IAS Maths Notes
Pure 1
, CHAPTER 1 : ALGEBRAIC EXPRESSIONS
11 Index Laws
am-index
↑
base
·
am Xan =
a
men ·
an =
· am + an = am
- n
·
an=am
·
(am)" =
amn ·
a -m-m
·
(ab)" = anbr ·
20 =
1 2
Expanding Brackets
.
The two term
product expressions found by multiplying each by eachother
·
is
of
(x + 5) (ix 2y+) -
= x(4x -
2y + 3)
+
5(4x 2y + 3) -
= 4x2 -
2xy
+
3x +
20x + 10y + 15
= 4x2 -
2xy + 23x -
10y + 15
3
1
Factorising
.
Expressions be written
product their factors
·
can as a of
3 x + 9 HeF is 3
= 3(x 3) +
·
Quadratic expressions are factorised differently
ax2 + bxx + c
1) find two factors of ae that add up to b
11) Rewrite the b term as the two factors
III) Factorise each
pair of terms
IV) Remove the common factor
* 5x-6 (factors 1
,
-6)
x2 + 1x -
6x -
6
x(x+) -
6(x + 1
-
(x -
G)(x 1) +
, 1 4 and Fractional Indices
Negative
.
·
The law of indices is used with
any rational power
>
- am =
ma >
-
an = am
>
-
am man >
-
a = 1
· at = the
positive
of only root of a
1 5 .
sures
any multiple of in
·
If n is not a square number, then is called a sure
·
Irrational numbers cannot be written in the form
-
A Surd is an irrational number
Surels
-
can be used to write exact answers to calculations
These surds
rules
manipulate
-
>
-
b =a xb
- =
wa = i
2 = x +g
= 3x22
= GE
denominators
↓ -
Rationalising
When
·
a surd is a denominator in a fraction ,
it can be rearranged so that
the denominator is rational
·
This is called rationalising the denominator
·
The rules in
rationalising are
S
, multiply the fraction by F
)
-
atts , multiply the fraction by (a -
56)
- multiply , the fraction by
Pure 1
, CHAPTER 1 : ALGEBRAIC EXPRESSIONS
11 Index Laws
am-index
↑
base
·
am Xan =
a
men ·
an =
· am + an = am
- n
·
an=am
·
(am)" =
amn ·
a -m-m
·
(ab)" = anbr ·
20 =
1 2
Expanding Brackets
.
The two term
product expressions found by multiplying each by eachother
·
is
of
(x + 5) (ix 2y+) -
= x(4x -
2y + 3)
+
5(4x 2y + 3) -
= 4x2 -
2xy
+
3x +
20x + 10y + 15
= 4x2 -
2xy + 23x -
10y + 15
3
1
Factorising
.
Expressions be written
product their factors
·
can as a of
3 x + 9 HeF is 3
= 3(x 3) +
·
Quadratic expressions are factorised differently
ax2 + bxx + c
1) find two factors of ae that add up to b
11) Rewrite the b term as the two factors
III) Factorise each
pair of terms
IV) Remove the common factor
* 5x-6 (factors 1
,
-6)
x2 + 1x -
6x -
6
x(x+) -
6(x + 1
-
(x -
G)(x 1) +
, 1 4 and Fractional Indices
Negative
.
·
The law of indices is used with
any rational power
>
- am =
ma >
-
an = am
>
-
am man >
-
a = 1
· at = the
positive
of only root of a
1 5 .
sures
any multiple of in
·
If n is not a square number, then is called a sure
·
Irrational numbers cannot be written in the form
-
A Surd is an irrational number
Surels
-
can be used to write exact answers to calculations
These surds
rules
manipulate
-
>
-
b =a xb
- =
wa = i
2 = x +g
= 3x22
= GE
denominators
↓ -
Rationalising
When
·
a surd is a denominator in a fraction ,
it can be rearranged so that
the denominator is rational
·
This is called rationalising the denominator
·
The rules in
rationalising are
S
, multiply the fraction by F
)
-
atts , multiply the fraction by (a -
56)
- multiply , the fraction by
