We, the IB tutors, have tried to weave our critical thoughts throughout the new IB Math curriculum taught with the new IB math courses.
The new IB Math curriculum with the new IB Math courses comprise of IB Math AA (Analysis and Approaches) and IB AI (Applications and Interpretation); both taught in HL and SL.
IB COURSES
The IB Diploma Programme has IB courses categorized under six subject groups: Language acquisition, Studies in language and literature, Individuals and societies, Sciences, Mathematics, The arts. IB Math is compulsory prerequisite to IB Diploma and can be opted either at the Higher Level (HL) or Standard Level (SL).
IB Math: AA or AI
Understanding the trade-off between IB Math: AA vs. AI and which is better for you is quite an overwhelming question. While for both AA and AI, Math HL has a more coverage in length and width compared to its corresponding Math SL. IB Math HL includes an additional paper (paper 3) unlike IB Math SL which has paper 1 and paper 2.
The choice between AA and AI for you, as an IB Diploma Programme student, is made on certain key factors:
- If you are very keen to pursue with core and advanced mathematics and mathematics related subjects like engineering, physical sciences, economics; you should go for IB Math AA. On the other hand, if you are interested to pursue mathematics applied trans-disciplinary subjects like natural sciences, social sciences, some economics, statistics, business analytics, art and design, psychology; you are best fit for IB Math AI.
- While IB Math AA tests your advanced mathematical thinking skills, IB Math AI evaluates to what extent you have strong math skills to apply math in real-life contexts.
- While IB Math AA assesses your problem-solving skills in solving real and abstract mathematical problems; IB Math AI tests how you solve real-life problems with the help of math and technology.
- While the focus of IB Math AA is on number and algebra as well as calculus, IB Math AI emphasizes on functions, statistics, and probability.
- If you critically analyse the focus on topics for IB Math AA and IB Math AI, you would see that why certain concepts draw special attention for each.
- Number and algebra opens up a new perspective of logically reasoning out a real life problem by breaking down the problem to find its solution. Also, abstract algebra adopts concepts like Group Theory which form the premise for cryptography, robotics, computer graphics, and computer vision. With the concepts of differentiation and integration in calculus, we get to understand how architecture, electrical infrastructures can be improved. The crux is calculus helps to understand physics, engineering better. To deal with certain economic and financial crisis, spread of diseases, population growth models; you would find calculus to be part and parcel of your survival mechanism.
- Functions as algebraic expressions have a special place in understanding the relation between variables in real life-say the relation between inputs and outputs in a business. Probability and statistics define the occurrence of random events in real-life and also focus on collection, analysis, and interpretation of numerical data. It is quite intuitive to reason out why statistics is a part of applied mathematics. Inferential statistics aims to generalize the sample data. Statistics uses the mathematical methods and reasoning to solve real life problems.
IB Math key concepts
The IB math key concepts are broad and big ideas which form the interconnection within the topics covered in IB Math. The concepts are approximation, change, equivalence of concepts or quantities or expressions, generalization, representative modelling for the real world, patterns of elements, quantity, relations between quantities, properties, and concepts, representation of data, space, systems of interrelated elements, validity of conclusion.
Calculator for IB Math AA and AI
Calculator for IB Math AA and AI is a Graphical Display calculator. Recommended ones are:
Texas Instruments TI-84 Plus CE and Texas Instruments TI-Nspire (a non CAS version)
IB Learner Profile-Math AA and AI
You are an inquirer of diverse topics, knowledgeable to explore methods and concepts, critical thinker to evaluate, communicator in collaborative learning, principled in maintain ethical stance for using other’s data, open-minded in adopting new approaches, caring towards others for assistance, risk-taker in adopting challenging mathematical techniques, holistically balanced, reflective in improving own learning tools.
IB Math formula booklet
The IB Math formula booklet has all formulae required for the course. The teachers ensure that each student is thorough with the contents of the IB math formula booklet. The IB math formula booklet is downloaded by the school and provided to each student during the IB exam.
The unique approach to assess a student in the IB Diploma Programme is not to assess how much the student has crammed up the theoretical concepts in IB math syllabus. It is more to do with how far the student has been critical in the thinking process and understanding the application of each and every mathematical formula and concept in the real life context.
IB Math syllabus
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 |
IB Math external assessment
- For IB Mathematics AA HL, Paper 1 has 30% weightage with short or long response questions to be answered within 120 mins. For IB Mathematics AA SL, Paper 1 has 40% weightage with short or long response questions to be answered within 90 mins.
- For IB Mathematics AA HL, Paper 2 has 30% short or long response questions to be answered within 120 mins. For IB Mathematics AA SL, Paper 2 has 40% weightage with short or long response questions to be answered within 90 mins.
- For IB Mathematics AA HL, Paper 3 has 20% weightage with 2 long problems to be answered within 60 mins. Paper 3 is exclusively for HL.
- For IB Mathematics AI HL, Paper 1 has 30% weightage with short or long response questions to be answered within 120 mins. For IB Mathematics AI SL, Paper 1 has 40% weightage with short or long response questions to be answered within 90 mins.
- For IB Mathematics AI HL, Paper 2 has 30% short or long response questions to be answered within 120 mins. For IB Mathemtics AI SL, Paper 2 has 40% weightage with short or long response questions to be answered within 90 mins.
- For IB Mathematics AI HL, Paper 3 has 20% weightage with 2 long problems to be answered within 60 mins. Paper 3 is exclusively for HL.
IB Math IA
For all the IB math courses, IB Math IA is of 20 marks. IB Math IA is assessed on five criteria-criterion A focusing on presentation worth of 4 marks, criterion B focusing on mathematical communication worth of 4 marks, criterion C focusing on personal engagement worth of 3 marks, criterion D on reflection worth of 3 marks, and criterion E on use of mathematics worth of 6 marks.
Criterion A on Presentation looks for a structured format and coherence of IA. Criterion B looks at the use of mathematical language throughout your exploration-like the use of notation, symbol, and terminology. Criterion C assesses your personal interest and engagement in exploring the IB Math IA topic. Criterion D is more on reflection or evaluation of the different mathematical tools you have used with the mention of the challenges you have encountered.
