**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.

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 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 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]< |

**Check Out Important Maths Tricks:**

**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
- 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 r
^{2 }h

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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

**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.

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