The topic that decides whether the rest of the course is about mathematics or about pressing buttons. A model is a choice, and the whole of 2.5 and 2.6 is about choosing one you can defend.
The first four sub-topics are stated in both guides as content common to Analysis and Applications, so those pages serve both courses and are not duplicated. From 2.5 onwards this is Applications only.
2.1 · Straight lines shared The three forms of a line, gradient and intercepts, parallel and perpendicular. A 1 in 12 ramp is 4.8 degrees, and the confusion always makes a slope sound gentler than it is. 2.2 · Functions, domain and range shared Function notation, domain, range, and the informal inverse as a reflection in y = x. Two reasons a domain stops, and only one of them is in the formula. 2.3 · Drawing and sketching shared What each command term requires, labelling key features, and getting a graph off the screen onto paper. A perfect unlabelled curve earns one mark of three. 2.4 · Key features shared Vertex, zeros, symmetry, asymptotes and intersections, with technology. A graph can cross its own horizontal asymptote, exactly. 2.5 · Choosing a model Linear, quadratic, exponential, direct and inverse variation, cubic and sinusoidal models, and what each shape is for. Two models fit three points exactly and differ by a factor of eighteen by hour ten. 2.6 · The modelling process Fitting parameters, judging whether a model is reasonable, and the dangers of reading past the data. The fit is perfect and the one-year prediction is 14.84 metres.Four more sub-topics that only Higher Level students take. They sit on top of everything above: 2.7 and 2.8 make the informal ideas in 2.2 exact, and 2.9 and 2.10 extend the modelling in 2.5 and 2.6.
2.7 · Composite and inverse functions HL Composition in context, finding an inverse, and restricting a domain so an inverse exists. Discount then VAT, or VAT then discount: seven baht apart at every price. 2.8 · Transformations of graphs HL Translations, reflections, stretches, and composite transformations. Stretch then shift gives 3x squared plus 2. The other order gives plus 6. 2.9 · Further models HL Half-life, natural logarithmic models, sinusoidal models with a phase shift, logistic models and piecewise models. A logistic fitted to the same two points levels at 180 where the exponential reached 2048. 2.10 · Linearising data HL Scaling with logarithms, and using a straight line to decide whether data is exponential or a power relationship. Two families agree exactly at two points. Only one of the log plots comes out straight.Sub-topics 2.1 to 2.4 above are yours too, word for word, because both guides state them as common content. Analysis then continues with its own 2.5 onwards, which goes further into quadratics, rational functions, exponentials and logarithms. Those pages live at the Analysis index.
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Written by a serving IB Diploma and Career-related Programme Coordinator and Head of Mathematics, who reads internal assessments across every subject group every year. If you then want the whole draft reviewed properly against all five criteria, that is the paid one, and it is refunded if it does not name at least three specific things to fix.
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