Summary Edexcel IAS Level Pure Mathematics 1 Complete Notes

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