# Core 3 Notes Edexcel

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

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

First 678 words of the document:

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

n g

any

fact

ors

w hi

ch

are

common

to

bot

h t

he nume r

ator

and t

he denominator

.

Al

gebrai

c Fract

ions

can be

simpli

fi

ed by

cancel

li

ng down.

To do t

his,

numerat

ors

and

denomi

n at

ors

mu st

be f

ull

y

factor

ised

fi

rst

.

If

t

here

are

fract

i

o ns

w i

thi

n t

he

numerat

or/

d enominator

,

mu l

ti

ply

by a

commo n f

act

or t

o get

ri

d of

t

hese and

creat

e an

equi

val

ent f

ract

ion:

1 x+1 ( 1 x+1)×6 3(x+2)

2

1 2 = ( 2

1

x+ 2 )×6

= 3x+6 3

2x+4 = 2(x+2) = 2

3 x+ 3 3 3

To

mu l

ti

ply

fr

acti

ons,

simpl

y mul

ti

ply

the

nume r

ator

s and

mu l

ti

ply

the

denomina t

ors.

I

f

possi

ble,

cancel

down

fi

rst

.

To

divi

de by

a f

ract

ion,

mul

ti

ply

by t

he reci

procal

of

t

he

f

ract

ion:

x+1 3 3(x+1)

2 × x2-1 = x+1 3 3

2 × (x+1)(x-1) = 2(x+1)(x-1) = 2(x+1)

To

add or

subt

ract

f

ract

ions,

t

hey must

have

the

same denomi

nat

or.

Thi

s i

s done

by

f

indi

ng

the

lowest

commo n mult

i

p l

e of

t

he

denominat

ors:

1 4 1(x+6) 4(x+1) (x+6)+4(x+1) 5x+10

(x+1) + (x+6) = (x+1)(x+6) + (x+6)(x+1) = (x+1)(x+6) = (x+1)(x+6)

When

the

nume rat

or

has t

he same

or

a hi

gher

degr

ee

than

the

denominator

(

it

i

s

an

i

mproper

f

ract

ion)

,

you c

a n

divi

de

the

ter

ms t

o pr

oduce

a mi

xed f

ract

ion:

Funct

ions

Funct

ions

are speci

al

types

of

mappings

su ch

that

ever

y el

eme nt

of

t

he domain

is

ma pped

to

exact

l

y one el

eme nt

i

n

the

range.

Thi

s i

s i

l

lustr

ated

below f

or

the

funct

ion

f

(x)

=

x +

2

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