All fifteen Applications sub-topics. The first five are shared with Analysis and Approaches.
1.1 to 1.5 are stated in both guides as content common to Analysis and Approaches and Applications and Interpretation. One set of pages, both courses, Standard and Higher Level alike.
1.1 · Standard form and order of magnitude SHARED a × 10k, the two conditions, calculator notation, and arithmetic including the addition everyone gets wrong. 10⁶ is not twice 10³. It is a thousand times, three short steps along. 1.2 · Arithmetic sequences and series SHARED The nth term, both sum formulae, working backwards for d or n, and models that are not quite arithmetic. Run u₁ + nd alongside the real formula and watch it sit one term ahead for ever. 1.3 · Geometric sequences and series SHARED The nth term, the sum, and the sum to infinity with the condition that makes it exist. Two sequences from the same first two terms. By n = 10 one is 51 times the other. 1.4 · Compound interest, depreciation and real value SHARED The FV formula, compounding frequency, depreciation as the same formula, and the inflation question that is on the syllabus. It grew to 1628.89 and buys 1212.03 of what it used to. 1.5 · Exponents and logarithms SHARED Laws of exponents, logs base 10 and e, the equivalence with powers, and solving exponential equations. 2 to the what gives 32? The graph answers it by reading the same point backwards.From 1.6 the two courses separate. These ten are the Applications route. Analysis students stop at 1.5 and continue on their own hub.
1.6 · Approximation, bounds and percentage error Decimal places and significant figures, upper and lower bounds, percentage error and estimation. Each side out by 4%, the area out by 12%. Errors grow when you multiply. 1.7 · Amortization and annuities Loans and annuities on the calculator, and what the six fields mean. Your first payment is 77.6% interest, and the crossover is payment 163 of 300. 1.8 · Solving systems and polynomials Linear systems in up to three variables, polynomial roots, and what the solver is actually finding. Tilt one line until the two are parallel and the solution disappears.Not built yet, and this list is honest about it.
Analysis continues from 1.5 with SL 1.6 to 1.9 and Higher Level 1.10 to 1.16. Topics 4 and 5 are complete for both courses in the meantime.
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