Search for notes by fellow students, in your own course and all over the country.
Browse our notes for titles which look like what you need, you can preview any of the notes via a sample of the contents. After you're happy these are the notes you're after simply pop them into your shopping cart.
Document Preview
Extracts from the notes are below, to see the PDF you'll receive please use the links above
Algebra,Algebra of Expressions
1
...
(a − b)2 = a2 − 2ab + b2 ; a2 + b2 = (a − b)2 + 2ab
3
...
(a + b)3 = a3 + b3 + 3ab(a + b); a3 + b3 = (a + b)3 − 3ab(a + b)
5
...
a2 − b2 = (a + b)(a − b)
7
...
a3 + b3 = (a + b)(a2 − ab + b2 )
9
...
an = a
...
a
...
am
...
n = am−n if m > n
a
=1
if m = n
1
= n−m if m < n; a ∈ R, a 6= 0
a
13
...
(ab)n = an
...
= n
b
b
16
...
a−n = n , an = −n
a√
a
18
...
If am = an and a 6= ±1, a 6= 0 then m = n
20
...
If x, y are quadratic surds and if a + x = y, then a = 0 and x = y
√ √
√
√
22
...
If a, m, n are positive real numbers and a 6= 1, then loga mn
= loga m+loga n
m
24
...
If a and m are positive real numbers, a 6= 1 then loga mn = n loga m
logk a
26
...
logb a =
where a, b are positive real numbers, a 6= 1, b 6= 1
loga b
28
...
if a + ib = 0
√
−1, then a = b = 0
√
where i = −1, then a = x and b = y
where i =
30
...
The roots of the quadratic equation ax2 +bx+c = 0; a 6= 0 are
(
The solution set of the equation is
√
√ )
−b + ∆ −b − ∆
,
2a
2a
−b ±
√
b2 − 4ac
2a
where ∆ = discriminant = b2 − 4ac
32
...
33
...
34
...
35
...
of x
=−
i) α + β =
a
coeff
...
of x2
36
...
e
...
e
...
37
...
P
...
i) nth term= tn = a + (n − 1)d
ii) The sum of the first (n) terms = Sn =
where l =last term= a + (n − 1)d
...
For a geometric progression (G
...
) whose first term is (a) and common ratio
is (γ),
i) nth term= tn = aγ n−1
...
if γ = 1
39
...
n
P
n
40
...
2
γ=1
n
P 2
n
41
...
6
γ=1
3
42
...
4
43
...
(2)
...
(n − 1)
...
44
...
45
...
46
...
n(n − 1) n−2 2 n(n − 1)(n − 2) n−3 3
a
b +
a
b +···+
2!
3!