Discover IBDP Math AI & AA HL/SL Syllabus 2021
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New IBDP Math syllabus for the university program
- The improvised IB MATH AI and AA HL/SL program is designed to give more career options and fit more students who have specific knacks, gifted abilities and specific needs to take up Math.
- It is based on the simple thumb rule in opening up more University doors for the students to take up trans-disciplinary courses requiring a strong foundation of Math.
- It also aims to recognize the contribution of Technology in Math, application and analysis.
- The purpose of improvisation in the IBDP Math syllabus is to open up more career opportunities for the students who have a deep passion for Math and also equipped with critical and analytical skills with a problem solving ability both in the real and abstract worlds.
- The Math AI specifically aims to draw a trans-disciplinary integration between Technology and the theoretical-practical aspects of mathematics.
Change in Math AI & AA HL/SL
- The IB has done away with the previous system entirely and come up with two new courses of Math- Math AA (Mathematics: analysis and approaches) and Math AI (Mathematics: applications and interpretations).
- Two new courses will become part of the Diploma Programme (DP) in 2019, both taught at the Higher level (HL) and Standard level (SL).
- The courses are separated by how they critically approach Mathematics with their analysis, applications and interpretations. https://www.ibo.org/programmes/diploma-programme/curriculum/mathematics/
What is Math AI & AA?
| Math AA | Math AI |
| Focus area-Emphasis on algebraic methods | Focus area-Modelling and Statistics |
| Aims and objectives-Develop strong skills in mathematical thinking | Aims and objectives-Develops strong skills in applying practical mathematical problems to the real-world |
| Deals with-Mathematical problem and exploring real and abstract applications | Deals with–Solving real mathematical problems using technology |
| Meant for– For students interested in mathematics, engineering physical sciences, and some economics | Meant for– For students interested in social sciences, natural sciences, medicine, statistics, business, engineering, some economics, psychology and design thinking |
What are the topics in Math AI & AA?
- Both Math AA and Math AI (SL and HL in each) cover the same 5 topics within mathematics:Â number and algebra, functions, geometry and trigonometry, statics and probability, and calculus.
How do I choose between Math AI & AA HL/SL?
- Math AA SL- Students who are moderate in Math and inclined to take up math application based courses Like Economics, Sciences for their undergraduate levels
- Math AA HL- Students who are extraordinary in Math and tend to take up undergraduate courses more reliant on Math like Engineering or a Math (Hons)
- Math AI SL- Students who are moderate in Math and inclined to pursue an undergraduate career involving Math and Technology
- Math AI HL- Students who are very adept in Math and inclined to pursue an undergraduate career involving Math and Technology
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How much time should be spent on Math AI & AA syllabus?
- It is with respect to the varying emphasis on the time dedicated to a given topic in SL and HL levels for both the courses. There are stipulated number of hours, which the IB says, must be spent on Math AI and Math AA syllabus however students can practice on their using other IB resources.
- For Math AA SL, the no. of instruction hours is 150, whereas for HL it is 240. The additional 90 hours in HL counts for 30 hours of Toolkit and Exploration and 60 hours of common SL core content.
- For Math AI SL, the no. of instruction hours is 150, whereas for HL it is 240. The additional 90 hours in HL counts for 30 hours of Toolkit and Exploration and 60 hours of common SL core content.
- In a gist, the SL courses are a complete subset of the HL courses.
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What are engaging activities for Math AI & AA HL/SL syllabus?
- The facilitator and the learners can have regular weekly opportunities to assess progress. The progress tracker assesses student achievement against formal criteria, such as worksheets, problem sets or quizlets. Learning can also be supported with discussion forums, study tips, wall planners for the academic year, interviews with the tutors, video series on every aspect of the concept of each topic. Many private IB tutors, IB Math tutors and IB online tuitions are available to support learning.
Recommended device for Math AI & AA HL/SL?
- A Graphical Display calculator is required for this course. Recommended ones are:
Texas Instruments TI-84 Plus CE
Texas Instruments TI-Nspire (a non CAS version)
How do I engage myself with Math AI & AA HL/SL?
- The sole focus is to develop self-regulated learners and encourage them to learn to set goals, inquire, explore, self-interrogate, self-critique, reflect on performance, generate perseverance, try out multiple ways of solving, customize their own learning process and challenge themselves.
- Adopting a constructivist approach where knowledge is not acquired but constructed would surely trigger the research skill of the students. The emphasis is on active learning with respect to real-life involvement, connectedness, and concurrency. IB Math AI and AA curriculum is all about thinking from design element and reimagine the problem statement in order to arrive at right solutions with meaningful engagement.
- The mentors are to figure out the academic challenges faced by each learner and help align them with self-paced progress, confidence, and grit. They can prepare an IEP for the aims and objectives feasible to attain, suggest tips to optimize time and strike a balance between academics, global awareness, and their areas of interest. Let them treat each learner as unique and give each one deeper insight into self-discovery. After all, the IBDP math AI and AA HL/SL syllabus closely exhibits IB learner profiles.
- The teaching-learning interface can allow a color-coded flag to rise if there is a challenge in learning faced by a student. The ATL and ATT, aka the pedagogy plays a key role.
- Learners can inculcate a strong set of affective skills through this process of learning.
- They can develop a solid hands-on dealing with the latest online tools.
- They have the liberty to adopt a self-paced organized planner for learning.
The aims and objectives of IBDP Math AI & AA HL/SL syllabus:
- develop an unquenchable thirst in learners and mentors to love, imbibe and assimilate Mathematics in depth
- understanding the fundamentals of Math, its concepts, nature, and principles
- nurture a growth mindset in every step of analyzing the critical and creative aspects of Mathematics
- inculcate the habit of framing hypothesis and arriving at abstraction or generalization
- develop the skill of knowledge sharing and transfer amongst peers when it comes to integrating Math with correlated subjects
- acknowledge and apply the inter-correlation between Mathematics and Technology
- infuse a moral, social and ethical quotient in the students to appreciate the work and contribution of the mathematicians
- appreciate the international-mindedness infused in the learning of the subject
- critique the contribution of Math to other disciplines and also as one of the AOK-s in the TOK course
- work independently and also in a team
- involve in peer-group collaboration, reflect on own and each other’s contributions
| Math AA SL & HL topics | Instructional hours (SL) | Instructional hours(HL) |
| Number and Algebra | 19 | 39 |
| Functions | 21 | 32 |
| Geometry and Trigonometry | 25 | 51 |
| Statistics and Probability | 27 | 33 |
| Calculus | 28 | 55 |
| Toolkit and Exploration | 30 | 30 |
| Total | 150 | 240 |
| Math AI SL & HL topics | Instructional hours (SL) | Instructional hours (HL) |
| Number and Algebra | 16 | 29 |
| Functions | 31 | 42 |
| Geometry and Trigonometry | 18 | 46 |
| Statistics and Probability | 36 | 52 |
| Calculus | 19 | 41 |
| Toolkit and Exploration | 30 | 30 |
| Total | 150 | 240 |
Topics in depth:
| Topics | SL in AA | HL in AA(What’s in addition to SL) |
| Number and Algebra | Scientific notation, arithmetic and geometric sequences and series and their applications including financial applications, laws of logarithms and exponentials, solving exponential equations, simple proof, approximations and errors, binomial theorem | Permutation and combination, partial fractions, complex numbers, proof by induction, contradiction and counter-example, solution of systems of linear equation |
| Functions | Equations of straight lines, concepts and properties of functions and their graphs, including composite, inverse, the identity, rational, exponential, logarithmic and quadratic functions | Factor and remainder theorems, sums and products of roots of polynomials, rational functions, odd and even functions, self-inverse functions, solving function inequalities and the modulus function |
| Geometry and Trigonometry | Volume and surface of 3d solids, right-angled and non-right-angled trigonometry including bearings and angles of elevation and depression, radian measure, the unit circle and the Pythagorean identity, double angle identity for sine and cosine, composite trigonometric functions, solving trigonometric equations | Reciprocal trigonometric ratios, inverse trigonometric functions, compound angle identities, double angle identity for tangent, symmetry properties of trigonometric graphs, vector theory, application with lines and planes, vector algebra |
| Statistics and Probability | Collecting data and using sampling techniques, presenting data in graphical form, measures of central tendency and spread, correlation, regression, calculating probabilities, probability diagrams, normal distribution with standardization of variables, binomial distribution | Bayes Theorem, probability distributions, probability density functions, expectation algebra |
| Calculus | Informal ideas of limits and convergence, differentiation including graphical behaviour of functions, finding equations of normal and tangents, optimization, kinematics involving displacement, velocity, acceleration and the total distance travelled, the chain, product and quotient rules, definite and indefinite integration | Introduction to continuity and differentiability, convergence and divergence, differentiation from first principles, limits and L’Hopital’s rule, implicit differentiation, derivatives of reciprocal and inverse trigonometric functions, integration by substitution and parts, volumes of revolution, solution of first order differential equations using Euler’s method by separating variables and using the integrating factor, Maclaurin series |
| Topics | SL in AI | HL in AI(What’s in addition to SL) |
| Number and Algebra | Scientific notation, arithmetic and geometric sequences and series and their applications including financial applications including loan repayments, simple treatment of logarithms and exponentials, simple proof, approximations and errors | Laws of logarithms, complex numbers and their practical applications, matrices and their applications for solving systems of equations for geometric transformations, and their applications to probability |
| Functions | Creating, fitting and using models with linear, exponential, natural logarithm, cubic and simple trigonometric functions | Use of log graphs, graph transformations, creating, fitting and using models with further trigonometric, logarithmic, rational, logistic and piecewise functions |
| Geometry and Trigonometry | Volume and surface of 3d solids, right-angled and non-right-angled trigonometry including bearings, surface area and volume of the composite 3d solids, establishing optimum positions and paths using Voronoi diagrams | Vector concepts and their applications in kinematics, applications of adjacency matrices, and tree and cycle algorithms |
| Statistics and Probability | Collecting data and using sampling techniques, presenting data in graphical form, measures of central tendency and spread, correlation using Pearson’s product-moment and Spearman’s rank correlation coefficients, regression, calculating probabilities, probability diagrams, normal distribution, Chi-squared test for independence and goodness of fit | Binomial and Poisson distributions, designing data collection methods, tests for reliability and validity, hypothesis testing and confidence intervals |
| Calculus | Differentiation including graphical behaviour of functions and optimization, using simple integration and the trapezium/trapezoidal rule to calculate areas of irregular shapes | Kinematics and practical problems involving rates of change, volumes of revolution, setting up and solving models involving differential equations using numerical and analytic methods, slope fields, coupled and second-order differential equations in context |
Math AI & AA HL/SL assessments
Connecting the IB Learner Profile with the approach towards learning Math AA and AI aims to:
- Nurture the thirst knowledge and understanding in learners
- Inculcate the art of problem-solving in real and abstract world
- Instil the art of communication and interpretation in the learners with the use of sketch or draw mathematical diagrams, graphs or constructions both on paper and using technology, record methods, solutions and conclusions using standardized notation, use appropriate notation and terminology
- Equip them with the optimum use of technology
- Inculcate the art of reasoning and meta-cognition through the construction of knowledge, mathematical arguments through the use of precise statements, logical deduction and inference and by the improvisation of mathematical expressions
- Make them inquirers who will be exploring unfamiliar real and abstract situations, organize, analyse, critique, frame hypothesis and draw conclusions by testing their validity.
The percentage weightage in response within the stipulated time period for SL and HL in both the courses:
| AA (SL) | AA (HL) | AI (SL) | AI (HL) | |
| Paper 1 | 40% (90mins) for Short/Long Response | 30% (120mins) for Short/Long Response | 40% (90mins) for Short Response | 30% (120mins) for Short Response |
| Paper 2 | 40% (90mins) for Short/Long Response | 30% (120mins) for Short/Long Response | 40% (90mins) for Long Response | 30% (120mins) for Long Response |
| Paper 3 | – | 20% (60mins) 2 Long Problems | – | 20% (60mins) 2 Long Problems |
| IA | 20% Exploration | 20% Exploration | 20% Exploration | 20% Exploration |
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