C2 key points revision notes

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C2 Revision Key points
Sequences and series
1. A
seque nce us
an
ordered se t
of
nu mb e rs,
a1,
a2,a3 ,
. . .,
a N, where aK i
s
th e gen er
al
ter
m
2. A
seri
es
is
the sum of
the t
e r
ms
o f
a se q ue nce
a1+ a2+ a 3+...+an
3. I
n an
arit
hme ti
c sequence, Ak +1=
A k +d w her
e
d i
s t
h e commo n d if
fere n ce
4. I
n a
geo metri
c sequence, A k
+ 1=
rA k w h ere r
i
s t
he c ommo n
rat
io
5. I
n a
periodi
c seque nce
A k+p= A k
fo r a f ix ed
int
eg er
,
p , c all
ed
the
p eri
od
6. I
n an
osc i
l
lati
ng sequence
the t
erms r
is e above and fa l l
be l
l
o w t
he
mid dle
v a l
ue
7. For
an ari
thme t
ic
seque nce w it
h f
ir
s t
t
e r m a,
commo n d i
ff
ere nce
d
and
n
te rms :
The
kth t
erm, Ak=
a + (
k 1)d
The
last
term,
l= a
+
(n1 )
d
The
nu mb er
of
terms,
n =
(l
a)/d
+1
The
commo n dif
fer
e nce,
d=
l ­ a/
n 1
The
sum of
the t
erms
= 1/2n( a
+
l)
= 1/2 n[2a
+
(n 1)
d ]
8. For
a
g eome t
ric
seque nce
w i t
h t
he first t
erm a,
commo n rat
io r
an d n ter ms :
The
kth t
erm, Ak=
a(r
to
the
p ow er
k 1)
The
last
term,
A n= a(
r powe r pf
n 1 )
The
sum of
terms = a(
r t
o t
h e
po we r
of
­ 1)
/(r
­
1 )
= a (1 ­ r
n)/
(1 ­ r
)
9. For
an i
nfi
nite
geo metri
c seri
e s t
o c o nv e rge,
1<r
<1
I
n t
his
case
the sum of
all
t
h e
terms
i s
g i
ven by a/
(
1 r
)
Logarithms
1. a t
o t
he pow er
of b =
c lo g C = b
( what power must a be raised to get c is the ans to b)
a
2. y
=
log
to t
he bas e a
x a
t o
th e p ow er
y =
x
3. Logari
thms
to an y
b ase
Mu l
ti
pli
cati
ons:
log
x +
log y
= lo gx y
D i
vi
sion:
log
x ­
log y
= l
o g
x/y
L oga r
it
hm o f
1
:
log 1
= 0
P o wers:
l
og x
to t
he p ow e r
of n = n l
o gx
R eci
procal
s:
log(1/
y) =
l
o g
y
R oot
s l
og n t
o t
he
po w er
r oot x = 1 /
n l
o g x
L oga r
it
hm to i
ts
ow n base
:
lo g to t he
ba se a a
= 1
4. L ogari
thms
ma y
b e
us ed
t o d i
s co ver
the r
elat
i on shi
p b etw e e n the v a riab l
es in tw o
t
yp es
of
sit
ua t
ion
Y = kn log y
= l
og k
+ nlog
x
Plot
log
y against
l
o g x:
t hi
s r
e lation shi p
g i
ves a s tr
aight
lin e w h ere n is the gra d i
e nt
and
lo g
k i
s t
he i
ntercept
5. Any positive number can be expressed as a power of 10 base 10
Trigonometery
1 .
0 30 45 60 90 180
Sin 0 1/2 1/ 2 3/2 1 0
Cos 1 3/2 1/ 2 1/2 0 -1

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Angles
can b e me asu r
e d
in radians.
r adi
ans
= 180 °
7. To
co nver
t
d e gr
e es int
o
radi an:
A ngl
e *
/180
8. To
co nver
t
ra dia ns i
n to d egr ees:
R ad i
a n *
180 /
9.…read more

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