Formula for Core 2

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  • Created on: 19-11-08 16:43
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CORE 2
SEQUENCES
K = term
a1 = first term
an = last term
d = common difference
n = number of terms in sequence
r = common ratio
Arithmetic- same value added/subtracted each time
for the kth term ak = a + (k-1) d
or for the last term L = a + (n-1) d
sum of terms S = ½ n (a + L)
Geometric- multiplying terms by a fixed number, common ratio, or r
for the kth term ak = a r k-1
or for the last term an = a r n-1
sum of n terms Sn = a (1 ­ rn )
(1­r)
sum of infinite terms S = a

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Trigonometry
Sine rule
Use for right angled triangles-
o unknown side ­ 2 angles and a side
o unknown angle ­ 2 sides and included angle
a = b = c
SinA SinB Sin C
Cosine rule
Used to fine-
o Unknown side ­ two sides and angle between given
o Unknown angle ­ 3 sides given
To find an angle ­
Cos A = b2 + c2 ­ a2
2bc
To find a side ­
a2 = b2 + c2 ­ 2 b c…read more

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Arcs and Sectors
Area of a sector (in radians)
Length of an arc (in radians)
Radians
To convert degrees into radians multiply by
To convert radians into degrees multiply by
Logarithms…read more

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The rules
1) logb(mn) = logb(m) + logb(n)
2) logb(m/n) = logb(m) ­ logb(n)
3) logb(mn) = n · logb(m)
4) log 1 = 0
5) logmm = 1
34 = 81 log381 = 4
base power base power
Sine, Cosine and Tangent
Cos (360 ­ x) and (x ± 360)
Sin (180 ­x) and (x ± 360)
tan (±180)…read more

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