All sixteen sub-topics. Four are shared with Applications, seven are Analysis at Standard Level, and five are Higher Level only.
Both guides state 2.1 to 2.4 as content common to the two courses, so these are the same pages Applications students use rather than a second copy that could drift.
2.1 · Straight lines SHARED Gradient, the three forms of the equation, parallel and perpendicular. A gradient read off the axes without checking the scales. 2.2 · Functions, domain and range SHARED Function notation, domain, range, and the inverse as a reflection in y = x. The model says 11,000 people in a town of 4,000. 2.3 · Drawing and sketching SHARED What a sketch has to show, and what a drawing has to show. An accurate plot with nothing labelled scores one mark of three. 2.4 · Key features of graphs SHARED Intercepts, asymptotes, symmetry, maxima and minima. A graph can cross its own asymptote.Five more sub-topics that only Higher Level students take. They sit on top of everything above, and 2.13 and 2.16 both extend the graph work rather than starting again.
2.12 · Polynomial functions HL Zeros, roots and factors, the factor and remainder theorems, and the sum and product of the roots. The product of the roots is +6 and the constant term is −6. 2.13 · Harder rational functions HL Quadratic over linear and linear over quadratic, with oblique asymptotes. The old rule gives y = 1, and the curve is 101 away from it. 2.14 · Odd, even and self-inverse HL Symmetry tests, inverses with a restricted domain, and functions that undo themselves. The square root of minus three squared is 3, not −3. 2.15 · Solving inequalities HL g(x) at or above f(x), graphically and algebraically. Multiplying by x loses every negative solution. 2.16 · Modulus and other transformed graphs HL The modulus of f, f of the modulus, the reciprocal, f(ax + b) and the square, with modulus equations. At x = −2 one reads 4 and the other reads 0.Sub-topics 2.1 to 2.4 above are yours too, word for word, because both guides state them as common content. Applications then continues with its own modelling strand rather than this one. Applications Topic 2 is here, all ten sub-topics.
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