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Maths Formulas: List Of Important Maths Formulas For Class 6th-12th: Check

Maths Formulas

Maths is a most difficult subject for some students because solving mathematical problems acquires lots of knowledge and formulas. Maths Formulas allow students for hands-on practice and assist them to score high both in class exam and board exam. You can check List of Important Maths Formulas for Class 6th-12th from here.

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Math Formula shows how things work out with assist of some equations like the equation for force or acceleration. When you understand the logic behind every problem and formulas, solving any kind of maths problem becomes easier. Competitive Exams are filled with Maths where you need Mathematical Formulas.

Maths Formulas

Maths Formulas for Class 6th to 10th:

Maths Formulas for Class 6th:

Important Maths Formulas Related to Number System
ab−−√=a−−√b√
ab−−√=a√b√
(a−−√+b√)(a−−√−b√)=a−b
(a+b√)(a−b√)=a2−b
(a−−√+b√)2=a+2ab−−√+b
apaq=ap+q
(ap)q=apq
apaq=ap−q
apbp=(ab)p
If a and b are integers, to rationalise the denominator of 1a√+b multiply it by a√−ba√−b
Formulas Related to Integer
Addition of integers is commutative a + b = b + a
Addition of integers is associative a + ( b + c ) = ( a + b) + c
0 is the identity element under addition a + 0 = 0 + a = a
Multiplication of integers is commutative. a x b = b x a
1 is the identity element under multiplication 1 x a = a x 1 = a
Formulas Related to Two dimensional Figures
2Dimensional FiguresArea (Sq.units)Perimeter (Units)
Square(side)24 x side
Triangle½ ( b x h )Sum of all sides
Rectanglelength x breadth2 ( length + breadth )
Circleπr22πr
Formulas Related to Basic Algebra
Consider the simple quadratic equation ax2+bx+c=0
Where, a is the coefficient of x2
b is the coefficient of x
c is a constant term
The quadratic equation to find the variable x is, x=−b±b2−4ac√2a

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Maths Formulas for Class 7th:

Maths Formulas Proportion Rules
Addition: ab+cd=ad+bcbd
Subtraction: ab−cd=ad−bcbd
Multiplication: ab=cd, then a*d = b*c
Division : abcd=adbc
Formula Related to Set Properties
Commutative property: A∪B=B∪A A∩B=B∩A
Associative property:(A∪B)∪C=A∪(B∪C) (A∩B)∩C=A∩(B∩C)
Formula Related to Algebraic Expansion
(a+b)2=a2+2ab+b2
(a−b)2=a2−2ab+b2
a2−b2=(a+b)(a−b)
(x+a)(x+b)=x2+x(a+b)+(ab)
Formula Related to Interest  
Simple Interest, S.I=PTR100,Where P=Principal,
T= Time in years, R=Rate of interest per annum
Rate, R=100∗S.IP∗T
Principal, P=100∗S.IR∗T
Time,T=100∗S.IR∗P
Discount = MP-SP
Principal = Amount – Simple Interest
If Rate of Discount is given,
Discount=PastRateofDiscount100
Formula Related to Time and Speed
Speed=Distance travelled Time taken
Number of Revolution=Distance travelled Circumference of the wheel
Formula Related to Area 2D and 3D Figures
Circle=pir2 Sq units, where r is the radius

Rectangle= l∗b Sq.units , where l = length and b is breadth

Total Surface Area for Cube = 6a2 sq.units
Total surface Area of cuboid =2(lb+bh+hl) Sq. units
Perimeter Formulas
Square = 4s units, where s is side of square
Rectangle= 2(l+b) units, where l is length and b is breadth
Volume Formulas:
Cube =l3 cu.unitsSphere=43πr3 cu.units,
where r is the radius of the sphere.
Cylinder= πr2h cu.units, where r is the radius of the base,h is the height of the cylinder.

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Maths Formulas for Class 8th:

Geometry Shapes Formulas for Class 8
Lateral /
Curved Surface Area
Total Surface AreaVolume
Cuboid
2h(l+b)2(lb+bh+hl)lbh
Cube
4a26a2a3
Right Prism
Perimeter of base× heightLateralSurfaceArea+
2(Area of One End)
Area of Base× Height
Right Circular Cylinder
2πrh2πr(r+h)πr2h
Right Pyramid
12Perimeterof
Base×SlantHeight
Lateral
Surface Area+
Area of the Base
13(Area of the Base)×height
Right Circular Cone
πrlπr(l+r)13πr2h
Maths Formulas Related to Sphere
4πr24πr243πr3
Hemisphere
2πr23πr223πr3
Maths Formulas Related to Geometric Area
Squarea2
Rectangleab
Circleπr2
Ellipseπr1r2
Triangle12bh

Maths Formulas for Class 9th:

Geometry Shapes Formulas
Geometric FigureAreaPerimeter
RectangleA= l × wP = 2 × (l+w )
TriangleA = (1⁄2) × b × hP = a + b + c
TrapezoidA = (1⁄2) × h × (b1+ b2)P = a + b + c + d
ParallelogramA = b × hP = 2 (b + h)
CircleA = π r2C = 2 π r
Algebraic Identities Formulas
(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=12[(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=12[(x−y)2+(y−z)2+(z−x)2]<

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Maths Formulas for Class 10th:

Linear Equations:

One Variableax+b=0a≠0 and a&b are real numbers
Two variableax+by+c = 0a≠0 & b≠0 and a,b & c are real numbers
Three Variableax+by+cz+d=0a≠0 , b≠0, c≠0 and a,b,c,d are real numbers

 Pair of Linear Equations in two variables:

a1x+b1+c1=0

a2x+b2+c2=0

  • Where a1, b1, c1, a2, b2, and c2 are all real numbers and a12+b12 ≠ 0 & a22 + b22 ≠ 0
  • These linear equations can also be represented in graphical form.
  • Algebra or algebraic equations

The standard form of Quadratic Equations:

ax2+bx+c=0 where a ≠ 0

And x = −b±b2−4ac√2a

 Algebraic formulae:

  • (a+b)2 = a2 + b2 + 2ab
  • (a-b)2 = a2 + b2 – 2ab
  • (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 =½ [(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 = ½ [(x-y)2 + (y-z)2 + (z-x)2]

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Basic formulas for powers

  • pm x pn = pm+n
  • {pm}⁄{pn} = pm-n
  • (pm)n = pmn
  • p-m = 1/pm
  • p1 = p
  • P0 = 1

Arithmetic Progression (AP)

  • If a1, a2, a3, a4, a5, a6,… are the terms of AP and d is the common difference between each term, then we can write the sequence as;
  • a, a+d, a+2d, a+3d, a+4d, a+5d,….,nth term… where a is the first term.
  • Now, nth term for Arithmetic progression is given as;
nth term = a + (n-1) d

Sum of nth term in Arithmetic Progression;

Sn = n/2 [a + (n-1) d]

Trigonometry Formulae

  • Let a right-angled triangle ABC is right-angled at point B and have ∠θ.
  • Sinθ= SideoppositetoangleθHypotenuse=PerpendicularHypotenuse = P/H
  • Cosθ = AdjacentsidetoangleθHypotenuse = AdjacentsideHypotenuse = B/H
  • Tanθ = SideoppositetoangleθAdjacentsidetoangleθ = P/B
  • Sec θ = 1cosθ
  • Cot θ = 1tanθ
  • Cosec θ = 1sinθ
  • Tan θ = SinθCosθ

Other Trigonometric formulas

  • sin(900 – θ) = cos θ
  • cos(900 – θ) = sin θ
  • tan(900 – θ) = cot θ
  • cot(900 – θ) = tan θ
  • sec(900 – θ) = cosecθ
  • cosec(900 – θ) = secθ
  • sin2θ + cos2 θ = 1
  • sec2 θ = 1 + tan2θ for 00 ≤ θ < 900
  • Cosec2 θ = 1 + cot2 θ for 00 ≤ θ ≤ 900

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Circles

  • Circumference of the circle = 2 π r
  • Area of the circle = π r2
  • Area of the sector of angle θ = θ360 X π r2
  • Length of an arc of a sector of angle θ = θ360 X 2 π r (r = radius of the circle)
  • Surface Area and Volumes

Sphere

  • Diameter of sphere = 2r
  • Circumference of Sphere = 2 π r
  • Surface area of sphere = 4 π r2
  • Volume of Cylinder = 4/3 π r2

Cylinder

  • Circumference of Cylinder = 2 π r h
  • Curved surface area of Cylinder = 2 π r2
  • Total surface area of Cylinder = Circumference of Cylinder + Curved surface area of Cylinder = 2 π r h + 2 π r2
  • Volume of Cylinder = π r2 h

Cone

  • Slant height of cone(s) = r2+h2−−−−−−√
  • Curved surface area of cone = π r s
  • Total surface area of cone = π r (s + r)
  • Volume of cone = ⅓ π rh

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Cuboid

  • Perimeter of cuboid = 4(l + b +h)
  • Length of the longest diagonal of a cuboid = l2+b2+h2−−−−−−−−−−√
  • Total surface area of cuboid = 2(l*b + b*h + l*h)
  • Volume of Cuboid = l*b*h
  • l = length, b = breadth and h = height
  • In case of Cube, put l = b = h = a, as cube all its sides of equal length, to find the surface area and volumes.

Statistics

  • The mean of the grouped data can be found by 3 methods.
  • Direct Method: x¯ = \(\frac{\sum_{i=1}^{n}fi xi}{\sum_{i=1}^{n}fi}\)

Where fi xi is the sum of observations from value i = 1 to n

And fi is the number of observations from value i = 1 to n

  • Assumed mean method : x¯ = a + \(\frac{\sum_{i=1}^{n}fi di}{\sum_{i=1}^{n}fi}\)
  • Step deviation method : x¯ = a + \(\frac{\sum_{i=1}^{n}fi ui}{\sum_{i=1}^{n}fi}\) X h

(II) The mode of grouped data;

Mode = l + \(\frac{f1 – f0}{2f1 – f0 – f2}\) X h

(III) The median for a grouped data;

Median = l + (n/2–cff) X h

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Maths Formulas Details:

Well here on this page we have provided List of Maths Formulas of Class 6, 7, 8, 9, 10 and shortcuts for Learning Maths Formulas. Now most of the Bank, Government and Private Organizations conduct various competitive exams in order to recruit well talented and deserving aspirants for filing up the vacant positions.

All these organizations ask many quantities and aptitude questions in these exams which create problem for the job seekers. So now you don’t need to worry more and download the Maths Formulas PDF free here. You can subscribe our free email service to get latest updates about Maths Formulas List.

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2 Responses to "Maths Formulas: List Of Important Maths Formulas For Class 6th-12th: Check"

  1. Jeena

    It is useful.Great!!!!

  2. DEEPAKDHONI

    it is more useful & thanks to all

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