Mathematics
1. Formulas of Derivatives and anti-derivative
2.
Permutation of different word
In
how many ways these words can be arranged
A.STATISTICS
B.PAKISTAN C.MATHEMATICS D.DOLLAR E.APRIL
The
formula of permutation is
P
=
n!
n
!, n !, n !, … … . . n !
A.STATISTICS
n=
10 s×3=3 T×3=3 I×2=2 A×1=1 C×1=1
P
=
10!
3!
∗ 3! ∗ 2! ∗ 1! ∗ 1!
P
=
10
∗ 9 ∗ 8 ∗ 7 ∗ 6 ∗ 5 ∗ 4 ∗ 3 ∗ 2 ∗ 1
3
∗ 2 ∗ 1 ∗ 3 ∗ 2 ∗ 1 ∗ 2 ∗ 1 ∗ 1 ∗ 1
P
=
3628800
72
P
= 50400ways
B.PAKISTAN
The
solving method is same as Statistics
P=20160
C.MATHEMATICS
The
solving method is same as Statistics
P=4989600
D.DOLLAR
The
solving method is same as Statistics
P=360
E.APRIL
The
solving method is same as Statistics
P=120
F.PAKPATTAN
The
solving method is same as Statistics
P=15120
G.ATTACKED
The
solving method is same as Statistics
P=10080
H.PANAMA
The
solving method is same as Statistics
P=120
3. Combination
4. Series
Find the 15th term of the A.P (Arithmetic
progression)
Tn
=term of the sequence
a
(a+d)(a+2d)………………(n-1)d
5
1
2
,6,6
1
2
,7,
… … … … …
1st term a=5
d=6-5 = n=15
Tn=a+(n-1)d
Tn=5 +(15-1)
Tn=5
+(14) Tn= + 7
Tn=
Tn= Ans
What
term of the A.P is if Tn=125
5,
10,15,20,25 n=?
Tn=125
a=5 d=10
Tn=a+
(n-1)d 125=5+(n-1)10
125=5+10n-10
125=10n-5
130=10n
n=13 Ans
Sum
of series
Sn=
{2a+(n-1)d}
Sn=Sum
of the series to the n terms
Find
the sum to 10 terms of the sequence
3,
10,17,24,31
A=3
d=7 n=10
Sn=
{2*3+(10-1)7} Sn=5{6+63}
Sn=5(69)
Sn=345Ans
Important
Question long course initial tests
1.∫ SecxTanx =
Secx + c
2.cos α + cos β
= 2 cos (α + β) cos (α - β)
3.cos(α - β )=cosαcosβ+SinαSinβ
4.Z
= a+ib then |Z|=√a + b
5.If
f(x)=0 then y=f(x)=0
6.
If L=1 , T=3 , E=2 R=4 then LETTER÷5 =?
LETTER=
× × × × × = =28.8Ans
7.If
Z = 4+5i then |z|= √16 + 25=√41
8.Sin(180-x)=Sinx
9.
Z = (a, b)Z = (c, d)ThenZ Z = (ac -
bd)
10.
If a.b=0 then a× b = 1
11.∫ e = e + c
12.
Period of Tanx=π
13.
Period of Sinx =2π
14.
∫ Tanx = lnSinx + c
15.
, 1: 3then , 1: 4
16.
( ° ) = -Cosx
17.Factorize
the equationx - 13x + 12
x=±1x = ±2√3
18.∫ sinxcotx =
-cosx + c
19.
is1: 3then is5: 9
20.
Time is to emit then 43501 is to 10534
21.
Compare isto 3246157 thenOpera is to 26751
22.
If Z=(x-iY) then |Z|= x + y
23.If
the distance from A to B is 2 feet and B to C is 2 feet then the distance
between A to C
=4feet
24.
Reciprocalof A.P is H.P
25.tan 90° = ∞
26.tan 270° = ∞
27.
If a=2 d=3 Tn=47 then n=?
Tn=a+(n-1)d
47=2+(n-1)3
47=2+3n-3
47=3n-1
48=3n
n=16 Ans
28.-1× i × -i × 3
= -3
29.x+y=0
x-y=0 then distance will be o
30.x - 7x + 11 =
0rootoftheequationr = 1
31.a=3
d=5 Sn=368 n=?
Sn=
{2a+(n-1)d} putting the values of all number and find n
32.2x-5=x+7
then find x=?
X=12
33.sin -x =
√
34.tan(90° - x) = cot x
35.Formula
of G.P is ar
36.∫ Tanθ = ln
sec θ + c
37.
a+b=0 and a & b are real number then b=-a
38.sin(180° - x) = sin x
39.
Bisecter and triangle are called Altitude
40.
A.M of 26 and 36 is …….
26
+ 36
2
= 31
41.
∫ tanx = lnsecx + c
42.
( ) = -2sin2x
43.
If Z = (2+0i) then |Z|=2
44.P = 120
45.
P = 66formula !
( )!
46.∫ csc x = ln|
csc x - cot x| + c
47.sin θ + tan θ
cos θ = 2 sin θ
48.
Peroidic function of sin x = 2 π
49.
Peroidic function of cot x = π
50.∫ cot x = ln|
sin x| + c
51.cos(90° - x) = sin x
52.
Equation of parabola is y = 4ax
53.If
A= {1,2,3,4} B={2,4,5,6} then A-B={1,3}
54.
Distance formula is D= (x - x ) + (y - y )
55.
Find the first term of …3….5, 7,9,11
56.
Find the next term of the 36, 18……..9….
57.i = -1or√-1
58.P = 6P = !
( )! =
(
)( )!
( )! = n(n - 1)
3(3-1)
=3(2) = 6Ans
59.C = C = 20
60C = C = 16
5. Percentage
P =
%age
100
× givenvalue
Case-1
When
%age is in unit and given value is also in unit then.
1%
of 1 = 0.001
2%
of 2 = 0.04
3%
of 3 = 0.09
4%
of 4 = 0.16
5%
0f 5 = 0.25
Case-2
When
%age and given value both are double digits without zero then.
18%
of 18=3.24 15% of 15 = 1.44
17%
of 17 = 2.89 19% of 19 = 3.61
22%
of 34 = 7.48 45% of 65 = 29.25
Case-3
When
%age and given value both are double digits within zero then.
20%
of 90 = 18 30% of 70 = 21
Case-4
When
%age and given value are in double digits and triple digits within zero then.
30%
0f 180 = 54 20% of 120 = 24
Case-5
When
%age is in unit and given value in double digits having zero then.
2%
of 90 = 1.8 3% of 70 = 2.1
Case-6
When
%age is in unit and given value in triple digits within 2 zero then.
2%
of 900 = 18 7% of 400 = 28
Case-7
When
%age is in unit and given value in double digits without zero then.
5%
of 75 = 3.75 5% of 85 = 4.25
6. Profit %age
Profit = sale price- cost price
Profit
%age =
.
×
100
If
cost price of a mobile is 2000. It sale in 2050.find profit %age
P=2050-2000=50
P %age = ∗ 100 = 2.5%
7. Lost %age
Lost=C.P-S.P
Lost
%age =
.
×
100
If
C.P of a pen is 50 and sale in 40.find lost %age
Lost=50-40=10
L %age= ∗ 100 = 20%
8. Discount %age
D.P= C.P-D %age
If
C.P of a shoes is 350 and 15% discount. Find sale price
15%
of 350 = 52.50
S.P=
350-52.50= 297.5rupees
9. Poles
If a poles have 80 feet length
And
20% in underground find the length of outer side
20%
of 80 = 16
80-16
= 74 outer side length is 74´
10. DozenAnd KG
If 1 dozen eggs have 55 rupees find the value of 5 eggs
=
= 4.583priceof1eggis4.583priceof5eggsis 5*4.583 =
22.9166
If
the price of 40 kg rice is 1500 find the value of 9kg rice 337.5
11. Distance Time Speed
1. If a bus goes 900KM/H find the distance in 45 min
=
15 1min=15km 45min=15×45=675km
2.
If a car goes 160km/h find the time if it go 600km.
600
160
= 3.75h
3.
If a bike goes 240km in 6h find the speed in h. 240
6
= 40km/h
12. Multiplication
Multiplication of decimal
0.02×0.0003=0.00006
0.1×0.001=0.001
13. Division
Division of decimal
0.5÷0.005=100
0.5÷0.25=2 0.9÷0.03=30 0.7÷0.07=10 0.1÷0.0001=1000
14. Greater fraction
Cross
product method
Which
is greater 2/3 or 3/4 2/3<3/4
1/3
or 3/9 1/3=3/9 , 3/4 or 5/7 3/4>5/7
15. Half of any number
Half of 1/7=1/14 half of 2/9=1/9
50%
of 3/11=3/22
16. Addition
1/2+2/3=5/6
3/4+3/2=9/4
17. Common
2+2×2÷2=4 2+2×2=6
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