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IB Math AA SL syllabus, topic map, and lessons
Build IB Math AA SL skills across number and algebra, functions, geometry and trigonometry, statistics and probability, and calculus. Students often call the first year “IB1,” but schools divide this two-year syllabus differently.
Course overview
IB Math AA SL syllabus at a glance
This independent guide covers Mathematics: Analysis and Approaches SL (IB AA SL). Its 5 course sections lead to the complete topic map below; open a written lesson where one has been published. Read the official IB subject guide for exact requirements.
این راهنمای مستقل دربارهٔ ریاضی: تحلیل و رویکردها سطح استاندارد (IB AA SL) است. از بخش‌های زیر برای پیدا کردن موضوع مورد نظر و درس‌های منتشرشده استفاده کنید. راهنمای رسمی درس آی‌بی
Course pathway: Diploma Programme Standard Level
مسیر تحصیلی: برنامهٔ دیپلم، سطح استاندارد
- 1 · Number and Algebra (عدد و جبر)
- 2 · Functions (توابع)
- 3 · Geometry and Trigonometry (هندسه و مثلثات)
- 4 · Statistics and Probability (آمار و احتمال)
- 5 · Calculus (حسابان)
Course questions
Studying IB AA SL: topics, lessons, and official requirements
The course map includes Number and Algebra, Functions, Geometry and Trigonometry, and 2 other sections. Follow the complete section list above for the full study path.
درس ریاضی: تحلیل و رویکردها سطح استاندارد (IB AA SL) چه مباحثی دارد؟ از جمله مباحث این درس عدد و جبر، توابع، هندسه و مثلثات است. فهرست کامل بخش‌ها در بالای صفحه قرار دارد.
45 of 45 written lessons are currently published and free to read. Open a linked lesson in the section map above. Check the official IB subject guide for exact requirements.
درس‌ها و راهنمای رسمی ریاضی: تحلیل و رویکردها سطح استاندارد را از کجا پیدا کنم؟ اکنون 45 درس از 45 درس نوشتاری منتشر شده و خواندن آن‌ها رایگان است. درس‌های دارای پیوند را در نقشهٔ بخش‌های بالا باز کنید. برای شرایط دقیق به راهنمای رسمی درس آی‌بی مراجعه کنید.
Publication status
45 of 45 written lessons published
The topic map covers the course expectations. A topic marked “written lesson not published” remains available for practice and tutoring, but does not have a reviewed written lecture yet.
IB1 naming note
One AA SL syllabus, different school sequences
IB1 AA SL usually means a student is in the first year of Mathematics: Analysis and Approaches at Standard Level. IB publishes one complete AA SL syllabus rather than a universal Year 1/Year 2 split, so your teacher may cover these topics in a different order. Use the codes in this map to find the topic currently taught at your school.
AA SL study path
Five compulsory areas of mathematics
Sequences, financial models, exponents, logarithms, proof, and binomial expansion.
Representations, transformations, quadratics, rational functions, exponentials, and logarithms.
Triangle rules, radians, identities, graphs, equations, and 3D applications.
Sampling, data summaries, regression, probability, random variables, binomial, and normal models.
Limits, derivatives, optimization, integration, accumulated change, and motion.
Review an Ontario functions pathway · Explore introductory statistics · Browse all courses
Free published lessons
Start learning IB AA SL
These lessons are public, free to read, and connected to the full course map below.
Measurements and calculations often produce numbers that are inconvenient to write in full. A distance may be many millions of…
Straight lines model relationships with a constant rate of change. For example, if a taxi fare has a fixed starting charge and then…
This lesson brings together several ways to describe shape and size. A distance is a length, a midpoint marks the halfway position…
Before interpreting a set of data, ask how it was collected. The people or objects of interest form the population; the smaller group…
A graph can show how one quantity changes as another changes. Between two points, its gradient describes an average change. At a…
An arithmetic sequence describes quantities that change by the same amount each time. This can model situations such as a regular…
A function is a rule that assigns exactly one output to each allowed input. Before working with a function, ask which inputs are…
Triangles can be described by their side lengths, their angles, or both. The useful method depends on which information is known.…
IB AA SL
Topics by strand
Develop numerical fluency, sequences, financial models, logarithms, proof, and binomial expansion.
- SL 1.1 · Use scientific notation, significant figures, and approximation (published written lesson)
- SL 1.2 · Model arithmetic sequences and series (published written lesson)
- SL 1.3 · Model geometric sequences and series (published written lesson)
- SL 1.4 · Apply geometric models to compound interest and depreciation (published written lesson)
- SL 1.5 · Apply exponent and logarithm laws (published written lesson)
- SL 1.6 · Use simple deductive proof and disprove statements with counterexamples (published written lesson)
- SL 1.7 · Expand binomials using the binomial theorem (published written lesson)
Represent, analyse, transform, combine, and solve with linear, quadratic, rational, exponential, and logarithmic functions.
- SL 2.1 · Use equations and features of straight lines (published written lesson)
- SL 2.2 · Use function notation, domain, range, and inverse ideas (published written lesson)
- SL 2.3 · Sketch and interpret graphs from mathematical information (published written lesson)
- SL 2.4 · Find key graph features and intersections with technology (published written lesson)
- SL 2.5 · Work with composite and inverse functions (published written lesson)
- SL 2.6 · Connect standard, factored, and vertex forms of a quadratic (published written lesson)
- SL 2.7 · Solve quadratic equations and inequalities and interpret the discriminant (published written lesson)
- SL 2.8 · Analyse reciprocal and linear-over-linear rational functions (published written lesson)
- SL 2.9 · Connect exponential and logarithmic functions as inverses (published written lesson)
- SL 2.10 · Solve exponential equations using logarithms (published written lesson)
- SL 2.11 · Transform graphs by translations, reflections, and stretches (published written lesson)
Solve two- and three-dimensional problems with measurement, trigonometric rules, radians, identities, graphs, and equations.
- SL 3.1 · Solve distance, midpoint, surface-area, volume, and angle problems (published written lesson)
- SL 3.2 · Apply right-triangle trigonometry, sine rule, cosine rule, and triangle area (published written lesson)
- SL 3.3 · Solve contextual two- and three-dimensional trigonometry problems (published written lesson)
- SL 3.4 · Use radians, arc length, and sector area (published written lesson)
- SL 3.5 · Use the unit circle and exact trigonometric values (published written lesson)
- SL 3.6 · Apply fundamental and double-angle trigonometric identities (published written lesson)
- SL 3.7 · Analyse and transform sine, cosine, and tangent graphs (published written lesson)
- SL 3.8 · Solve trigonometric equations on a specified interval (published written lesson)
Collect, display, summarize, model, and interpret data and chance while checking assumptions and limitations.
- SL 4.1 · Distinguish populations, samples, variables, sampling methods, and bias (published written lesson)
- SL 4.2 · Organize and display discrete and continuous data (published written lesson)
- SL 4.3 · Calculate and interpret measures of centre, position, and dispersion (published written lesson)
- SL 4.4 · Analyse correlation and linear regression with appropriate caution (published written lesson)
- SL 4.5 · Use sample spaces, events, complements, and expected frequencies (published written lesson)
- SL 4.6 · Solve combined and conditional probability problems (published written lesson)
- SL 4.7 · Use discrete random-variable distributions and expected value (published written lesson)
- SL 4.8 · Model repeated independent trials with the binomial distribution (published written lesson)
- SL 4.9 · Solve and interpret normal-distribution problems (published written lesson)
Use limits, derivatives, and integrals to analyse change, optimize quantities, find areas, and model motion.
- SL 5.1 · Interpret limits and derivatives as gradients and rates of change (published written lesson)
- SL 5.2 · Connect derivative functions to increasing and decreasing behaviour (published written lesson)
- SL 5.3 · Differentiate powers, trigonometric, exponential, and logarithmic functions (published written lesson)
- SL 5.4 · Apply chain, product, and quotient rules (published written lesson)
- SL 5.5 · Use second derivatives and interpret concavity (published written lesson)
- SL 5.6 · Find and classify stationary points (published written lesson)
- SL 5.7 · Solve contextual optimization problems (published written lesson)
- SL 5.8 · Find antiderivatives and apply initial conditions (published written lesson)
- SL 5.9 · Use definite integrals and numerical methods to find accumulated change and area (published written lesson)
- SL 5.10 · Model displacement, velocity, and acceleration with calculus (published written lesson)
Worked examples
Start with worked IB AA SL examples
These original examples introduce selected IB AA SL topics. The full topic map is not a complete set of published written lessons or a substitute for official course materials and assignments. The topic titles below are concise study-guide paraphrases of the source syllabus sections.
A balance of CAD 2,000 earns 4% annually. Find its value after 5 years.
Worked method: Use a geometric growth factor: 2000(1.04)^5 ≈ 2433.31. The model assumes the same annual rate and no deposits or withdrawals.
فارسی · توضیح مثال
موجودی ۲۰۰۰ دلار کانادا سالانه ۴٪ سود می‌گیرد. ارزش آن را پس از ۵ سال بیابید. از ضریب رشد هندسی استفاده می‌کنیم: 2000(1.04)^5 ≈ 2433.31. مدل نرخ سالانه ثابت و نبود واریز یا برداشت را فرض می‌کند.
Describe the graph of y = 2(x − 3)^2 + 1 from y = x^2.
Worked method: Translate 3 units right, stretch vertically by factor 2, then translate 1 unit up. The vertex is (3, 1) and the axis is x = 3.
فارسی · توضیح مثال
نمودار y = 2(x − 3)^2 + 1 را نسبت به y = x^2 توصیف کنید. ۳ واحد به راست انتقال دهید، کشیدگی عمودی با ضریب ۲ انجام دهید و سپس ۱ واحد بالا بروید. رأس (3, 1) و محور x = 3 است.
For s(t) = t^3 − 6t^2 + 9t, find the instantaneous velocity at t = 2.
Worked method: Differentiate: v(t) = 3t^2 − 12t + 9. Then v(2) = 12 − 24 + 9 = −3, so the velocity is −3 distance units per time unit.
فارسی · توضیح مثال
برای s(t) = t^3 − 6t^2 + 9t سرعت لحظه‌ای را در t = 2 بیابید. مشتق می‌گیریم: v(t) = 3t^2 − 12t + 9. سپس v(2) = 12 − 24 + 9 = −3، پس سرعت برابر منفی ۳ واحد فاصله بر واحد زمان است.
Try independently, then check
Write your own solution before opening each answer. If a step is unclear, review the matching topic or the stated course prerequisites.
Solve 3^(2x − 1) = 20 and give x to three significant figures.
Show worked answer
Take logarithms: (2x − 1)ln 3 = ln 20, so x = (1 + ln 20/ln 3)/2 ≈ 1.86.
فارسی · تمرین و پاسخ
معادله 3^(2x − 1) = 20 را حل کنید و x را با سه رقم معنادار بنویسید. لگاریتم می‌گیریم: (2x − 1)ln 3 = ln 20، پس x = (1 + ln 20/ln 3)/2 ≈ 1.86.
A normal variable has mean 50 and standard deviation 8. Find the z-score of 62.
Show worked answer
z = (62 − 50)/8 = 1.5, so 62 is 1.5 standard deviations above the mean.
فارسی · تمرین و پاسخ
متغیر نرمالی میانگین ۵۰ و انحراف معیار ۸ دارد. نمره z برای ۶۲ را بیابید. z = (62 − 50)/8 = 1.5، پس ۶۲ به‌اندازه ۱٫۵ انحراف معیار بالاتر از میانگین است.
Mathematical processes across topics
These processes are practised throughout the course, rather than listed as separate lessons.
- Connect symbolic, graphical, numerical, and contextual representations. (نمایش‌های نمادی، نموداری، عددی و کاربردی را به هم مرتبط کنید.)
- State assumptions, domains, units, and the meaning of parameters. (فرض‌ها، دامنه‌ها، واحدها و معنای پارامترها را بیان کنید.)
- Choose technology purposefully and show enough reasoning to make the method clear. (فناوری را هدفمند انتخاب کنید و استدلال کافی برای روشن شدن روش نشان دهید.)
- Use exact values when appropriate and round only after adequate intermediate precision. (در جای مناسب از مقدار دقیق استفاده کنید و پس از حفظ دقت میانی کافی گرد کنید.)
- Check results algebraically, graphically, numerically, and in context when possible. (در صورت امکان نتیجه را جبری، نموداری، عددی و در بافت مسئله بررسی کنید.)
- Communicate a coherent argument rather than listing calculator outputs. (به‌جای فهرست کردن خروجی ماشین‌حساب، استدلالی منسجم ارائه کنید.)
Source and coverage
Prerequisite: Strong secondary-school algebra, geometry, and introductory trigonometry; confirm your school’s placement requirements. Confirm your current school timetable and admission requirements.
The topic map follows the official International Baccalaureate (IB) course guide. Titles are concise study-guide paraphrases; consult the official source for exact requirements. Browse all courses.
Sources and editorial process
Curriculum-aligned and reviewed before publication
This independent study guide follows the official course source. It is not an official government, school, or university publication.
Lessons may be AI-assisted or editorially prepared. Published content is checked for structure, notation, calculations, course boundaries, and readability before release. Because corrections can still be necessary, readers can report a problem.
Related courses and next steps
Review a prerequisite or explore a related course. Follow your school or university requirements when choosing your next course.
پیش‌نیازها و درس‌های مرتبط را مرور کنید و برای انتخاب درس بعدی، مقررات مدرسه یا دانشگاه را بررسی کنید.
- Math 30-3 · Mathematics 30-3 (Alberta) ریاضی ۳۰-۳ آلبرتا
- Math 20-1 · Mathematics 20-1 (Alberta) ریاضی ۲۰-۱ آلبرتا
- Math 20-2 · Mathematics 20-2 (Alberta) ریاضی ۲۰-۲ آلبرتا
- Math 20-3 · Mathematics 20-3 (Alberta) ریاضی ۲۰-۳ آلبرتا
Get help while studying IB AA SL
Use the IB AA SL lessons and topic map first, then try a question on your own. For example, bring an attempt from Number and Algebra and Functions and mark the first step you cannot explain. A live tutor can help you show each step of your attempt and compare it with a worked example; ask them to confirm they can support your particular course before booking a regular session.
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ابتدا درس‌ها و فهرست مباحث IB AA SL را بخوانید و یک سؤال را خودتان حل کنید. نخستین گام مبهم را مشخص کنید تا در جلسه بتوانید گام‌های تلاش خود را نشان دهید و آن را با یک نمونهٔ حل‌شده مقایسه کنید. راهنمای معلم ریاضی را ببینید یا جلسهٔ معارفهٔ رایگان ۳۰ دقیقه‌ای درخواست کنید. دربارهٔ امکان تدریس همین درس از معلم تأیید بگیرید.