--- title: "Best IB Math: Analysis & Approaches Study Guide and Notes for SL, HL" description: How do you study for IB Math SL/HL? Read our set of IB Math notes and our free study guide for the best resources available. image: https://360031.fs1.hubspotusercontent-na1.net/hubfs/360031/body_math-805.jpg --- **[![PrepScholar](https://www.prepscholar.com/wp-content/uploads/2023/03/PrepScholar-Logo-Colored.png)](https://www.prepscholar.com/)** CALL NOW: [+1 (866) 811-5546](tel:18668115546) [![Start Free Trial](https://no-cache.hubspot.com/cta/default/360031/interactive-171805697634.png)](https://cta-service-cms2.hubspot.com/web-interactives/public/v1/track/redirect?encryptedPayload=AVxigLKJluK2NyG3jpAJh%2F2lClc1fhnVHyMZoQonqRxtJngB8FMX6lc78F84JqOaVAL0d36TA5%2FYuH%2FLCJw8AG3ewREi%2F7a3XDouZgjxWfYCBUge6z76KnSykOxONl3avMK0gUjJGpJdyJE2BDTx8g3bsgHwMtx4Kr9Jfh6Jr7WA2XEIgtLw1OoVvAMo4Kw%3D&webInteractiveContentId=171805697634&portalId=360031) ## Choose Your Test SAT Prep ACT Prep [PrepScholar Advice Blog](https://blog.prepscholar.com/) ☰ - Search Blogs By Category - [SAT](https://blog.prepscholar.com/topic/sat) - [ACT](https://blog.prepscholar.com/topic/act) - [College Admissions](https://blog.prepscholar.com/topic/college-admissions) - [AP and IB Exams](https://blog.prepscholar.com/topic/advanced-placement-ap) - [PSAT](https://blog.prepscholar.com/topic/psat-info-and-strategies) - [TOEFL](https://blog.prepscholar.com/topic/toefl) - [GPA and Coursework](https://blog.prepscholar.com/topic/coursework-gpa) # [The Best IB Math: Analysis & Approaches Study Guide and Notes for SL/HL](https://blog.prepscholar.com/the-best-ib-math-study-guide-and-notes-sl-hl) ![author image](http://cdn2.hubspot.net/hubfs/360031/author_lauren.png) Posted by [Dora Seigel](https://blog.prepscholar.com/author/dora-seigel) | Updated on August 19, 2024 [International Baccalaureate (IB)](https://blog.prepscholar.com/topic/international-baccalaureate-ib)   ![body_math-805](https://360031.fs1.hubspotusercontent-na1.net/hub/360031/hubfs/body_math-805.jpg?width=366&name=body_math-805.jpg) IB Mathematics: Analysis & Approaches Standard Level (SL) and IB Mathematics: Analysis & Approaches Higher Level (HL) (which are revised versions of the previous IB Math courses) are two of the toughest classes in the IB Diploma Programme curriculum, so it's no surprise if you need a little extra help in either class. **In this article, we've compiled the best free online materials for Analysis & Approaches SL/HL** so you can get all the IB Math notes you need in one place. For convenience, we ordered the resources following the [IB Math: Analysis & Approaches syllabus](https://www.ibo.org/contentassets/5895a05412144fe890312bad52b17044/subject-brief-dp-math-analysis-and-approaches-en.pdf).   ## How to Use This IB Math Analysis & Approaches Guide If you're in search of information on one topic, **use the ctrl + f function on your computer to search this guide for that specific topic**. For instance, if you want to read about Algebraic Sequences, use ctrl + f to bring up the search function. Type "Algebraic Sequences," and your computer will show you all the study materials for Algebraic Sequences listed in this article. We split the following material up into three categories: - **Broad Notes:** Longer (generally 3-10 pages) that provide an overview of most or all of the subjects covered in a topic - **Specific Subjects:** Shorter summaries of specific subjects within a topic - **Videos:** Demonstration videos of how to solve past paper problems related to the subject   ## Common Study Errors That IB Math Students Make The Analysis & Approaches courses cover a lot of material. With so much material, you can't afford to fall behind because you won't be able to catch up. You'll need to master the subjects during the school year in order to excel on the [IB Math SL/HL papers](https://blog.prepscholar.com/ib-math-past-papers-free-official). Common errors that IB Math students make include: - **Ignoring the material you don't understand:** If you didn't understand it from your teacher, then you need to look for outside help. This IB Math study guide is a great start, but you may need to supplement with outside tutoring, too. - **Only studying right before the exam:** As we said before, there are too many topics for both courses to master in only a few weeks (that's why these courses are spread out over a couple of years!). This is why it's so important that you master the subjects when you're learning them in class. If you're still struggling, this guide can help—but don't be afraid to get tutoring from a teacher or other expert.   ![body_calc-2](https://360031.fs1.hubspotusercontent-na1.net/hub/360031/hubfs/body_calc-2.jpg?width=479&name=body_calc-2.jpg)   ## IB Math: Analysis & Approaches Core Topics (150 Hours for SL, 240 Hours for HL) For IB Math: Analysis & Approaches SL and HL, all students study the topics listed below. Here's a complete set of IB Math notes you can use in your review.   ### Complete IB Math Topics Overview: Standard Level [This 167-page set of notes](https://www.dropbox.com/s/ez2ssg6fsfa2ps8/IBMathsStandardNotes.pdf?dl=0) includes every topic covered in the old version of the IB Math SL course. It hasn't been updated for the Analysis & Approaches courses, but the curricula for the new courses largely stayed the same, so this is still a good resource. This guide is definitely not something you want to read in one night, but it's great to reference as you review different IB Math topics. It's highly organized, so you can search the table of contents to find the exact topic you want to study. Another great set of review-worthy [notes for HL can be found here](https://ib-academy.nl/s/ib-academynl-Mathematics-AA-HL.pdf), and [another set of notes for SL here](https://ib-academy.nl/s/ib-academynl-Mathematics-AA-SL.pdf). There’s unfortunately not a lot of explanation in either, but these have been updated for the Analysis and Approaches course, and cover every topic in the new version. These documents are also quite long, so pace yourself as you do your review.   #### Topic 1: Numbers and Algebra (19 Hours SL, 39 Hours HL) - **Broad Notes** - [Topic 1: Algebra](https://docs.wixstatic.com/ugd/1a2afc_c703ad62bbb544218c328af041133e43.pdf) - **Specific Subjects** - [Arithmetic and geometric series](https://ibmathstuff.wikidot.com/series) - [Binomial theorem](https://ibmathstuff.wikidot.com/binomial-theorem) - [Sigma notation](https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-3/a/review-summation-notation) - [Law of exponents](https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8th-exponent-properties/a/exponent-properties-review) - [Law of logarithms](https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:change-of-base/a/logarithm-properties-review) - [Completing the square](https://ibmathstuff.wikidot.com/completing-the-square) -   - **Videos** - [Arithmetic Sequences and Series](https://www.youtube.com/watch?v=rmK89uPhYoY) - [Geometric Sequences and Series](https://www.youtube.com/watch?v=5jpsHZRYcQ0) - [Sigma Notation](https://www.youtube.com/watch?v=UrKh28F77HU) - [Exponents (Laws and Solving)](https://www.youtube.com/watch?v=o1AJSNGUGZA) - [Logarithms (Laws and Solving)](https://www.youtube.com/watch?v=qWWjCy9euPQ) - [Binomial Theorem](https://www.youtube.com/watch?v=SZw-5-_TY_A)   #### Topic 2: Functions (21 Hours SL, 32 Hours HL) - **Broad Notes** - [Topic 2: Functions and Equations](https://docs.wixstatic.com/ugd/1a2afc_88980aed735744e290abbdbcb5a337f3.pdf) - **Specific Subjects** - [Composite function](https://ibmathstuff.wikidot.com/composite-function) - [Concept and notation](https://ibmathstuff.wikidot.com/concept-and-notation) - [Exponentials and logarithms](https://ibmathstuff.wikidot.com/exponential-logarithms) - - [Factor theorem](https://ibmathstuff.wikidot.com/factor-theorem) - [Inverse function](https://ibmathstuff.wikidot.com/inverse-function) - [Linear functions](https://www.khanacademy.org/math/algebra-home/alg-linear-eq-func) - [Simultaneous equations](https://thirdspacelearning.com/gcse-maths/algebra/simultaneous-equations/) - [Key functions of graphs (GDC)](https://dl.uncw.edu/digilib/Mathematics/Algebra/mat111hb/functions/graphs/graphs.html) - [Quadratic functions](https://ibmathstuff.wikidot.com/quadratics-functions) - [Quadratic forms](https://ibmathstuff.wikidot.com/quadratic-forms) - - Functions - [Quadratic functions](https://dl.uncw.edu/digilib/Mathematics/Algebra/mat111hb/PandR/quadratic/quadratic.html#:~:text=A%20quadratic%20function%20is%20one,same%20basic%20%22U%22%20shape.) - [Reciprocal functions](https://www.storyofmathematics.com/reciprocal-function) - [Exponential functions](https://web.archive.org/web/20170909080425/https://kokminglee.125mb.com/math/exponential.html) - **Videos** - [Functions (Domain and Range, Composite, Inverse)](https://www.youtube.com/watch?v=btpaHKDcCK8) - [Functions (Transformations)](https://www.youtube.com/watch?v=5bX5gi51vaA) - [Factorizing Quadratics](https://www.youtube.com/watch?v=nKGOak3iF68) - [Completing the Square (Quadratics)](https://www.youtube.com/watch?v=yn4PE6evHJE) - [Discriminant Test (Quadratics)](https://www.youtube.com/watch?v=mPzSzPMJ45s) - [Rational Functions (Asymptotes and Sketching)](https://www.youtube.com/watch?v=fPCBuVtGYfc) - [Exponential and Logarithmic Functions](https://www.youtube.com/watch?v=NeRJ2PGpsJw) - [Sketching Functions With a Calculator](https://www.youtube.com/watch?v=YvizfF8YcYM)   ![body_trig](https://360031.fs1.hubspotusercontent-na1.net/hub/360031/hubfs/body_trig.png?width=184&name=body_trig.png)   #### Topic 3: Geometry and Trigonometry (25 Hours SL, 51 Hours HL) - **Broad Notes** - [Topic 3: Circular Functions and Trigonometry](https://docs.wixstatic.com/ugd/1a2afc_3465a9b1e1ca488080ddf76073b5b332.pdf) - **Specific Subjects** - [Equations of lines](https://aweidaibmath.weebly.com/uploads/3/7/4/4/37448805/3.2_equations_of_lines.pdf) - [Trig ratios](https://aweidaibmath.weebly.com/uploads/3/7/4/4/37448805/3.3_trig_ratios.pdf) - [Sine and cosine rules](https://aweidaibmath.weebly.com/uploads/3/7/4/4/37448805/3.4_sine_and_cosine_laws.pdf) - [Radian, arc, and degree](https://www.cuemath.com/trigonometry/what-is-a-radian/) - [Circular functions](https://www.cliffsnotes.com/study-guides/trigonometry/graphs-of-trigonometric-functions/circular-functions) - [Trigonomic functions](https://www.cuemath.com/trigonometry/trigonometric-functions/) - [Sine rule, cosine rule, and area](https://www.siyavula.com/read/maths/grade-11/trigonometry/06-trigonometry-05) - **Videos** - [Radians, Length of Arc, Area of Sector](https://www.youtube.com/watch?v=HQGiDt2qKvE) - [Unit Circle and Trig Ratios](https://www.youtube.com/watch?v=rtb50rGhmho) - [Trig Identities](https://www.youtube.com/watch?v=45MBgxnoh8g) - [Trig Graphs (Circular Functions)](https://www.youtube.com/watch?v=GzcxXM356zQ) - [Solving Trig Functions](https://www.youtube.com/watch?v=ZIjVfwu8L-4) - [Sine and Cosine Rule, Area of a Triangle](https://www.youtube.com/watch?v=zf1fbJEZ0zo) - [Degrees vs Radians](https://www.youtube.com/watch?v=PlrNb3l1GGc)   #### Topic 4: Statistics and Probability (27 Hours SL, 33 Hours HL) - **Broad Notes** - [Topic 5: Statistics and Probability](https://docs.wixstatic.com/ugd/1a2afc_cdca09ede9004fc9a64ebcb04ac0b0eb.pdf) - **Specific Subjects** - [Binomial distribution](https://ibmathstuff.wikidot.com/binomialdistribution) - [Probability rules](https://ibmathstuff.wikidot.com/probabilityrules) - Discrete data - [Grouped data](https://www.cuemath.com/data/mean-of-grouped-data/) - [Cumulative frequency curves](https://www.toppr.com/guides/maths/statistics/cumulative-frequency-curve/#:~:text=A%20curve%20that%20represents%20the,the%20data%20and%20derive%20results.) - [Linear regression](https://towardsdatascience.com/linear-regression-explained-1b36f97b7572) - [Representations of probability](https://ibmathstuff.wikidot.com/representationsprobability) - [Continuous variables](https://ibmathstuff.wikidot.com/continuousvariables) - [Discrete variables](https://ibmathstuff.wikidot.com/discretevariables) - [Standard deviation](https://ibmathstuff.wikidot.com/standarddeviation) - [Statistics representations](https://ibmathstuff.wikidot.com/statsrepresentations) - [Stats vocabulary](https://ibmathstuff.wikidot.com/statistics-vocabulary) - [Mutually exclusive and independent events](https://byjus.com/maths/difference-between-mutually-exclusive-and-independent-events/#:~:text=The%20difference%20between%20mutually%20exclusive,occurrence%20of%20the%20other%20event.) - [Using normal distributions](https://ibmathstuff.wikidot.com/usingnormaldistributions) -   -   -   - **Videos** - [Mean, Standard Deviation, and Variance](https://www.youtube.com/watch?v=_u_EHRt5STw) - [Bivariate Statistics](https://www.youtube.com/watch?v=kG8OQQTDv_k) - [Venn Diagrams and Probability](https://www.youtube.com/watch?v=Iu48YR9vr7I) - [Conditional Probability](https://www.youtube.com/watch?v=EwhS2lJxPxk) - [Probability Distribution](https://www.youtube.com/watch?v=BTFRqupQOII) - [Binomial Distribution](https://www.youtube.com/watch?v=i0OiWyeJefs) - [Normal Distribution](https://www.youtube.com/watch?v=0H_gP2zl91o)   ![body_calculus-2](https://360031.fs1.hubspotusercontent-na1.net/hub/360031/hubfs/body_calculus-2.jpg?width=522&name=body_calculus-2.jpg)   #### Topic 5: Calculus (28 Hours SL, 55 Hours HL) - **Broad Notes** - [Topic 6: Calculus](https://docs.wixstatic.com/ugd/1a2afc_9403764b069649f18b1d7cd6715116c7.pdf) - [Introduction to calculus](https://web.archive.org/web/20180218154202/https://kokminglee.125mb.com/math/calculus1.html) - **Specific Subjects** - [Derivatives by first principle](https://ibmathstuff.wikidot.com/firstprinciple) - [Intro to derivatives](https://ibmathstuff.wikidot.com/intro-to-derivatives) - [Derivatives of more complex functions](https://ibmathstuff.wikidot.com/derivatives-of-more-complex-functions) - [Derivatives part 1](https://ibmathstuff.wikidot.com/derivatives-part-1) - [Derivatives part 2](https://ibmathstuff.wikidot.com/derivatives-part-2) - [More on derivatives](https://www.khanacademy.org/math/differential-calculus/dc-diff-intro) - [Second derivatives](https://www.mathsisfun.com/calculus/second-derivative.html) - [Intro to integration](https://ibmathstuff.wikidot.com/intro-to-integration) - [Indefinite integrals](https://ibmathstuff.wikidot.com/indefinite-integrals) - [Integration: finding C](https://www.mathsisfun.com/calculus/integration-introduction.html) - [Kinematics](https://ibmathstuff.wikidot.com/kinematics) - [Limits](https://ibmathstuff.wikidot.com/limits) - [Local max and min](https://ibmathstuff.wikidot.com/maxandmin) - [Chain rule](https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-2-new/ab-3-1a/a/chain-rule-review) - [Optimization](https://ibmathstuff.wikidot.com/optimization) - [Tangent and normals](https://ibmathstuff.wikidot.com/tangentnormals) - [Area under curves](https://ibmathstuff.wikidot.com/intro-to-integration) - [Volumes of revolution](https://ibmathstuff.wikidot.com/volumesofrevolution) - **Videos** - [Differentiation Rules](https://www.youtube.com/watch?v=XxPAnirR1cM) - [Equation of a Tangent](https://www.youtube.com/watch?v=vmgj2Vxib_s) - [Optimization and Calculus Curves](https://www.youtube.com/watch?v=vNph8YIlRBA) - [Integration Rules](https://www.youtube.com/watch?v=rc4pSeX34Lk) - [Integration by Substitution](https://www.youtube.com/watch?v=S5d6yh08WIQ) - [Volume of Revolution](https://www.youtube.com/watch?v=VL5KLy3ijf8) - [Kinematics](https://www.youtube.com/watch?v=K6KkicxXacA)   ## Summary: The Best IB Math: Analysis & Approaches Study Materials **The Analysis & Approaches courses both have five core topics** that both SL and HL students study (for different amounts of time): - Topic 1: Number and Algebra - Topic 2: Functions - Topic 3: Geometry and Trigonometry - Topic 4: Statistics and Probability - Topic 5: Calculus There are many free IB Math notes and study resources available online, especially compared with other IB classes, which often have few high-quality online resources. **This makes it easier to keep up with what you're learning in IB Math and be prepared for all the exams for the class.** There are multiple types of IB Math study resources, including general study guides, in-depth notes, and videos. Try out each of them to see which ones work best for your study style. Remember, you want to study **early and consistently** in order to be well prepared throughout the school year and for the final IB exam!   ![body-chalkboard-what's-next-1](https://360031.fs1.hubspotusercontent-na1.net/hub/360031/hubfs/body-chalkboard-what's-next-1.jpg?width=400&name=body-chalkboard-what's-next-1.jpg)   ## What's Next? Learn more about IB Math by checking out [every IB Math: Analysis & Approaches paper available](https://blog.prepscholar.com/ib-math-past-papers-free-official). **Looking for more resources for IB Math review?** Read our articles on [trig identities](https://blog.prepscholar.com/verifying-trig-identities), [completing the square](https://blog.prepscholar.com/completing-the-square-formula), [finding the mean of a set of numbers](https://blog.prepscholar.com/how-to-find-the-mean), and [calculating statistical significance](https://blog.prepscholar.com/statistical-significance-definition). **Want to learn more about other IB classes?** You're in luck! 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She loves watching students succeed and is committed to helping you get there. Dora received a full-tuition merit based scholarship to University of Southern California. She graduated magna cum laude and scored in the 99th percentile on the ACT. She is also passionate about acting, writing, and photography. ## Ask a Question Below Have any questions about this article or other topics? 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All rights reserved SAT® is a registered trademark of the College Entrance Examination BoardTM. The College Entrance Examination BoardTM does not endorse, nor is it affiliated in any way with the owner or any content of this web site. ACT® is a registered trademark belonging to ACT Education Corporation ("ACT"). ACT is not involved with or affiliated with PrepScholar Inc., nor does ACT endorse or sponsor any of the products or services offered by PrepScholar Inc. GRE® and TOEFL® are registered trademarks of the ETS®. The ETS® does not endorse, nor is it affiliated in any way with, the owner or any content of this web site. GMAT® is a registered trademark of the Graduate Management Admissions Council®. The Graduate Management Admissions Council® does not endorse, nor is it affiliated in any way with, the owner or any content of this website. ```json { "@context" : "https://schema.org", "@type" : "BlogPosting", "author" : { "@type" : "Person", "name" : "Dora Seigel", "url" : "https://blog.prepscholar.com/author/dora-seigel" }, "dateModified" : "2024-08-19T13:19:31+00:00", "datePublished" : "2022-04-14T15:00:00+00:00", "description" : "How do you study for IB Math SL/HL? Read our set of IB Math notes and our free study guide for the best resources available.", "headline" : "The Best IB Math: Analysis & Approaches Study Guide and Notes for SL/HL", "image" : "http://cdn2.hubspot.net/hubfs/360031/body_math-805.jpg", "mainEntityOfPage" : { "@id" : "https://blog.prepscholar.com/the-best-ib-math-study-guide-and-notes-sl-hl", "@type" : "WebPage" }, "publisher" : { "@type" : "Organization", "logo" : { "@type" : "ImageObject", "url" : "https://www.prepscholar.com/wp-content/uploads/2023/03/PrepScholar-Logo-Colored.png" }, "name" : "PrepScholar" } } ```