AI SL and AA students, all at different school progressions. So we first confirm your Subjects, levels and school progress, and then decide on teaching arrangements.
Course features
- Distinguished by subjects and levels: The scope of AI HL and AI SL is obviously different (graph theory, Markov chains, matrices, and complex numbers are all unique to HL), and they will not be processed with the same set of content.
- SL and HL range check: When starting the course, first make sure that your review scope does not mistake SL content for HL (Voronoi diagram, chi-square test), or vice versa.
- GDC six functional training: From basic operations to regression and hypothesis testing, and train the operation speed under time constraints.
- Statistics and modelling question type training: The focus is on the judgment of model selection and the situational interpretation of the results - this is the core assessment of AI, not the calculation itself.
- Complete writing of hypothesis test: Hypothesis statements and situational conclusions often account for half of the score for this question, and the computer will not write them for you.
- IA Five Principles Guidance: Specifically aimed at the most common problem of insufficient depth of Criterion E among AI students; the principle is to assist students to complete it on their own.
- Paper 3 Special Project (HL): How to deal with segmented guidance questions and habits for checking calculations in the previous section.
- Can be taught entirely in English: Match the international school language environment and English answer format, including the correct expression of statistical terms.
Schedule and fees
| project | Details |
|---|---|
| schedule | Thursday 16:30–18:00 (IB/A-Level/IGCSE combined) |
| Duration of each class | 1.5 hours |
| Number of classes per month | 4 classes |
| monthly tuition | HK$1,600 |
| average hourly | About HK$267 |
| class size | About 12 to 14 people, two tutors (teacher-student ratio no more than 1:7) |
| Textbook | Compiled by subject and level, including past test practice and IA guidance |
| trial lesson | The first class is half price; the first month’s tuition will be deducted for daily reading |
Because the mix of IB students varies greatly, we also offer One to one and self-organized classes (at least 3 people in a class, same subject and level). For full charges see Fees and Tuition Page, see course overview IB/GCE maths tuition.
The class location is Room A, 9/F, Landmark City, 761 Nathan Road, Prince Edward, Kowloon (About 2 minutes’ walk from Exit C1 of MTR Prince Edward Station), WhatsApp 9651 3910. Please see the instructor’s qualifications Maths Tutors.
Suitable for objects
- Students taking IB Mathematics AI HL or SL in international schools
- Students who are not proficient in GDC operations or lose more points in statistics questions
- Students who need in-depth guidance on IA topic selection and mathematics
- HL students require specialized training in graph theory, Markov chains or matrices
- HL students need Paper 3 specialized training
- Students who transfer from AA, DSE or other courses to AI and need to compare the differences in scope
Shares from graduates include IB maths students progressing to political science and law at the University of Hong Kong, see Testimonials and Results.
IB Mathematics AI FAQ
Is AI easier than AA?
It’s not that it’s difficult or easy, it’s that the direction is different. All AI test papers can use computers, but the focus of the assessment has therefore changed from "calculating the answer" to "judging which method to use and interpreting the result." AI is more suitable for students who are good at data interpretation, and AA is more suitable for students who are good at abstract deduction.
The most critical difference between AI and AA?
Computer rules: All AI test papers can be used in GDC, AA Paper 1 is not allowed to be used. This determines that the abilities required by the two subjects are different. See details IB Mathematics AA page.
Are Voronoi diagrams unique to HL?
No, it falls within the SL range (Geometry and Trigonometry). The chi-square test is also SL. Treating these two items as HL content will make SL students miss out - this is a fairly common misconception.
What content is exclusive to AI HL?
Graph theory and adjacency matrices, matrix operations, Markov chains and steady states, complex numbers, numerical methods for differential equations (slope fields and Euler methods), advanced applications of vectors. To check, look at the AHL designation in the official subject guide.
What computers can be used for AI?
A graphics computer is generally required and must not have CAS capabilities. Common approved models include TI-84 Plus CE series, TI-Nspire CX II (Non-CAS version) with the Casio fx-CG50 series. CAS and non-CAS versions of the same series have different regulations. You must confirm the current regulations with the school before purchasing.
How many digits should be kept in the answer?
Unless otherwise specified in the title, three significant figures are generally required. Intermediate values should retain full precision (using the computer's memory function) and should be rounded only in the final answer.
Is there no need to write down the steps if I have a computer?
To write. Grading is based on method. You may lose most of your points by just writing answers. The methods or models used, the substituted values and results should be written down; statistical questions must state the tests or distributions used and their parameters.
Where do AI students lose marks most easily in their IA?
Mathematical depth in Criterion E. A common situation is that a large amount of data is collected and beautiful charts are made, but the mathematics only stops at the average and a linear regression - which is already shallow for SL and even more obviously insufficient for HL. See you in the direction of improvement Section 7.
Is there a big difference between AI HL and SL?
Quite big. The difference in teaching hours is 90 hours, and HL has content such as graph theory, Markov chains, matrices, complex numbers, etc. that SL does not have at all, plus Paper 3, which accounts for 20%. If your maths ability is average, SL is a safer choice.
What are the requirements for AI in universities?
Varies by university, department and year. Business and social sciences majors are more likely to accept AI, while engineering, physics and mathematics majors are more likely to require AA HL; however, you must directly check the requirements published by the target department in that year - we do not list a comparison table because outdated information will affect the subject selection decision.