- The core difference between AA and AI: computer rules
- Assessment structure for HL and SL
- Five subject areas and HL additional content
- Internal Assessment (IA): five scoring criteria
- IA Topic Selection: The Most Common Reasons for Losing Points
- Paper 1 Computer-Free Answering Strategies
- Paper 3 (HL Proprietary)
- Basis for judging subject selection
- Course schedule and fees
1. The core difference between AA and AI: 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. The old Mathematics HL/SL and Mathematical Studies will be reorganized into two subjects:Mathematics: Analysis and Approaches (AA) and Mathematics: Applications and Interpretation (AI), each subject has HL and SL.
The most critical difference is the computer rule: AA's Paper 1 is not allowed to use computers, while all AI papers can use graphics computers (GDC).
This one deserves more attention than the difference in course content, because it determines which ability you need: AA requirements Algebra and Calculus fluency purely by hand;AI requirements GDC function proficiency and model selection judgment. The two can be independent of each other—students who are fast at hand calculation may not be good at judging which statistical model to use, and vice versa.
| Compare items | AA (Analysis and Approaches) | AI (Applications and Interpretation) |
|---|---|---|
| Paper 1 Computer | Not allowed to use | GDC available |
| Paper 2 Computer | GDC available | GDC available |
| core orientation | Analytical skills in algebraic deduction, functions and calculus; emphasis on rigor in argumentation | Statistics, modelling and technology application; emphasis on interpretation and application of results |
| main difficulty | Pure hand calculation fluency and complete demonstration of proof questions | Regression analysis, model selection, GDC functional proficiency |
| Common study directions | Engineering, Physics, Mathematics, Actuarial Science, Quantitative Economics | Design, Social Sciences, Business Analysis, Psychology |
| Details | this page | IB Mathematics AI page |
The names of the five subject areas of the two subjects are the same, but the depth and focus are different. AA goes deeper in Functions and Calculus, and AI goes deeper in Statistics and Probability. This is why transferring subjects (such as SL AI to SL AA) is usually not just a matter of "filling in a little bit" - it requires the system to make up for the foundation of Algebra and Calculus.
- IB Math AI
- 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 (without computer) | 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%, that is, the part without a computer is equally important as the part with a computer. You can't just practice one form.
- HL students: three papers plus IA, of which Paper 3 accounts for 20% and has only two questions - this means that the weight of a single question is extremely high, and a missed question will have a great impact.
- IA 20% for both- Same as HL's single test paper. This is the only part that you have enough time to revise over and over again, so the returns are the most stable.
3. Five subject areas and HL additional content
AA's curriculum is divided into five subject areas. HL and SL share the same area names, but HL has additional in-depth content in each area.
| category | Common core content of SL and HL |
|---|---|
| Number and Algebra (Numbers and Algebra) |
Sequences and series (arithmetical differences, geometric proportions), exponents and logarithms, binomial expansions, basic forms of proofs |
| Functions (function) |
The concept and representation of functions, function images and transformations, quadratic functions, basic situations of rational functions, logarithms and exponential functions |
| Geometry and Trigonometry (Geometry and Trigonometry) |
Solid geometry, trigonometric ratios and radians, trigonometric identities, trigonometric equations, sine and cosine formulas |
| Statistics and Probability (Statistics and Probability) |
Description and presentation of data, basic concepts of probability, discrete and continuous random variables, binomial distribution, normal distribution |
| Calculus (Calculus) |
Concepts of limits and derivatives, derivation rules, tangents and normals, extreme values and optimization, integrals and definite integrals, area calculations |
Extras for HL (not covered by SL)
| category | HL Extras |
|---|---|
| Number and Algebra | plural (Including polar form and Euler form, operations and geometric meaning of complex numbers),mathematical induction, partial fractions, wider binomial expansions (including fractions and negative exponents), proof by contradiction and counterexamples |
| Functions | Advanced situations of rational functions, odd and even functions, advanced processing of synthesis of functions and inverse functions, relationship between factors and roots of polynomials, graphical illustration and algebraic processing of inequalities |
| Geometry and Trigonometry | vector (Representation of vector, scalar product,vector product, equations of straight lines and planes, intersection angles and distances between planes and straight lines), advanced applications of complex angle and multiple angle formulas, inverse trigonometric functions |
| Statistics and Probability | Bayes theorem, Advanced processing of discrete and continuous random variables (including calculation of expected value and variance), variable transformation |
| Calculus | Extreme advanced processing and continuity,Implicit function derivation, related variability,differential equations (Including variable separation, Euler method),Maclaurin series, advanced points skills (substitution, division),Volume of rotation, the basic situation of abnormal integrals |
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 skill requires proof, whether a certain distribution requires hand calculation) 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. Internal Assessment (IA): five scoring criteria
Internal assessment Mathematical Exploration accounts for the final grade 20%, general recommendations for length 12 to 20 pages. It is scored out of 20 on five criteria.
| 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 |
Criterion A: Presentation
4 points Scoring logicGradually upgrade from "somewhat coherent or organized" to "coherent, well organized and streamline". The highest level requires simplicity - which is often misunderstood.
Common misunderstandingsI think writing long means being serious. In fact, points will be deducted for verbosity: irrelevant presentation, repeated calculations, and paragraphs irrelevant to the purpose of the inquiry will weaken this aspect. There should be a clear logical progression from research objectives to conclusions.
Criterion B: Mathematical Communication
4 points Scoring logicFrom "Partially Appropriate" to "Relevant, Appropriate and Consistent throughout". The key word is consistency.
Specific requirements- All variables must be defined before use.
- Symbols and terminology are correct and consistent (do not use them in the preceding paragraph
x, for later usetrepresent the same quantity). - Charts have titles and axis labels.
- Express reasoning in mathematical language rather than verbal language.
Criterion C: Personal Engagement
3 points Scoring logicGradually upgrade from "There is some evidence of personal investment" to "There is Outstanding evidence of personal investment”.
most common mistakesThink of it as "write a reflection." In fact, the review is What did you actually do in the inquiry?, rather than what you said about your feelings - such as collecting data by yourself, designing verification methods by yourself, trying another processing besides standard methods, and coming up with your own explanations for unexpected results.
Correct approachPersonal input should be visible throughout the inquiry Choice and Judgment, rather than the beginning or end of a paragraph.
Criterion D: Reflection
3 points Scoring logicGradually upgrade from "limited reflective evidence" to critical reflection.
The easiest thing to lose pointsIn our observation, this one, along with Criterion C, is the most underrated. Students write general sentences such as “My results could be more accurate” or “Time is limited”—these will not be scored because they apply to any inquiry.
High score requirement- specific: Indicate which assumption affects the results and the direction of the effect (overestimation or underestimation).
- Mathematics itself: The evaluation is about the critical judgment of mathematics, not the reflection on the process of doing homework.
- There is an extension: Suggest what would happen if another method was used, or what new questions this result raises.
Criterion E: Use of Mathematics
6 points (highest score) four requirementsMathematics required Related, commensurate with course level, correct,and demonstrate understanding.
Special attention for HL students"Appropriate to course level" is a real restriction for HL students: if the entire IA only uses SL level methods, even if it is done perfectly, the score for this item will be limited. HL students should use HL techniques—such as differential equations, Maclaurin series, advanced applications of complex numbers, or vectors.
"demonstrate understanding" meansIt is not just about applying the formula to get a number, but it is about explaining why this method is suitable for this situation and whether its conditions are met. This is relevant to us Paper 1 Answering Tips The reasoning writing emphasized in is the same ability.
The specific level description of the guidelines should be based on official documents. This section explains the allocation and scoring logic of each criterion; the complete description (Descriptor) of each level is clearly stated in the IA guide or official subject guide provided by the school, and should be compared item by item when writing.
5. IA Topic Selection: The Most Common Reasons for Losing Points
The most common point loss for IA is not doing maths wrongly, but choosing the wrong questions. The problem of topic selection cannot be fixed later - once you invest two months on an unsuitable topic, you can only try to make up for it in the limited space.
| Topic selection question | Symptoms | Affected Guidelines |
|---|---|---|
| The question is too big | It can't be finished, and in the end it can only be described without being able to go into depth. | Criterion E (insufficient mathematical depth), Criterion A (loose structure) |
| The question is too detailed | Only use the most basic tools in the course | Criterion E (not commensurate with the course level, especially HL) |
| Data cannot be obtained | The idea was great, but reliable data could not be obtained, so I was forced to change the question midway. | All criteria (time is wasted) |
| Copy common online questions | There is no trace of personal judgment in the inquiry process | Criterion C (Personal Engagement) |
Four checks in the topic selection stage
- I can tell in one sentence what question this inquiry is going to answer.
- I am sure I can use mathematical methods appropriate to my course level (HL students: can use HL skills)
- I have confirmed that the required data or information is available
- I have a specific personal perspective on this topic rather than just following a ready-made topic
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 online questions will directly affect Criterion C:
- Use calculus to analyze change processes: Any phenomenon that changes over time and can be modeled. HL students can work with differential equations.
- Use statistical methods to analyze self-collected data: The key is "self-collection" - this also supports Criterion C.
- Use vectors or triangles to solve spatial problems: Suitable for HL students using vector products and plane equations.
- Explore the properties of a mathematical structure: For example, the convergence behavior of a sequence and the transformation rules of certain types of functions. HL students can use mathematical induction or series expansion.
- Compare the performance of two mathematical methods on the same problem: This structure naturally supports Criterion D’s reflections.
time schedule
- Diploma first year second semester: Topic selection and preliminary exploration. At this time, the two risks of "unavailable data" and "insufficient mathematical depth" should be verified first.
- first year summer vacation: Complete the main mathematical processing.
- First semester of second year: Complete the first draft and self-evaluate each item according to the five criteria.
- before submission: Specially deals with Criterion B (symbolic consistency) and Criterion A (simplification) - these two items can be improved by modification.
On the boundaries of mentoring: The IA must be the student's own work. Teachers and tutors can give opinions on the direction of the topic, the appropriateness of mathematical methods and the structure of the writing, but they are not allowed to write or provide answers. Our IA guidance is based on the principle of assisting students to complete it on their own, and meets the academic integrity requirements of the IB - this is also important for the students themselves, because the IA needs to be submitted and may be randomly checked.
6. Paper 1 Answering Strategy Without Computer
This is the part where AA students need the most specialized training, and it is also the biggest gap for students transferring to AA from AI or other courses.
Content that must be immediately available
- Exact values of trigonometric functions for common angles: Since there were no computers, these had to be written directly (and familiarity with radians notation required).
- Basic logarithmic and exponential relationships: Including base changing, logarithmic law, and
erelationship to the natural logarithm. - Basic derivation and integration results: Standard results for polynomial, exponential, logarithmic, and trigonometric functions.
- Commonly used algebraic identities: Difference of squares, perfect squares, sum of cubes, trigonometric identities.
Three key habits
| Habit | practice | Why it matters |
|---|---|---|
| Preserve exact form | Answers should be expressed in radicals, fractions, or in the form of π, without converting to decimals. | Paper 1 usually requires precise values; converting to decimals will result in loss of points, and the calculation is not accurate without a computer. |
| Simplify first and then substitute | Simplify the algebra to its simplest form before substituting the numerical values | Every extra step when calculating by hand is an opportunity for error; simplification can greatly reduce the amount of calculations. |
| Write down the steps | Each step is in an independent line. Use the formula to write the formula first. | Points are given according to the method - the probability of making mistakes in hand calculations is higher, so points for steps are insurance. |
training method
- Put away the computer and work on the entire Paper 1. Hand calculation fluency can only be established through actual hand calculations - using a computer to do Paper 1 questions is equivalent to not practicing.
- pure speed exercise: Find 20 simplified questions that you already know how to do and complete them within a time limit. This trains operation speed rather than problem-solving ability.
- Checking habits: Substitute the answer back into the original form. This is the only way to check without a computer.
GDC training for Paper 2 cannot be omitted
Paper 2 is also 40% for SL (30% for HL) and it is available at GDC. So another set of training is needed: equation solving, graphs of functions and intersections, statistical functions, numerical integration. The two test papers require different abilities, you can’t just practice one form.
7. 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 is the most underestimated part. It counts for 20% - the same as IA - but has very few questions (usually two), meaning 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.
Therefore, it cannot be solved by memorizing question types, nor can it be solved quickly by practicing before the exam - what is needed is long-term accumulation of problem-solving strategies.
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 on how to deal with "when you can't see the direction": Reverse possible paths based on known conditions 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.
- Complete all previous Paper 3: The style of this paper is obviously different from Paper 1 and 2 and must be practiced separately.
8. Basis for judging subject selection
"You should choose AA or AI" should not just look at the direction of further studies, because the two subjects require different abilities.
| Ability characteristics | How to observe | point to |
|---|---|---|
| Pure hand calculation fluency | What is the 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 |
| Situational judgment and model selection | Faced with a set of data, can you determine which analysis method to use? | strong → AI |
| Use of technological tools | Are you good at using GDC or software to process data and images? | strong → AI |
Regarding university requirements: The requirements for IB Mathematics in different universities and departments are not consistent and will be adjusted annually - generally speaking, engineering, physics, mathematics and other directions have more requirements or preference for AA HL, but specific subjects 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.
Transferring to AA from other courses
- Upgrading from MYP or local courses to AA: The most common gap is insufficient fluency in algebraic operations. The Pre-IB stage is the best time for reinforcement - the algebra skills gained at this time will continue to pay off in the next two years.
- From AI to AA: The system needs to replenish the basics of Algebra and Calculus and re-establish the habit of not relying on computers. This is usually not something that can be dealt with by "making up for it".
- From DSE to AA: The differences are in three aspects - IA and AA Paper 1, which accounts for 20% of the IB, are not allowed to use computers, and the answering language and format are different. Range comparison see DSE course page.
9. Course Arrangements and Fees
IB students have very different subject and level mixes - the same class may have AA HL, AA SL and AI 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: AA HL and AA SL have different teaching focuses and will not be treated with the same set of content.
- Paper 1 Special training without computer: This is the part that AA students need the most but the least systematic training for.
- GDC operational training: Functions and judgments required for Paper 2 and Paper 3.
- IA Five Principles Guidance: From topic selection evaluation, mathematical in-depth examination, research method suggestions to text modification; 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.
- cross-institutional comparison: The tutor has mastered DSE, IB and IAL at the same time and can list the differences in scope and the order of make-up lessons for transfer students.
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
- International school students taking IB Mathematics AA HL or SL
- Students who need to strengthen their algebra foundation at the Pre-IB or MYP stage
- Students who need guidance on IA topic selection and writing
- Paper 1 Students who lost more points in the non-computer section
- HL students need Paper 3 specialized training
- Students who transfer from AI, DSE or other courses to AA 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 AA FAQ
What is the most critical difference between AA and AI?
Computer rules:Computer use is not allowed in Paper 1 of AA, all AI test papers are available at GDC. This is more likely to determine your suitability for AA than differences in course content.
How big are HL and SL?
Recommended teaching hours are 150 hours for SL and 240 hours for HL. SL is Paper 1 (40%), Paper 2 (40%), IA (20%); HL is Paper 1 (30%), Paper 2 (30%), Paper 3 (20%), IA (20%). HL has additional content in five areas, such as complex numbers, mathematical induction, vector progression, differential equations, and Maclaurin series.
What are the scoring criteria and points assigned for IA?
Five criteria worth 20 points in total: Presentation 4, Mathematical Communication 4, Personal Engagement 3, Reflection 3, and Use of Mathematics 6. IA accounts for 20% of the final grade and is generally 12 to 20 pages in length.
What is the area where IA is most likely to lose points?
Reflection and Personal Engagement. General sentences such as "the results can be more accurate" will not be scored for reflection; high scores require specific identification of which hypothesis affects the results and the direction of the influence. Personal Engagement is not a final thought, but a personal choice and judgment that can be seen in the entire exploration.
Are there any special requirements for IA for HL students?
Criterion E requires mathematics to be "appropriate to the level of the course." If the entire IA only uses SL level methods, even if it is done perfectly, the score for this item will be limited - HL students apply HL skills.
Paper 1 How to prepare without a computer?
Three things: memorize the exact values of commonly used angle-trigonometric functions and the relationship between basic logarithmic exponents; train to retain the exact forms (radicals, fractions, including π) instead of converting to decimals; and actually put away the computer and do the entire Paper 1 during daily practice.
How to prepare for Paper 3?
It accounts for 20% but has very few questions. It tests the ability to use learned tools in unfamiliar situations. The key point is that the questions in the first section must be checked (the latter section relies on it), training in inferring paths from known conditions, and practicing the previous Paper 3 alone - its style is obviously different from the other two papers.
When should IA begin?
Topic selection and preliminary exploration in the second semester of the first year (data availability and mathematical depth are first verified at this time), the main mathematical processing is completed during the summer, and the first draft is completed in the first semester of the second year and self-evaluated according to the five criteria.
Can AA HL self-study?
The content can be self-study, but two things are more difficult to handle on your own: IA requires someone to give opinions based on the five criteria (especially the level judgment of Criterion D and E), and the hand calculation habit of Paper 1 requires someone to supervise and not use a computer.
What are the college requirements for IB Mathematics?
Varies by university, department and year. The Engineering Physics and Mathematics direction has more requirements or preference for AA HL, but for specific requirements, you must directly check the information published by the target department in that year - we do not list a comparison table, because outdated information will affect the subject selection decision.