Question

All important formulas for class 10 Maths C.B.S.E

Answer 1

Important formula of Algebra:

(a + b)2 = a2 + 2ab + b2

(a – b)2  = a2 – 2ab + b2

(a + b) (a – b) = a2 – b2

(x + a)(x + b)  = x2 + (a + b)x + ab

(x + a)(x – b)  = x2 + (a – b)x – ab

(x – a)(x + b)  = x2 + (b – a)x – ab

(x – a)(x – b)  = x2  – (a + b)x + ab

(a + b)3  = a3 + b3 + 3ab(a + b)

(a – b)3  =  a3 – b3 – 3ab(a – b)

(x + y + z) 2  = x2 + y2 + z2 + 2xy + 2yz + 2xz

(x + y – z) 2  =  x2 + y2 + z2 + 2xy – 2yz – 2xz

(x – y + z)2  = x2 + y2 + z2 – 2xy – 2yz + 2xz

(x – y – z)2  = x2 + y2 + z2 – 2xy +  2yz – 2xz

x3 + y3 + z3 – 3xyz  = (x + y + z)(x2 + y2 + z2 – xy – yz -xz)

x2 + y2  = 1212 [(x + y)2 + (x – y)2]

(x + a) (x + b) (x + c) = x3 + (a + b +c)x2 + (ab + bc + ca)x + abc

x3 + y3 = (x + y) (x2 – xy + y2)

x3 – y3  = (x – y) (x2 + xy + y2)

x2 + y2 + z2 -xy – yz – zx = 1212 [(x-y)2 + (y-z)2 + (z-x)2]

Important formula of Powers:

amxan  = am+n

aman=am−naman=am−n

(am)n  =  amn

(ambn)p =   ampb np

a-m = 1am1am

amn=am−−−√namn=amn

Rules of Zero:

a1  = a

a0 = 1

a*0 = 0

a is undefined

Important formula of Similarity

 If two triangles are similar then, ratio of their sides are equal.

i.e if triangle ABC~ triangle PQR then AB/PQ = BC/QR = AC/PR

If triangle ABC ~ triangle PQR then (Area of triangle ABC)/ Area of triangle PQR) = (side*side) /(side*side) = ( AB*AB) /( PQ*PQ) =( BC*BC)/( QR*QR) = (AC*AC)/ (PR*PR)


Important formula of Trigonometry



 sin^2(x) + cos^2(x) = 1

tan^2(x) + 1 = sec^2(x)

cot^2(x) + 1 = csc^2(x)

tan(x+ y) = (tan x +tan y) / (1 – tan x tan y)

sin(2x) = 2 sin x cos x

cos(2x) = cos^2(x) – sin^2(x) = 2 cos^2(x) – 1 = 1 – 2 sin^2(x)

tan(2x) = 2 tan(x) / (1 – tan^2(x))

sin^2(x) = 1/2 – 1/2 cos(2x)

cos^2(x) = 1/2 + 1/2 cos(2x)

sin x – sin y = 2 sin( (x – y)/2 ) cos( (x + y)/2 )

cos x – cos y = -2 sin( (x – y)/2 ) sin( (x + y)/2 )


Important formula of Circles and Tangents

Equal chords of a circle are equidistant from the centre .( Chord Property)

The perpendicular drawn from the centre of a circle, bisects the chord of the circle. (Chord Property)

The angle subtended at the centre by an arc= Double the angle at any part of the circumference of the circle .(Angle Property)

Angles subtended by the same arc in the same segment are equal.(Angle property)

To a circle, if a tangent is drawn and a chord is drawn from the point of contact , then angle made between the chord and the tangent = angle made in the alternate segment(Tangent property)

The sum of opposite angles of a cyclic quadrilateral is always 180 degree.

Important formula of Circumference and area of a circle

Area of a circle = pi(r*r)

Perimeter of a circle = 2*pi*r

Area of sector = theta/360 ( pi*r*r)

Length of an arc = theta / 360 (2*pi*r)

Area of ring = pi (R*R- r*r)

Distance moved by a wheel in one revolution = Circumference of the wheel.

Number of revolutions=Total distance moved/Circumference of the wheel.

Important formula of Solids

 Cylinder  : Volume of a cylinder= pi* r*r *h

Curved surface area = 2*pi*r*h

Total surface area = 2*pi*r*h + 2*pi*r*r = 2*pi*r ( h+r)

Volume of hollow cylinder = pi * R*R*h- pi*r*r*h= pi(R*R-r*r) h

TSA of hollow cylinder = Outer CSA + Inner CSA+ 2. Area of ring .

Cone: Volume  of a cone =1/3  pi*r*r*h

CSA of a cone = pi*r*l( here ‘l’ refers to ‘slant height’) [where l= [(h*h + r*r)]^.5

TSA of a cone = pi*r*l + pi*r*r = pi*r (l+r)

Sphere  :  Surface area of a sphere = 4*pi*r*r( Incase of sphere , CSA=TSA i.e they are same)

Volume of hemisphere = 2/3 pi*r*r*r [take half the volume of a sphere]

CSA of hemisphere = 2*pi*r*r [Take half the SA of a sphere]

TSA of hemisphere= 2*pi*r*r+pi*r*r = 3*pi*r*r

Volume of a sphere = 4/3 pi*r*r*r

Volume of spherical shell= Outer volume-Inner volume = 4/3*pi*(R^3-r^3)

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