14 formula use in solving mathematics for all school students.

I took my time to put these formulas together to help my learners learn mathematics easily.
With these formulas you can't fail mathematics again.

1.Rank correlation coefficient (speraman's)
P = 1- 6£d²/N(N² - 1)

2.Mensuration:
Length of arc = ø/360 x 2ňr

Area of sector = ø/360 x ňr²

3.Cone
Area of curved surface. = ňrl

Volume. = ¹/3ñr²h

4.Cylinder
Area of curved surface. 2ňrh

Volume. = ňr²h

ň=22/7 or 3.142
5.Motion with constant acceleration
V=u + at

S = ut + ½at²

V² = u² + 2as

S = ½(u + v)t

6.Trapezium rule
b

] f(x)dx=½h(Yo + yn) + 2(y1

a

+y2+y3....yn-1)

h= b-a/n n = number of stripes.

= 1/2h[(1st + last ordinate) + h(sum of all other ordinate)]

7.Simpson's rule
b

[ f(x)dx = 1/3h ( Y0 +yn) + 4(y1 + y3..) +2(y2 + a

y4+..)

1/3h[(first + last ordinate + (4x sum of even orienate)+ (2x sum of remaining odd ordinate)]

8.Sequence
Linear

Ist term = a

Constant differences = d

The nth term is given by the mapping

n = a+(n - 1)d

And the sum of the first n term is given by

½n[2a + (n - 1)] or ½n(a -l)

Where l is the last term

EXPONENTIAL

for an exponential sequence whose

Ist term = a

Constant ratio = r

The nth term is given by the mapping

n = arª~¹

And the sum of the first n term is given by

a = 1- rª/1-r or a = rª - 1/r -1

And the limit of this sum is a/1 - r

9.Equation of a straight line
Ya - Yb/Xa - Xb = m

Ya - Yb = m (Xa - Xb)

Equation of line between two point

Y - Ya/X - Xa = Yb -Ya/Xb -Xa

Equation of a circle

If the center of the circle is at the origin,then. (x - a)² +(y - b)² = r²

Expanding ,we have x² + y² +2gx + 2fy + c = 0

Where c = a² + b² - r²

This is the called the general form of the equation of a circle.

10.Trigonometric identities
Sin(180-0)º. = sinø

Sin(180+ø)º. = -sinøº

Sin(360-ø)º. = -sinøº

SinA. = 2t/1 +r²

Cos(180 - ø)º. = -cosøº

Cos (180 + ø)º. =-cosøº

Cos A. = 1- t²/1 +r²

Tan(180 - ø)º. = -tanøº

Tan(180 + ø)º. = tanøº

Tan A. = 2t/1 - r²

1. Binomial expansion
   (X + Y)ª = Xª + aXª··¹ Y + a(a - 1) xª··²/2! + a(a - 1)(a - 2)Xª··³ Y³/3! +.... + Yn

a is represented by n while ·· represent -

Where n can be positive, negative or fraction.

1. Permutation& combination
   ªPr. = a!/(a - r)!

Combination

ªCr. = a!/(a - r)! r !

a is represented .by n.

1. Arithmetic progression
   Sn = n/2(2a + (n - 1)d)

Geometric progression

Sn. = a( rª - 1)/r - 1

a is the first term...while ª is represented by n

1. Differentiation
   Product rule:

Y = uv

dy/dx = udv/dx + vdu/dx

Quotient rule:

Y = u/v

dy/dx = vdu/dx - udv/dx/ v²

V² divide all

Chain rule

dy/dx = dy/du X du/dx