# Core 3 Notes Edexcel

notes for core 3, edexcel exam board but i think they generally overlaps with a few other exam boards

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- Created on: 06-06-11 14:07

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## Pages in this set

### Page 1

Al

gebr

aic

Fr

act

i

o ns

An

algebrai

c f

ract

i

o n

can al

w ays

be expr

essed

in

differ

ent

,

yet

equival

ent

for

ms.

A

f

ract

ion

is

expressed

in

it

s si

mp l

est

for

m by

cancell

i…

gebr

aic

Fr

act

i

o ns

An

algebrai

c f

ract

i

o n

can al

w ays

be expr

essed

in

differ

ent

,

yet

equival

ent

for

ms.

A

f

ract

ion

is

expressed

in

it

s si

mp l

est

for

m by

cancell

i…

### Page 2

The

set

of

a l

l

numb ers

that

we can

feed i

nto

a funct

ion

is

call

ed t

he

doma i

n of

the

funct

ion.

The

set

of

a l

l

numb ers

that

t

h e

funct

ion

produces i

s cal

led

the r…

set

of

a l

l

numb ers

that

we can

feed i

nto

a funct

ion

is

call

ed t

he

doma i

n of

the

funct

ion.

The

set

of

a l

l

numb ers

that

t

h e

funct

ion

produces i

s cal

led

the r…

### Page 3

For

exampl

e,

consi

der

t

he

expr

essi

on

y = ±x .

Noti

ce

that

any val

ue

o f

x

in

the

doma i

n,

e xc ept

x = 0

,

(

i.

e.

any posi

ti

ve r

eal

numb er)

i

s mapped to…

exampl

e,

consi

der

t

he

expr

essi

on

y = ±x .

Noti

ce

that

any val

ue

o f

x

in

the

doma i

n,

e xc ept

x = 0

,

(

i.

e.

any posi

ti

ve r

eal

numb er)

i

s mapped to…

### Page 4

Consi

der

t

he

simpl

e,

li

near

f

unct

ionf (

x)

=

3x

27.

I

f

w e

feed

x =

2 i

nto

thi

s f

unct

ion,

we

get

out

f (

2)

=

21.

Suppose

that

we

are

tol

d t

hat

t

he

funct…

der

t

he

simpl

e,

li

near

f

unct

ionf (

x)

=

3x

27.

I

f

w e

feed

x =

2 i

nto

thi

s f

unct

ion,

we

get

out

f (

2)

=

21.

Suppose

that

we

are

tol

d t

hat

t

he

funct…

### Page 5

The

Modul

us

Funct

ion

The mo du lu s sig n in d i

c ate s tha t

w e ta k e t

h e ab s o lu t e va l

u e o f

th e expr

essi

on

insi

de

the

mod u…

Modul

us

Funct

ion

The mo du lu s sig n in d i

c ate s tha t

w e ta k e t

h e ab s o lu t e va l

u e o f

th e expr

essi

on

insi

de

the

mod u…

### Page 6

To

sol

ve

the

equat

ion

|ax + b| = |cx + d|

it

i

s easi

est

t

o squar

e bot

h si

des

to

remove

the

modul

us si

gn.

Equat

ions

of

the

for

m |ax + b| = cx + d

need

to

be

sol…

sol

ve

the

equat

ion

|ax + b| = |cx + d|

it

i

s easi

est

t

o squar

e bot

h si

des

to

remove

the

modul

us si

gn.

Equat

ions

of

the

for

m |ax + b| = cx + d

need

to

be

sol…

### Page 7

Numer

ical

Met

hods

I

n rea l lif

e si

tuat

ions , w e ar e o ften

faced wi

th

equa ti

o n s

w h i

c h ha ve n o ana l

ytic

s o l

ution.

Th at is to

say we…

ical

Met

hods

I

n rea l lif

e si

tuat

ions , w e ar e o ften

faced wi

th

equa ti

o n s

w h i

c h ha ve n o ana l

ytic

s o l

ution.

Th at is to

say we…

### Page 8

t

hat

t

he

sol

uti

on

is

somewher

e ar

ound

x = 0.7

.

We

noti

ce t

h at

t

o t

he

lef

t

of

the

root

,

the

funct

ion

is

posi

ti

ve

and

to

the

ri

ght

of

t

he

root

t

he…

hat

t

he

sol

uti

on

is

somewher

e ar

ound

x = 0.7

.

We

noti

ce t

h at

t

o t

he

lef

t

of

the

root

,

the

funct

ion

is

posi

ti

ve

and

to

the

ri

ght

of

t

he

root

t

he…

### Page 9

Exponent

ial

and

Log

Funct

ions

The

exponent

ial

f

uncti

on

(e) a n d the

n a t

u ra l

logar

it

hm

funct

ion

(l

n)

are

bot

h t

he

inver

se

oper

ati

ons

of

one anot

her.

eln(

x) = ln x

(e…

ial

and

Log

Funct

ions

The

exponent

ial

f

uncti

on

(e) a n d the

n a t

u ra l

logar

it

hm

funct

ion

(l

n)

are

bot

h t

he

inver

se

oper

ati

ons

of

one anot

her.

eln(

x) = ln x

(e…

### Page 10

Tr

igonomet

ry

For

o ne to one f

uncti

ons,

you

can draw i

ts i

nver

se graph by r

efl

ecti

ng i

t

in

the

li

ne y

= x.

The three

tr

ig

funct

ions

sin(

x ),

cos (

x)

an d t

an(x)…

igonomet

ry

For

o ne to one f

uncti

ons,

you

can draw i

ts i

nver

se graph by r

efl

ecti

ng i

t

in

the

li

ne y

= x.

The three

tr

ig

funct

ions

sin(

x ),

cos (

x)

an d t

an(x)…

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