Year 12 mathematics formulas

Feb 3rd, 2012
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Formulas for students of Year 12 (in the Australian education system) sitting Mathematics in the Preliminary and HSC years. Topics covered: probability, series, geometric applications of calculus, integration, trigonometric functions, exponential and logarithmic functions, calculus in the real world

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MATHEMATICS FORMULASPROBABILITYProbability is the study of how likely an event will happenSimple probabilityThe probability of an event occurring is given by:Complementary eventsP(E) + P(not E) = 1or P(E) = 1 - P(not E)Non-mutually-exclusive eventsP(A or B) = P(A) + P(B) - P(A and B)Product ruleP(AB) = P(A) P(B)Tree diagramsP(A or B) = P(A) + P(B)SERIESA series is the infinite sum of a sequence of other numbers or termsGeneral series + Sigma notationSeries are often written in sigma notation (?); it stands for the sum of a seriesArithmetic seriesIn an arithmetic series, each term is a constant amount more than the previous term. The constant is called common differenceIf T1, T2 and T3 are consecutive terms of an arithmetic series thend = T2 - T1 = T3 - T2a + (a + d) + (a + 2d) + (a + 3d) + ? + [a + (n - 1)d] + ?is an arithmetic series with the first term a, common difference d and nth term given by:Tn = a + (n - 1)dSum of an arithmetic series Where l = last or nth termGeometric seriesIn a geometric series each term is formed by multiplying the preceding term by a constant, called the common ratioIf T1 + T2 + T3 + ? is a geometric series then In general, if T1 + T2 + T3 + T4 + ? + Tn - 1 + Tn is a geometric series thenTerms of a geometric seriesa + ar + ar2 + ar3 + ? + arn - 1 + ? is a geometric series with first term a, common ratio r and nth term given by:Tn = arn - 1Sum of a geometric seriesSum to infinity (limiting sum)Compound i

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