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Year 12 mathematics formulas

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

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

P
(
E
)
=
Number of ways an event can occur
Totalnumber of all possible outcomes
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 
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-
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,
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-
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,
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S
n
=
n
2
(a+l)
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S
n=
n
2
[2a +
(
n1
)
d ]
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1

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)
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,
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-
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r=
T
2
T
1
=
T
3
T
2
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-
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3
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r=
T
2
T
1
=
T
3
T
2
=
T
4
T
3
=
T
n
T
n1
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,
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-
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S
n
=
a(r
n
1)
r1
for
r
>1
S
n
=
a(1r
n
)
1r
for
r
<1
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If
r
<1 then S
=
a
1r
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
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4$!
5
""
"/
P(1+
r
100
)
1

P(1+
r
100
)
2
.
P(1+
r
100
)
n1

P(1+
r
100
)
n
2

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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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