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
Source
Plagiarism is the copying & pasting of others work without giving credit to the original author or artist. Plagiarized posts are considered fraud and violate the intellectual property rights of the original creator.
Fraud is discouraged by the community and may result in the account being Blacklisted.
If you believe this comment is in error, please contact us in #appeals in Discord.