# 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 Figures Area (Sq.units) Perimeter (Units) Square (side)2 4 x side Triangle ½ ( b x h ) Sum of all sides Rectangle length x breadth 2 ( length + breadth ) Circle πr2 2πr 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 radiusRectangle= 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 Area Volume Cuboid 2h(l+b) 2(lb+bh+hl) lbh Cube 4a2 6a2 a3 Right Prism Perimeter of base× height LateralSurfaceArea+ 2(Area of One End) Area of Base× Height Right Circular Cylinder 2πrh 2πr(r+h) πr2h Right Pyramid 12Perimeterof Base×SlantHeight Lateral Surface Area+ Area of the Base 13(Area of the Base)×height Right Circular Cone πrl πr(l+r) 13πr2h Maths Formulas Related to Sphere 4πr2 4πr2 43πr3 Hemisphere 2πr2 3πr2 23πr3 Maths Formulas Related to Geometric Area Square a2 Rectangle ab Circle πr2 Ellipse πr1r2 Triangle 12bh

Maths Formulas for Class 9th:

 Geometry Shapes Formulas Geometric Figure Area Perimeter Rectangle A= l × w P = 2 × (l+w ) Triangle A = (1⁄2) × b × h P = a + b + c Trapezoid A = (1⁄2) × h × (b1+ b2) P = a + b + c + d Parallelogram A = b × h P = 2 (b + h) Circle A = π r2 C = 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 Variable ax+b=0 a≠0 and a&b are real numbers Two variable ax+by+c = 0 a≠0 & b≠0 and a,b & c are real numbers Three Variable ax+by+cz+d=0 a≠0 , b≠0, c≠0 and a,b,c,d are real numbers

Pair of Linear Equations in two variables:

 a1x+b1+c1=0a2x+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 ≠ 0And 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
• 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

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2. DEEPAKDHONI

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