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Math Applications and Interpretation vs Analysis and Approaches


kw0573

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In general, Applications and Interpretation covers a broad range of materials, but Analysis and Approaches covers a narrower range in greater depth. Below lists the main topics in each course, by color code from 2014-2020 syllabus Studies, SL and HL (including Further HL). New topics are italicized. HL includes all SL topics of the same course.

Common topics in all new Math courses:

Algebra: scientific notation, arithmetic/geometric progression, compound interest, annual depreciation, exponents/logarithms

Functions: lines, graph of a function, domain/range, definition of inverse, identifying extremas, intercepts, symmetry, zeros, asymptotes

Geometry/Trig: distances and midpoints, volume and surface area of solids, angle between 2 lines or line and a plane, solving triangles, angles of elevation/depression, bearings, arcs/sectors

Stats: samplingoutliers, data presentation (tables, graphs, central tendency/spread, cumulative frequency, box and whisker, model class), linear correlation of bivariate data, Pearson's correlation coefficient, scatter plot, equation of the regression line of y on x (y given x), Probability: complements, Venn/tree diagrams, combined eventsconditional probability, discrete random variables and expected value, binomial/normal distributions

Calculus: increasing/decreasing functions, calculus of polynomialstangents/normalssolving simple ODE with a boundary condition, definite integrals, first derivative test, optimization

Topics in Applications and Interpretation SL and HL:

Algebra: amortization and annuities

Functions: modelling

Geometry/Trig: equations of perpendicular bisectors, Voronoi diagrams

Probability/Stats: Spearman's rank, null and alternate hypotheses, significant levels, p-values, chi-squared test for independence, for goodness of fit, one-tailed/two-tailed t tests

Calculus: Approximations with trapezoidal rule

Topics only in Applications and Interpretation HL:

Algebra: adding sinusoidal functions of different arguments, matrices, eigenvalues/eigenvectors

Functions: scaling with log notations, log-log and semi-log plots

Geometry/Trig: matrix transformations, determinantsgraph theory/trees, adjacency matrices, walks, Eulerian/Hamiltonian, MST, Kruskal's and Prim's algorithms, Chinese postman problem algorithm, Travelling salesman problem, nearest neighbour and deleted vertex algorithms

Probability/Stats: design of data collection, non-linear regression, sum of square residuals, coefficient of determination, unbiased estimates of mean and standard deviation, central limit theorem, confidence intervals of the mean, Poisson distribution, critical values, test for proportion using binomial distribution, test for population mean using Poisson distribution, bivariate normal distribution and p-value, Types I and II errors, transition matrices and to solve system of linear equations, Markhov chains

Calculus: setting up rates of change ODEsslope fields, Euler's method of a system of 2 ODEs or a second-order ODE, phase portrait

Topics in Analysis and Approaches SL and HL: (topics also in Applications and Interpretation HL are in an enlarged font)

Algebra: binomial theorem/Pascal's triangle

Functions: quadratic functions/equations/inequalities, reciprocal, rational functions, graphs of exponential/logarithmic functions, transformations

Geometry/Trig: radians, sine rule ambiguous case, sin and cos in relation to unit circle, exact sin and cos valuesPythagorean identity, graphs of trig functions, solving trig equations graphically and analytically, quadratic trig equations

Probability/Stats: equation of the regression line of x on y (x given y), standardized normal distribution

Calculus: common derivatives/antiderivatives, chain/product/quotient rules, rates of change, second derivative test, points of inflexion, definite integrals, area enclosed by a curve and the axes, area between curves, kinematics

Topics only in Analysis and Approaches HL: (topics also in Applications and Interpretation HL are underlined)

Algebra: permutations/combinations, partial fractions, complex numbers, De Moivre's theorem, proofs by induction/contradiction/counterexample, analytical solutions of system of 3 equations

Functions: factor/remainder theorems, sum and product of roots of polynomials, odd/even functions, inequalities, absolute value functions, square of functions

Geometry/Trig: reciprocal trig functions, compound angle identities, symmetries in trig functions, vectors: unit/base vectors, position vectors, normalizing, vector equation of a line, dot/cross products, components, system of 2 lines, vector equations of a plane, intersections of line/plane, of 2 planes, of 3 planes

Probability/Stats: Bayes' theorem, continuous random variables, linear transformations of a random variable

Calculus: informal ideas of continuity and differentiability, derive with first principles, higher derivatives, l'Hopital rule, Maclaurin series, related rates, implicit differentiation, trig antideratives, integrate with partial fractions, integration by substitutionrepeated use of integration by parts, first order ODE, Euler's method for a single ODE, separation of variables, homogeneous ODE, integrating factor, calculus of series

TL;DR ~~~~~~~~~~~~~~~~~~

1) Vectors are now HL only.

2) Rank of difficulty: current Studies < AI SL < AA SL (easier than current SL if better at stats than vectors) < AA HL < current HL <= AI HL 

AI SL is mostly Studies. AI HL is studies but with about 30-40% of Further Maths HL. AA SL is pretty much SL. and AA HL is HL with only 20-30% of the Calculus option. 

3) AI HL for the fast learner. AA HL for the inquisitive learner. If you are not that strong at math, the recommendation is AA SL. AI SL is still quite a bit easier than AA SL and only choose it if you are fine with dealing with lots of data. 

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Hi there, 

Thanks for all the information.

I am planning to take engineering in the future, and have opted for the Math A/A SL and Physics HL. Unfortunately, Math A/A HL may be needed to get into an engineering school; however, I think I might find HL quite difficult. The good news is I still have an opportunity to change the course, not sure what to do tbh. 

Let me tell you a brief background about me. I am currently in MYP5, and have started learning the Math SL syllabus, and have covered the following topics in SL: T1 - everything except for 1.3, T2 - nearly everything, T3 - everything, and T6 - differentiation and starting integration. 

Do you have any suggestions? Thanks :) 

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This was helpful!

I'm starting ib next fall and I'm currently trying to figure out which math would suit my future plans. I'm inetersted in studying economics/finance etc. I'm guessing A/I HL would be best for economics but I wouldn't want math to consume my whole life.. 😕 I think I could manage A/I HL but not A/A HL (the ib considers it to be the closest to the old HL). Therefore I'm still thinking about A/A SL. 

If you have an opinion on what I should do it would be super helpful! Thanks

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@igene80 @hissu

I believe that Analysis/Approaches HL is easier than the 2014 version of Math HL (back when it was a minute per mark) because over 80% of the Calculus option (then the most popular Option) was taken out and there are no longer Options. New A/A HL content are some of the new statistics topics that mostly rely upon a calculator or prior learning topics (like volume of 3D shapes).

A/A HL is about depth (despite a lot of topics taken out) and A/I HL is breadth. I double down on my belief that A/I HL is slightly more difficult just because a lot of the A/I HL only topics and are quite abstract. I think for most schools A/A SL is sufficient, but you can try taking one of the HLs (both are perfectly fine for economics and engineering) if you want to be competitive. Remember, it's ALWAYS easier to go from HL to SL than it is from SL to HL.

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Hi! Thanks for the info. It was really useful. I need to choose my IB options for next year and the paper needs to be handed in a few weeks time! Teachers at my school are very unfamiliar with this new syllabus and told us to do our own research 😫

I am planning to study geology in the future and advanced mathematics is deeply recommended (as it is important like for any science), covering topics like algebra, geometry, trig, calculus I and II, differential equations, linear algebra and quite a lot of statistics. I am going to take physics HL too. I am quite good at maths as I also took additional mathematics for the IGCSE. Which one would you recommend?

Thanks in advance!

Edited by MikahTannert
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Hello,

My name is Sanjot and I have just finished MYP 5 (grade 10) in China. Throughout MYP  3-5 (grade 8-10) I have remained in Math SL and have always averaged 6. I want to pursue engineering and have taken physics HL, chem SL and HL math AI. I don't want to take math AA HL since it is the harder one and I have already chosen two sciences. I plan to study in Canada since I am Canadian myself. Would you happen to know if Canadian universities that offer engineering degrees only want math AA HL or is HL math AI acceptable too?

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51 minutes ago, kw0573 said:

@Sanjot I am not so sure that Math AA is the hardest course, but AA and AI should be similar in difficulty yet in different ways. Canadian schools are not generally strict about pre-requistes and either one at HL are ok.

Thanks for your feedback and in return let me summarize to you what I have found so far that differentiates AA from AI. Basically, AA SL is similar to the past IB math SL course and AA HL is similar to past IB math HL course. AI SL is like math studies and AI HL is somewhat between SL and HL as it incorporates both past levels content (the content of SL and HL math). Therefore, math AA is the harder level compared to AI.  AA is more traditional and sometimes calculators and not permitted in exams. It is more algebra heavy. AI involves a new topic called statistics and is more practical/modern. 

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The key is that the new AA HL is easier than the current HL, with an entire Option removed (the Option takes about 3 months to cover if having classes 5 times a week going at a moderate-fast pace). You are correct that AA emphasizes on algebraic working and mathematical rigor, as well as only AA Paper 1 forbids calculators. Calculator questions are not necessarily easy. Also AI HL Paper 3 has two 30-minute questions. Imagine making a mistake early into a problem.

The following is my second attempt to quickly compare AA with AI HL, categorized by "big" units.

Topics in both: sequences/series, complex numbers, functions and transformations, geometry, trigonometry, vectors, data analysis, distributions/random variables, differentiation/integration, and ODEs. 

Topics in AA HL (~10% of the course): combinatorics, and elementary proofs

Topics in AI HL (~40% of the course): matrices, eigenvalues/eigenvectors, group theory, modelling, and statistical tests 

At the end of the day, it comes down to whether you want to study 12 topics (AA HL) somewhat evenly or 15 topics (AI HL) at varying depths, including deeper coverage of data analysis and ODEs than AA HL as well as thorough coverage of matrices, group theory, and statistical tests. The problem is that many AI HL topics have steep learning curves at the beginning (especially group theory and statistical tests), whereas most of the AA HL topics are simply continuations of SL.

Hope that paints a more complete and accurate picture of AA and AI HL. 

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@kw0573

Hello,

I am Jaya and I will be starting IB in a month.I really want to do math in higher level but quite confused about which  one to choose(A/I OR A/A).Which one would be recommended for someone who wants to pursue business management according to you?

Edited by kw0573
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  • 3 weeks later...

In response to a question about applying to Engineering/CS. 

To be competitive in applying to Engineering/CS majors, you will need A/A HL or A/I HL. I found that A/I HL is highly suitable for CS, mostly because of all the discrete math stuff. However, a lot of engineering school admissions office will prefer A/A HL. A/A HL is like pre-calculus and AP Calculus I. A/I HL has some potentially useful stats, useful complex numbers and vectors, useful yet early coverage of matrices and eigenvalues, but only a bare minimum of functions and calculus so schools will be conservative about its value (Engineering schools really cares about calculus).

A/A HL is not that bad. It's most likely easier than the current Math HL. The best preparation for either HL is to use a site like Khan Academy and ensure that you are rock solid on all math covered up to now. You don't really need to study ahead, just make sure you can do grade 7-10 math with speed and confidence. Allocate 1.5 hours of math studying every day, in the next two school years. You will not do well in A/I HL if you treat it as a backup option to A/A HL.

For schools that do no require either at HL (usually American and Canadian schools), basically to be competitive you need a 7 in A/A SL along with a really good application. But generally they are happier to see HL at 6 than SL at 7. Basically if you back out of HL in a few weeks then it may mean you are not fully ready for SL either to secure the 7. Let's just say there is a school that has a 60% probability of admitting you if you get 6 in A/A HL. That number may drop to 50% for A/I HL 6 and 20% if A/A SL 7, all else held equal. The more prestigious the school you are applying, the worse switching from HL to SL is. SL can get you into some engineering and CS schools, but you have to step up your game in your first and second years otherwise you'll likely be "weeded out". The best option is to prepare for HL as much as you can, and at least give it a full year before even consider switching to SL. 

AI HL vs AA SL?

If you are not that good at math, your immediate goal should be to catch up on any weakness you may have in the last 3-4 years of math learning. AI HL is much, much more difficult than AA SL, and schools will reward you for taking it. It is more important that you feel comfortable with everything up to Pre-Calculus, because otherwise, AA SL will be a struggle as well. 

The only reason that schools don't think highly of AI HL is due to one misleading document that says AI HL is Studies but more advanced. The truth of the matter is, AI HL has nearly half of Further Math HL curriculum. Neither course at HL is intended for students ok at math, but taking AA SL will put you at a significant disadvantage when applying for computer engineering/science. As I have said previously, AI HL is more suitable for CS because of all the discrete math, and it is more difficult than AA HL. 

AI HL vs AP Calculus AB?

AI HL does not cover the following topics in AB
1) Analyze for intervals of continuity 2) differentiability vs continuity 3) Intermediate value theorem 4) L'Hopital's rule 5) Mean Value Theorem. It is interesting to note that AA HL does not cover IVT and MVT either, and likely not slope fields which are covered by AI HL. 

AI HL also covers the following from BC
1) Derivative of trigonometric, exponential and logarithmic functions 2) Integration by substitution 3) Areas in the Cartesian plane 4) Vectors 5) Euler's Methods

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On 8/4/2019 at 8:59 PM, mioi said:

AA HL clearly has more Calculus in it.

Yes, 55 vs 41 teaching hours, but AI HL has topics outside of AA.

On 8/4/2019 at 8:59 PM, mioi said:

Does AA hl and AI HL have similar topics of calculus

The topics in the courses are listed above, in my first post. AI HL has about 80% of AA SL Calculus, 15% of AA HL Calculus, along with a couple of additional topics. 

On 8/4/2019 at 8:59 PM, mioi said:

since I have done no form of calculus should I go in AA or AI?

Calculus should not be a big factor in AA vs AI. You can find online calculus help EASILY. The big question is are you confident in studying the much of three Further Math HL topics: Linear Algebra (Matrices), Discrete Math and Statistics? Can you handle 30-40% of Further Math, the hands-down most challenging IB HL course? If yes, AI HL is a great, great course for CS. 

I want you to understand the difficulty of these two HL courses. While I think either at HL is excellent for both engineering and CS, I want you to know that AI HL is more difficult than people say it is. 

Before IB, it is far more important to master (with speed, efficiency, and confidence) the pre-requisites, rather learning IB topics. Either course at HL will be a struggle if your strategy is to learn ahead while admitting that you are not that good at math. 

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Hey! I am planning on pursuing medical-related courses in the future, but I am confused about which Math course I should take. I already listed for AI HL along with HL Chem, HL Bio, SL Economics, SL French B, SL English LL. My school made it look like AA HL is much harder than AI HL making me more confused about the actuality of the difficulty of these Math courses. I am quite comfortable with math and am exerting more effort into it. Which course do you think is most suitable if I want to pursue Medicine? 

Edited by Arathi3000
I forgot to finish a sentence lol
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While difficulty is subjective, it should be quite agreed upon that the new HL courses are much harder than the new SL courses. I still recommend that if you are a fast learner, you should take AI HL, if you are an inquisitive learner, take AA HL.

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  • 2 weeks later...

Kinda off-topic, but I'm forced to pick between AA SL and AI SL, my counselor is saying that SL AA is really hard, I am not the best in math but at the same time AI will not help me in my future, should I challenge myself and risk a bad score or take the safe way.

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@Ayav

Math AI SL is the definition of a useless IB course. I think the more competitive schools you are applying to, the better AA SL is. AA SL is still calibrated for the average IB math student, but AI SL is more of those who are really bad at math so they can get the diploma. 

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  • 2 weeks later...

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