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
- 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.
- Permutation& combination
ªPr. = a!/(a - r)!
Combination
ªCr. = a!/(a - r)! r !
a is represented .by n.
- 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
- 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