1)Remember first 25 Prime numbers
2,3,5,7,97
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1
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-1,3,7,9
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2
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5
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8
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-3,9
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3
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6
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1,7
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4
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- 1,3,7
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7
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- 1,3,9
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1.
a2 – b2 = (a – b)(a + b)
2.
(a+b)2 = a2 + 2ab + b2
3.
a2 + b2 = (a – b)2 + 2ab
4.
(a – b)2 = a2 – 2ab + b2
5.
(a + b + c)2 = a2 + b2 + c2 + 2ab + 2ac +
2bc
6.
(a – b – c)2 = a2 + b2 + c2 – 2ab – 2ac +
2bc
7.
(a + b)3 = a3 + 3a2b + 3ab2 + b3 ; (a + b)3 =
a3 + b3 + 3ab(a + b)
8.
(a – b)3 = a3 – 3a2b + 3ab2 – b3
9.
a3 – b3 = (a – b)(a2 + ab + b2)
10.
a3 + b3 = (a + b)(a2 – ab + b2)
11.
(a + b)3 = a3 + 3a2b + 3ab2 + b3
12.
(a – b)3 = a3 – 3a2b + 3ab2 – b3
13.
(a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4)
14.
(a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4)
15.
a4 – b4 = (a – b)(a + b)(a2 + b2)
16.
a5 – b5 = (a – b)(a4 + a3b + a2b2 + ab3 +
b4)
17.
If n is a natural number, an – bn = (a – b)(an-1 + an-2b+…+
bn-2a + bn-1)
18.
If n is even (n = 2k), an + bn = (a + b)(an-1 – an-2b
+…+ bn-2a – bn-1)
19.
If n is odd (n = 2k + 1), an + bn = (a + b)(an-1 – an-2b
+…- bn-2a + bn-1)
20.
(1+2+3+…+n)=n(n+1)/2=AVG/(n+1)/2
21.
(12+22+32+…n2)=n(n+1)(2n+1)/6
22.
(13+23+33+….n3)=[n(n+1)/2]2 =n2(n+1)2/4
23.
Arithmetic Progressions
a, a+d,a+2d,a+3d,…..
first term=a, common difference=d
Let
the nth term tn and let last term=tn=l then
a)
nth term=a+(n-1)d
b)
sum of n terms =n/2[2a+(n-1)d]
24.
Geomantic Progressions a,ar,ar2,ar3,…in
GP first term=a, common difference=r
n th term=a+(n-1)d
sum of n terms
a)
a(1-rn)/1-r where
r<1
b)
a(rn -1)/r-1 where
r>1
25.
L.C.M X H.C.F = a X b
26.
H.C.F=(H.C.F of
Numerators)/(L.C.M of Denominators)
27.
L.C.M=(L.C.M of
Denominators)/ (H.C.F of Numerators)
28.
Time and Work Formula
M=Men,T=Time,W=work
MxT/(RS/W)
29.
BODMAS RULE
Brackets of,Divison,Multiplication,Addition,subtraction
30.
Average=(sum of Observation)/(no of Observation)
31. AverageSpeed=2xy/(x+y) kmph
32.
Price of commodity increases by r% then the reduction is
consumption so as not to increase the expenditure
[r/(100+r)X 100]%
33.
Price of commodity decrease by r% then the increase in
consumption so as to decreases the expenditure
[r/(100-r)X 100]%
34.
Population increase or decrease by R% rate per annum
a)
Population after n years=p(1+(r/100))n increases r%
b)
Population after n years=p(1-(r/100))n decrease r%
c)
Population n years ago= p/(1+(r/100))n increases r%
d)
Population n years ago= p/(1-(r/100))n decrease r%
35.
C.P=Cost Price S.P=selling Price Profit(or) gain=S.P-C.P loss=C.P-S.P
a)
X%= X x 100/C.P where X=profit
/loss
b)
S.P/C.P= (100+X%)/100 where
X% Profit
c)
S.P/C.P= (100-X%)/100 Where
X% loss
36.
If an article is sold at
again of say 35% then S.P=135% of C.P
37.
If an article is sold at
loss of say 35% then S.P=65% of C.P
38.
When a person sells 2
similar items, one at a gain of say x%
and other at a loss of x%,then the
seller always incurs a loss given by
Loss%=(common loss and gain%/10)2 =(x/10)2
39.
If a trader professes to
sell his goods at cost price, but uses false
weights then
Gain%=[error/(trueValue-error)X
100)]%
40.
a/b = a:b
(ancedent:consequent)
a:b=c:d =>
(bXc)=(aXd)
a/b=c/d =>
[ a+b/(a-b)=c+d/(c-d)]
41.
Time and Work
tA=Time taken to A to complete a
work tB=Time taken to B to complete a work
tAB=Time
taken to AB to complete a work
tAB=[
(tA x tB)/( tA+ tB)] (OR) tAB=[(1/ tA)+(1/tB)]
42.
s=Speed, d=distance
,t=time
S=d/t
43. x km/hr=[X
x (5/18)] m/sec x m/sec=[X x (18/5)] km/hr
44.
where a=distance of faster train, b is
distance of slower train u is the
velocity of faster train and v is the velocity of slower train
Faster
train to cross slower train=(a+b)/(u-v) sec
45.
If 2 trains coming in
opposite direction when they will meet each other
AS:BS = Sqrt of b :Sqrt of a where a,b is distance and AS,BS is
velocity of trains
46.
If the speed of a boat is
still water is u km/hr and the speed of the stream is v km/hr then
a)
Speed of Downstream SD=(u+v) km/hr
(same direction of boat and stream)
b)
Speed of Upstream SD=(u-v) km/hr
(opposite direction of boat and stream)
47.
If the speed downstream
is a km/hr & speed upstream is b
km/hr then
a)
Speed in still water=(a+b)/2
km/hr
b)
Rate of stream =(a-b)/2
km/hr
48.
Rule of allegation: if 2 ingredients
are mixed then
(Quality of cheaper)/(Quality of dearer)=
[(C.P of dearer- mean Price) /(mean
price -C.P of cheaper)]
49.
Suppose a container
contains x units of liquid from which y units are taken out and replaced by
water. After n operations,the quality of pure liquid
[x(1-(y/x))n] units
50.
P=principal (or) sum R =rate T=time S.I=simple interest
S.I=[PTR/100]
51.
For Compound interest
P=principal
(or) sum R=rate per annum T= n years A=Amount
a)
Annually compound interest A=[p(1+(r/100))n]
b)
When interest compounded
Half early A=[p(1+((r/2)/100))2n]
c)
When interest compounded Quartly
early A=[p(1+((r/4)/100))4n]
d)
Annually compound interest,
but time is in fraction like 3 X2/5 years
A=[p(1+(r/100))3
X ((1+((2/5)/100)))]
52.
When rates are different for
different years,say r1%,r2%,r3% for 1 st,2 nd and 3 rd year respectively then
amount
A=p(1+(r1/100))X(1+(r2/100))X(1+(r3/100))
Your
got X rupees of n years Present Worth=[X/(1+(r/100))n]
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