SQUARE LESS THAN 100

SQUARE  LESS THAN 100

 

Mathematics Sign

Mathematics sign

Important formula of Powers:

Important formula of Powers:

a^mxaⁿ  = a^m+n

aman=am−naman=am−n

(a^m)ⁿ  =  a^mn

(a^mbⁿ)^p =   a^mpb ^np

a^-m = 1am1am

amn=am−−−√namn=amn

Rules of Zero:

a¹  = a

a⁰ = 1

a*0 = 0

a is undefined

IMPORTANT MATHS FORMULAE FOR CLASS X BOARD EXAM

IMPORTANT MATHS FORMULAE FOR CLASS X BOARD EXAM

Important formula of Algebra:

1. (a + b)² = a² + 2ab + b²

2. (a – b)²  = a² – 2ab + b²

3. (a + b) (a – b) = a² – b²

4. (x + a)(x + b)  = x² + (a + b)x + ab

5. (x + a)(x – b)  = x² + (a – b)x – ab

6. (x – a)(x + b)  = x² + (b – a)x – ab

7. (x – a)(x – b)  = x²  – (a + b)x + ab

8. (a + b)³  = a³ + b³ + 3ab(a + b)

9. (a – b)³  =  a³ – b³ – 3ab(a – b)

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

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

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

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

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

15. x² + y²  = 1212 [(x + y)² + (x – y)²]

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

17. x³ + y³ = (x + y) (x² – xy + y²)

18. x³ – y³  = (x – y) (x² + xy + y²)

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

Mathematics sign

8th Class Student

MY STUDENT OF 8TH C LASS

Sahil Chopra

Pardeep chopra

Mathematics formule

Math formule

All math Formule upto 10th class

SOLID SHAPE FORMULE

SIN X- COS X   FORMULE

Important formula of Mensuration

Important formula of Mensuration

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

Important formula of Circles and Tangents

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 Equation of a line

Important formula of Equation of a line

• If two points are given, then Slope (m) = (y2-y1)/(x2-x1)
• If a point , and slope are given , then Slope (m)= (y-y1)/(x-x1)
• If two lines are ‘Parallel’ to each other then their slopes are equal i.e m1=m2.
• If two lines are ‘Perpendicular’ to each other then product of their slopes is -1 i.e m1 *m2 = -1
• Depending upon the question You may have to use equation of straight line as

a)      Y=mx + c, where ‘c’ is the y- intercept. OR    b) (y-y1)= m.( x-x1)

Important formula of Probability

Important formula of Probability

P(E) =   (Number of outcomes favorable to E)/ (Total Number of Possible Outcomes)

Probability of an event : P(event)= Number of favourable outcomes/ Total number of outcomes

If probability of happening an event is x then probability of not happening that event is (1-x).

(Spades in black colour ) having A,2,3,4,5,6,7,8,9,10,J,K and Q total 13 cards

(Clubs in black colour) having A,2,3,4,5,6,7,8,9,10,J,K and Q total 13 cards.

(Hearts in red colour) having A,2,3,4,5,6,7,8,9,10,J,K and Q total 13 cards.

(Diamond in red colour) having A,2,3,4,5,6,7,8,9,10,J,K and Q total 13 cards.

• Jack , king and queen are known as face cards.
• If one coin is tossed the total number of outcomes are 2 either a head or a tail.
• If two coins are tossed the total number of outcomes are 2*2 = 4
• If three coins are tossed the total number of outcomes are 2*2*2 = 8
• Similarly for dice, in a single roll total number of outcomes are 6
• If two Dices are rolled , total number of outcomes are 6*6 = 36.

TRIGONOMETRY FORMULA

Important formula of Trigonometry:

Wherever ‘square’ appears think of using the identities

•  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 )