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  1. 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: sampling, outliers, 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 events, conditional probability, discrete random variables and expected value, binomial/normal distributions Calculus: increasing/decreasing functions, calculus of polynomials, tangents/normals, solving 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, determinants, graph 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 ODEs, slope 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 values, Pythagorean 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 substitution, repeated 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.
  2. Hi, this is my first time creating a forum post and I might not be as specific or on topic as I need to be to get my points and thoughts across so please bear with me. Currently I am in the midst or writing the first draft for my Computer Science Extended Essay and I seem to have hit a snag. The Research Question I have come up with is: To what extent has Artificial Intelligence impacted the space exploration industry? I would appreciate it if anyone could answer a few of my concerns about my RQ: Is it too broad? If it is, how can I narrow it without changing too much, as I already put up my first reflection which includes my RQ. (Kind of rushed and got myself into trouble here) Also, are there any fresh or unique takes on this topic? All I seem to be able to think of are the basics. (I just really wanted to do my EE on AIs and now I regret being so adamant) Below are the Self-Reflections I have posted in the RRS to give you an idea of my direction: First: My main points of focus and essay outline are as follows: Introduction: Why AI's should be implemented or researched etc. How AI's imitate human behaviour: Mental Processes and Procedural thinking. Efficiency of algorithms: Analyse the Machine Learning Algorithm and improve on efficiency if possible. Why AI's are suitable for use in space: Benefits and Drawbacks. Two current uses of AI in space: Rovers (AEGIS) and Environmental Maintenance (BioSphere). Possible future uses: Extraterrestrial exploration, Interplanetary travel (Passengers). Conclusion: To what extent has Artificial Intelligence impacted the space exploration industry? Second: Outline of Introduction: Context: Artificial Intelligence is an industry in itself as there are various uses for a technology which can simulate human behaviour however this also means that it can be used in various other industries. One such industry which has a potentially bright future for Artificial Intelligence technology is the Space Exploration industry, which has already implemented a few AIs and is planning to upgrade and implement more. Outline of Argument: This essay seeks to analyse the core function of AIs and how and why they are useful in the Space Exploration Industry. Scope: The essay will also include a couple examples of present uses of AIs in Space Exploration along with an analysis into their limitations and possible adjustments to make them more self-sufficient as Space requires largely self sufficient mechanisms or environments due to the amount of time it takes to communicate with Earth from distances further than the moon. Worthiness of investigation: This research question is worthy of investigation because it is a potential turning point in both the development of Artificial Intelligence technology and the advancement of Space Exploration (and its technology) to grander heights and it could be one of the keys to travelling to further distances physically. And honestly this is as far as I have gotten, except for a few lines into the actual Introduction. Is this a good start? Or do I need something a little more interesting or important? Any additional advice or constructive criticism which is not a direct answer to any of my questions will also be appreciated and considered. Thank you for your time.
  3. Version 1.0.0


    These are the first version guides (Feb 2019) and specimen for the new math courses with exams starting in 2021.
  4. I had a discussion with my supervisor about my EE and we came up with a research question, "How does the Turing Test differentiate between biological and artificial intelligence?". I wonder is this question appropriate for an EE question as it is hard to include an reasoned arguments, therefore, difficult to get point on Criteria E.
  5. So I keep getting told to keep my IA simple, because it's not graded for being groundbreaking or anything. I'm skeptical about this though and I do want a good grade. I'm investigating the viscosity of different liquids and under different conditions. So too simple?:/
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