Formulas Flashcards
a * b =
LCM(a. b) * HCF(a . b)
LCM of p³q and q4p
p³q4
if we have to find at what time two or three bells will ring at same time
find LCM
Quadratic equation form
ax²+bx+c=0
Cubic equation form
ax³+bx²+cx+d=0
How many zeros will quadratic and cubic equation will have respectively
2 and 3
If ax³+bx²+cx+d is completely divisible by ax²+bx+c that means
α and β of quadratic equation also will be the two zeros of cubic equation .
α+β=
-b/a
αβ=
c/a
Quadratic equation in the form of (α+β) & αβ
x² - (α+β)x + αβ = 0
α²+β²=
(α+β)² - 2αβ
α³+β³=
(α+β)³ - 3αβ(α+β)
1/α + 1/β =
(α+β)/αβ
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
5
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
3
Condition for coincident lines
a1/a2 = b1/b2 = c1/c2 (infinitely many solutions)
Condition for intersecting lines
a1/a2 not equals to b1/b2(only one solution)
Condition for parallel lines
a1/a2 = b1/b2 not equals to c1/c2(no solutions)
Formula to find x of equation ax²+bx+c=0
x = (-b +- √D)/ 2a
Formula of discriminant
D = b²-4ac
If D = 0
equal roots
If D > 0
different roots
If D < 0
no real roots
an =
a +(n-1)d
Sn =
n/2 (2a + (n-1)d)
Formula of Sn with l
Sn = n/2 ( a + l )
Distance Formula =
√(x2-x1)² + (y2-y1)²
Section formula =
(mx2 + nx1)/ m+n
Similarity criteria for triangles
SSS.(ratio) SAS. AAA.
The tangent at any point of a circle is ——– to the radius through the point of contact
perpendicular
The lengths of tangents drawn from an external point to a circle are
equal.
Sin x
= P/H
cos x
= B/H
Tan x
= P/B
Sec x
= H/B
Cosec x
= H/P
Cot x
= B/P
Tan30
= 1/√3
Sin30
= 1/2
Cos30
= √3/2
Tan45
= 1
Sin45
= 1/√2
Cos45
= 1/√2
Tan60
= √3
Sin60
= √3/2
Cos60
= 1/2
Sin0
= 0
Tan0
= 0
Cos0
= 1
Tan90
= infinite
Cos90
= 0
Sin90
= 1
Three identity of trigonometry
Sin²x + Cos²x = 1. Sec²x - Tan²x = 1. Cosec²x - Cot²x = 1.
For a triangle with 30° angle if B = x what will be P and H
x/√3 and 2(x/√3)
For a triangle with 60° angle if B = x what will be P and H
x√3 and 2x.
Area of a sector with center angle x°
(x°/360°) * πr²
Area of segment with centre angle x°
(x°/360°) * πr² - area of triangle.
Length of chord with centre angle x°
(x°/360°) * 2πr
TSA of cuboid
2(lb+bh+hl)
LSA of cuboid
2(bh+hl)
Volume of cuboid
lbh
TSA of cube
6a²
LSA of cube
4a²
Volume of cube
a³
TSA of cylinder
2πr(r+h)
LSA of cylinder
2πrh
Volume of cylinder
πr²h
TSA of sphere
4πr²
Volume of sphere
4/3 πr³
TSA of hemisphere
3πr²
LSA of hemisphere
2πr²
Volume of hemisphere
2/3 πr³
TSA of cone
πr(l+r)
slant height l =
√h²+r²
CSA of cone
πrl
Volume of Cone
1/3 (πr²h)
If base angel is 45° with B = x, then P and H are..
x and x√2
Another name of mean and it’s formulae
Average ,
x = ( sum of all observation ) / ( no. of observation)
Class mark(xi) =
(Upper limit +Lower limit) / 2
Direct method mean formula
x = Σ (fi . xi) / Σ (fi)
assume mean method Formula
x = a + [ Σ (fi. di) / Σ (fi) ]
formula of deviation (di)
xi - a , ‘a’ is assumed mean from xi
To find median we have to find first
All cumulative frequency (cf). By adding fi
2nd step of finding median.
Find total number ‘N’ of fi ( which is last cf)
next step to find median after finding N.
Find N/2 ,
how to find median class
Class with cf greater than N/2
What is ‘h’ in the formula of median
Class size = upper limit - lower limit
What is ‘l’ in the formula of median
Lower limit of median class
what is the formula of median
l + [ ( N/2 - cf) / f ] * h
Mode means…
Data with maximum frequency
formula of mode..
l + [ ( f1-f0 ) / (2f1 - f0 - f2) ] * h
What does f1, f0, f2 mean.
f0 = frequency preceding of modal
f1 = frequency of modal class
f2 = frequency successive of modal class
(x+a) (x+b) =
x² + (a+b)x + ab
