Maths - C1 (entire syllabus)

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C1
Surds
Squar
e Number
­
The
product
of
an
ident
ical
i
nteger
mul
ti
pli
ed
by
it
sel
f
e.g. 1, 4, 9, 16....
Sur
ds
­ The
squar
e r
oot
of
a
nonsquar
ed
int
eger
e.g. 2
Al
l
sur
ds
are
ir
rat
ional
I
rr
ati
onal
number
­
a number
t
hat
can'
t
be
put
i
nto
a f
ract
ion
Mul
ti
ply
ing
sur
ds
To
simpl
if
y a
sur
d you
must
check
w het
her
any
squar
e number
s di
vi
de
int
o t
he
int
eger
wi
thi
n t
he
squar
e r
oot
e.g. 8 = 4*2 = 22
Addi
ng
and
Subt
ract
ing
Sur
ds
You
can
onl
y add
and
subt
ract
sur
ds
if
t
hey
have
the
same
int
eger
i
n t
he
root
e.g. 72 + 42 = 112
Rat
ional
number
­
can
be
w r
it
ten
as
a f
ract
ion,
ei
ther
t
ermi
nat
ing
or
reoccur
ri
ng
Ter
minat
ing
deci
mal
­
deci
mal
t
hat
st
ops
e.
g.
0.1,
0.
55667,
0.
6666666666668
Reoccur
ri
ng
deci
mal
­
indef
ini
te
amount
of
uni
ts
aft
er
the
deci
mal
Rat
ional
isi
ng
the
denomi
nat
or
Al
gebr
aical
ly
, f
ract
ions
are
much
easi
er
to
w or
k wi
th
w i
thout
sur
ds
in
the
denomi
nat
or
hence
w e
rat
ional
is
e
the
denomi
nat
or.
e.
g.
2/3
(we
mul
ti
ply
by
the
denomi
nat
or)
2 3/
3
2
2
e.
g.
1)
( 5
+ 3)
(
5
3)
=
5 3 =
5 ­
3 =
2
2)
2/
3 +
2
= 2(
3 2)
/92
= (
6 2 2)
/7
I
ndi
ces
I
n gener
al,
i
f
the
power
i
s negat
iv
e
then
we
reci
procat
e (
fl
ip
the
fr
act
ion
and
make
it
negat
ive)
1
e.
g.
2x =
1/2x
Al
gebr
aic
Expr
essi
ons
Addi
ng,
subt
ract
ing
and
mul
ti
ply
ing
algebr
aic
expr
essi
ons

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Page 2

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Pol
ynomi
al
­ somet
hing
that
j
ust
has
a s
ingl
e l
ett
er
rai
sed
to
any
power
e.g. Ax² + Axn1 + Ax3
Ascending/ descending powers ­ ordering powers
e.g. (descending power) 9x2 + 6x + 3
(ascending powers) 3 + 6x + 9x2
Degree ­ The biggest power in your polynomial
e.g.…read more

Page 3

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We can write the `sum' of an arithmetic progression using sigma:
e.g.
n = 47 - 14 a= 25/-3 d=2
33/2((2*25) +2(32)) = 1881
Simultaneous Equations
With simultaneous equations we have more than one unknown, each unknown takes the same value in each equations. To solve
simultaneous equations we need as many equations as unknowns. There are three ways of solving these:
1) Graphical ­ if we have 2 unknowns then we can plot both equations on a graph.…read more

Page 4

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We can use the "b2 - 4ac" part from our formula to determine whether or not the curves will pass through each other more than once,
once or never.
b2 - 4ac > 1 = Two or more solutions
b2 - 4ac = 0, One solution
b2 - 4ac< 0 = No solutions
E.g. x2 + 2x + 1. b2 - 4ac = (22 ­ 4 x 1 x 1) 0.…read more

Page 5

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Add one to the power
2) Divide the coefficient of x by the new power.
Graphs
Asymptote ­ the line that comes close to the curve but never quite touches it.…read more

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