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IB Mathematics: Analysis and Approaches SL lessons and topic map
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.
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.
- SL 1.1 · Use scientific notation, significant figures, and approximation
- SL 1.2 · Model arithmetic sequences and series
- SL 1.3 · Model geometric sequences and series
- SL 1.4 · Apply geometric models to compound interest and depreciation
- SL 1.5 · Apply exponent and logarithm laws
- SL 1.6 · Use simple deductive proof and disprove statements with counterexamples
- SL 1.7 · Expand binomials using the binomial theorem
- SL 2.1 · Use equations and features of straight lines
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.
Lesson drafts are AI-assisted, checked for structure, notation, calculations, course boundaries, and readability, and made public only after administrator approval. Because corrections can still be necessary, readers can report a problem.