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10th > Formulas > Flashcards

Formulas Flashcards

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1
Q

a * b =

A

LCM(a. b) * HCF(a . b)

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2
Q

LCM of p³q and q4p

A

p³q4

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3
Q

if we have to find at what time two or three bells will ring at same time

A

find LCM

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4
Q

Quadratic equation form

A

ax²+bx+c=0

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5
Q

Cubic equation form

A

ax³+bx²+cx+d=0

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6
Q

How many zeros will quadratic and cubic equation will have respectively

A

2 and 3

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7
Q

If ax³+bx²+cx+d is completely divisible by ax²+bx+c that means

A

α and β of quadratic equation also will be the two zeros of cubic equation .

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8
Q

α+β=

A

-b/a

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9
Q

αβ=

A

c/a

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10
Q

Quadratic equation in the form of (α+β) & αβ

A

x² - (α+β)x + αβ = 0

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11
Q

α²+β²=

A

(α+β)² - 2αβ

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12
Q

α³+β³=

A

(α+β)³ - 3αβ(α+β)

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13
Q

1/α + 1/β =

A

(α+β)/αβ

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14
Q

If a curve cuts x-axis and y-axis. 3 times and 5 times respectively then equation ay²+by+c will have how many zeros

A

5

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15
Q

If a curve cuts x-axis and y-axis. 3 times and 5 times respectively then equation ax²+bx+c will have how many zeros

A

3

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16
Q

Condition for coincident lines

A

a1/a2 = b1/b2 = c1/c2 (infinitely many solutions)

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17
Q

Condition for intersecting lines

A

a1/a2 not equals to b1/b2(only one solution)

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18
Q

Condition for parallel lines

A

a1/a2 = b1/b2 not equals to c1/c2(no solutions)

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19
Q

Formula to find x of equation ax²+bx+c=0

A

x = (-b +- √D)/ 2a

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20
Q

Formula of discriminant

A

D = b²-4ac

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21
Q

If D = 0

A

equal roots

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22
Q

If D > 0

A

different roots

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23
Q

If D < 0

A

no real roots

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24
Q

an =

A

a +(n-1)d

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25
Sn =
n/2 (2a + (n-1)d)
26
Formula of Sn with l
Sn = n/2 ( a + l )
27
Distance Formula =
√(x2-x1)² + (y2-y1)²
28
Section formula =
(mx2 + nx1)/ m+n
29
Similarity criteria for triangles
SSS.(ratio) SAS. AAA.
30
The tangent at any point of a circle is -------- to the radius through the point of contact
perpendicular
31
The lengths of tangents drawn from an external point to a circle are
equal.
32
Sin x
= P/H
33
cos x
= B/H
34
Tan x
= P/B
35
Sec x
= H/B
36
Cosec x
= H/P
37
Cot x
= B/P
38
Tan30
= 1/√3
39
Sin30
= 1/2
40
Cos30
= √3/2
41
Tan45
= 1
42
Sin45
= 1/√2
43
Cos45
= 1/√2
44
Tan60
= √3
45
Sin60
= √3/2
46
Cos60
= 1/2
47
Sin0
= 0
48
Tan0
= 0
49
Cos0
= 1
50
Tan90
= infinite
51
Cos90
= 0
52
Sin90
= 1
53
Three identity of trigonometry
Sin²x + Cos²x = 1. Sec²x - Tan²x = 1. Cosec²x - Cot²x = 1.
54
For a triangle with 30° angle if B = x what will be P and H
x/√3 and 2(x/√3)
55
For a triangle with 60° angle if B = x what will be P and H
x√3 and 2x.
56
Area of a sector with center angle x°
(x°/360°) * πr²
57
Area of segment with centre angle x°
(x°/360°) * πr² - area of triangle.
58
Length of chord with centre angle x°
(x°/360°) * 2πr
59
TSA of cuboid
2(lb+bh+hl)
60
LSA of cuboid
2(bh+hl)
61
Volume of cuboid
l*b*h
62
TSA of cube
6a²
63
LSA of cube
4a²
64
Volume of cube
a³
65
TSA of cylinder
2πr(r+h)
66
LSA of cylinder
2πrh
67
Volume of cylinder
πr²h
68
TSA of sphere
4πr²
69
Volume of sphere
4/3 πr³
70
TSA of hemisphere
3πr²
71
LSA of hemisphere
2πr²
72
Volume of hemisphere
2/3 πr³
73
TSA of cone
πr(l+r)
74
slant height l =
√h²+r²
75
CSA of cone
πrl
76
Volume of Cone
1/3 (πr²h)
77
If base angel is 45° with B = x, then P and H are..
x and x√2
78
Another name of mean and it's formulae
Average , x = ( sum of all observation ) / ( no. of observation)
79
Class mark(xi) =
(Upper limit +Lower limit) / 2
80
Direct method mean formula
x = Σ (fi . xi) / Σ (fi)
81
assume mean method Formula
x = a + [ Σ (fi. di) / Σ (fi) ]
82
formula of deviation (di)
xi - a , 'a' is assumed mean from xi
83
To find median we have to find first
All cumulative frequency (cf). By adding fi
84
2nd step of finding median.
Find total number 'N' of fi ( which is last cf)
85
next step to find median after finding N.
Find N/2 ,
86
how to find median class
Class with cf greater than N/2
87
What is 'h' in the formula of median
Class size = upper limit - lower limit
88
What is 'l' in the formula of median
Lower limit of median class
89
what is the formula of median
l + [ ( N/2 - cf) / f ] * h
90
Mode means...
Data with maximum frequency
91
formula of mode..
l + [ ( f1-f0 ) / (2f1 - f0 - f2) ] * h
92
What does f1, f0, f2 mean.
f0 = frequency preceding of modal f1 = frequency of modal class f2 = frequency successive of modal class
93
(x+a) (x+b) =
x² + (a+b)x + ab

10th (2 decks)

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