**Maths Formulas for Class 6th to 12th & Most important to Competitive Exams 2024 – 2025**

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Maths Formulas for Class 6th to 12th Pdf Download 2024 | 6 వ తరగతి నుండి 12వ తరగతి వరకు గణిత సూత్రాలు Pdf డౌన్లోడ్ Download The Maths Formula Booklet Sheet for Classes 6th, 7th, 8th, 9th, 10th, 1th1, and 12th and Competitive Exams in PDF Format. Mathematics important Formulas For CBSE, ICSE, NCERT, and SCERT Classes From 6th to 12th Class, As well as All Competitive Exams like as CAT, IAS, RRB, IBPS, JEE, GATE, NDA, RBI, SBI, and others.

**FA1 Question Papers 2024: Download (Updated)**

** 10th Class Maths Formulas 2024 **These Books are Also Classified as Level-1, Level-2, Level-3, and Class – Based. So you can Download your Needed Mathematics Formulae Book Sheet pdf For free of Cost.Maths Formulas for Class 6th to 12th Pdf Download. Chapter Wise Maths Formulas for Class 6th to 12th. Chapter Wise Maths Formulas for Class 6th to 12th.

## Important Maths Formula Booklet for 6th to 12th Classes

Maths Formulas for Class 6th to 12th Pdf Download & important Math formulas from algebra, trigonometry, integers, engineering formulas, polynomials, derivatives, and other important sections are divided here. Our main aim is to provide **Important Formulas in Mathematics**.Maths Formulas for Class 6th to 12th Pdf Download.

## Some Basic Algebra Formulas Discussing

Maths formulas covering Classes 6th–12th aid in a greater understanding of the topic. Many students face difficulties while solving arithmetic problems but a strong foundation in basic maths formulas can considerably improve problem-Solving efficiency. To efficiently handle mathematical problems, students should prioritise Memorising Basic Maths Formulas Based on Algebra, Arithmetic, and Geometry. Unlike many other Courses, Mathematics Requires Consistent practice. Students can Get a Strong Grasp of Arithmetic Formulas by Thorough and Consistent practice, Making Them Easily Accessible when Needed.Maths Formulas for Class 6th to 12th Pdf Download

## Math Formulas PDF Download 2024|Maths Formulas for Class 6th to 12th Pdf Download

Mathematical formulae are Essential Tools for Students, Allowing them to Handle Mathematical obstacles more Easily and Efficiently. Students who have a solid understanding of basic maths Concepts can approach complicated problems Utilising a variety of ways and Techniques. Performing well in Mathematics is Not an impossible Endeavour; it Requires a Combination of Consistent hard work and smart work. The approach entails thoroughly analysing an issue to determine its requirements before Applying Relevant Maths formulas to Arrive at a Solution. Individuals studying for competitive exams can also Benefit from having access to a comprehensive collection of fundamental **Mathematics **formulas in one handy location, which will help them Better Comprehend the Topic.Maths Formulas for Class 6th to 12th Pdf Download 2024 |

### Formulas For SQuare

- (a + b)
^{2 }= a^{2 }+ b^{2 }+ 2ab - (a − b)
^{2 }= a^{2 }+ b^{2 }− 2ab - a
^{2 }− b^{2 }= (a − b) (a + b) - (x + a) (x + b) = x
^{2 }+ (a + b) x + ab - (a + b + c)
^{2 }= a^{2 }+ b^{2 }+ c^{2 }+ 2ab + 2bc + 2ca - (a + (−b) + (−c))
^{2 }= a^{2 }+ (−b)^{2 }+ (−c)^{2 }+ 2a (−b) + 2 (−b) (−c) + 2a (−c) - (a – b – c)
^{2 }= a^{2 }+ b^{2 }+ c^{2 }− 2ab + 2bc − 2ca

### Formulas for Cube

- (a + b)
^{3 }= a^{3 }+ b^{3 }+ 3ab(a + b) - (a − b)
^{3 }= a^{3 }– b^{3 }– 3ab(a – b) - a
^{3 }− b^{3 }= (a − b) (a^{2 }+ b^{2 }+ ab) - a
^{3 }+ b^{3 }= (a + b) (a^{2 }+ b^{2 }− ab) - (a + b + c)
^{3 }= a^{3 }+ b^{3 }+ c^{3 }+ 3(a + b)(b + c)(c + a) - a
^{3 }+ b^{3 }+ c^{3 }− 3abc = (a + b + c) (a^{2 }+ b^{2 }+ c^{2 }− ab − bc − ac) - If (a + b + c) = 0, a
^{3 }+ b^{3 }+ c^{3 }= 3abc

### Special Case Formulas

a ^{n }− b ^{n }= (a − b) (a ^{n−1 }+ a ^{n−2 }b ^{1 } + a ^{n−3 }b ^{2 }+ …. + a ^{1 }b ^{n−2 }+ b ^{n−1 })

- √a = a
^{1/2} - ∛a = a
^{1/3} ^{n }√a = a^{1/n}- a
^{p. }a^{q }= a^{p + q} - a
^{p }/ a^{q }= a^{p – q} - a
^{p. }b^{p }= (ab)^{p} - (a
^{p })^{q. }= a^{pq} - a
^{0 }^{. }= 1 - a
^{–n. }= 1/a^{n}

**Arithmetic Formulas **

- an = a + (n – 1) d, where an is the nth term.
- Sn= n/2 [2a + (n – 1)d]

**Trigonometry Formulas**

- sin(90° – A) = cos A
- cos(90° – A) = sin A
- tan(90° – A) = cot A
- cot(90° – A) = tan A
- sec(90° – A) = cosec A
- cosec(90° – A) = sec A
- sin2 θ + cos2 θ = 1 ⇒ sin2 θ = 1 – cos2θ ⇒ cos2θ = 1 – sin2 θ
- Cosec 2θ – cot2 θ = 1 ⇒ cosec 2θ = 1 + cot2 θ ⇒ cot2 θ = cosec2θ – 1
- sec2 θ – tan2 θ = 1 ⇒ sec2 θ = 1 + tan2 θ ⇒ tan2 θ = sec2 θ – 1
- sin θ cosec θ = 1 ⇒ cos θ sec θ = 1 ⇒ tan θ cot θ = 1

**Area and Volume Formulas**

- The volume of Sphere = 4/3 ×π r3
- Lateral Surface Area of Sphere (LSA) = 4π r2
- Total Surface Area of Sphere (TSA) = 4πr2
- The volume of the Right Circular Cylinder = πr2h
- Lateral Surface Area of Right Circular Cylinder (LSA) = 2×(πrh)
- Total Surface Area of Right Circular Cylinder (TSA) = 2πr×(r + h)
- The volume of Hemisphere = ⅔ x (πr3)
- Lateral Surface Area of Hemisphere (LSA) = 2π r2
- Total Surface Area of Hemisphere (TSA) = 3π r2
- The volume of Prism = B × h
- Lateral Surface Area of Prism (LSA) = p × h

**Quadratic Formula: **The roots of a Quadratic Equation ax^{2} + bx + c = 0 are given by x = [-b ± √(b^{2} – 4ac)]/2a.

6th Class Maths important Formulas pdf Download 2024

7th Class Maths important Formulas pdf Download 2024

8th Class Maths important Formulas pdf Download 2024

9th Class Maths important Formulas pdf Download 2024

10th Class Maths important Formulas pdf Download 2024

**Math Formulas for Basic Algebra**

- (a + b)2 = a2 + 2ab + b2
- (a – b)2 = a2 – 2ab + b2
- a2 – b2 = (a – b)(a + b)
- a2 + b2 = (a + b)2 – 2ab
- (a – b – c)2 = a2 + b2 + c2 – 2ab + 2bc – 2ca
- (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
- (a +b+ c+…)2=a2+b2+c2+⋯+2(ab +ac+ bc +⋯
- (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
- (a + b)3 = a3 + 3a2b + 3ab2 + b3 ; (a + b)3 = a3 + b3 + 3ab(a + b)
- (a – b)3 = a3 – 3a2b + 3ab2 – b3 = a3 – b3 – 3ab(a – b)
- a3 + b3 = (a + b)(a2 – ab + b2)
- a3 – b3 = (a – b)(a2 + ab + b2)
- x3+y3+z3−3xyz=(x+ y+ z)(x2+y2+z2−xy−yz−xz)
- x3+y3=(x+ y)(x2−xy+y2)
- x3−y3=(x−y)(x2+xy+y2)
- (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4
- (a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4
- a4 – b4 = (a – b)(a + b)(a2 + b2)
- a5 – b5 = (a – b)(a4 + a3b + a2b2 + ab3 + b4)
- x2+y2+z2−xy−yz−zx=1/2[(x−y)2+(y−z)2+(z−x)2]
- x2+y2=1/2[(x+ y)2+(x−y)2]
- (x +a)(x +b)(x +c)=x3+(a +b+ c)x2+(ab +bc+ ca)x+ abc.

**Class 7th Maths formulas 2024**

Class 7th mathematics Syllabus, Several Essential Maths Topics are Covered. Here, you’ll find a Compilation of important Maths Formulas for Class 7th :

- Profit of Percentage = (Profit / Cost price) × 100
- Loss of Percentage = (Loss / Cost price) × 100
- Simple Interest = (Principal × Rate × Time) / 100
- Amount = Principal + Interest
- Percentage Change = (Change / Original Amount) × 100
- Product of rational numbers = (Product of Numerators) / (Product of Denominators)
- Multiplication of a rational number by the reciprocal of another rational number.
- Law of Product : am × an = am+n
- Law of Quotient : am / an = am-n
- Law of Zero Exponent : a0 = 1
- Law of Negative Exponent : a-m = 1 / am
- Law of Power of a Quotient : (a/b)^m = am / bm
- Law of Power of a Power : (a^m)^n = a(mn)
- Law of Power of a Product : (ab)m = am * bm
- Perimeter of a Rectangle = 2 × (Length + Breadth)
- Area of Rectangle = Length × Breadth
- Area of a Square = Side2
- Area of Triangle = (1/2) × Base × Height
- Perimeter of a Square = 4 × Side
- Area of a Parallelogram = Base × Height
- Area of a Circle = πr2
- Circumference of a Circle = πd, where ‘d’ is the Diameter of the Circle, and π ≈ 3.14 or 22/7.

**Class 8th Maths formulas 2024**

- Additive inverse of a Rational Number: a/b = -b/a
- Multiplicative Inverse of a/b = c/d, if a/b × c/d = 1
- Distributive property: a(b – c) = ab – ac
- Simple Interest = (Principal × Rate × Time) / 100
- Amount = Principal + Interest
- Compound Interest formula = Amount – Principal. In the case of annual interest calculation, Amount = Principal × (1 + Rate/100)^n, where ‘n’ is the period.
- Probability of the occurrence of an event = Number of outcomes comprising the event / Total number of outcomes

**Class 9th Maths formulas 2024**

**Real Numbers **

- √ab = √a √b
- √(a/b) = √a / √b
- (√a + √b) (√a – √b) = a – b
- (√a + √b)2 = a + 2√ab + b
- (a + √b) (a – √b) = a2 – b
- (a + b) (a – b) = a2 – b2

**Geometry Formulas **

- Geometrical Shapes

Area (A)

**Perimeter**

**Rectangle**

A = Length x Width

P = 2(Length + Width)

**Triangle**

- A = ½ x Breadth x Height
- P = Sum of all the three sides of a triangle

**Trapezoid**

- A = ½ x Height x (b₁ x b₂)
- P = Sum of all the sides of a trapezoid

**Parallelogram,**

- A = Breadth x Height
- P = 2( a+ b)
- Here. a = side
- B = base

**Circle**

- A = πr²
- P = 2 πr

**Algebra Identities **

- (x + β)² = x² + β² + 2 x β
- (x – β)² = x² + β² – 2 x β
- (x + θ) (x – θ) = x² – θ²
- (x + α)(x + θ) = x² + (α + θ)x + αθ
- (x + α)(x – θ) = x² + (α – θ)x – αθ
- (x – α)(x + θ) = x² + (θ – α)x – xθ
- (x – α)(x – θ) = x² – (α + θ)x + αq
- (α + θ)³ = α³ + θ³ + 3αθ(α + θ)
- (α – θ)³ = α³ + θ³ – 3αθ(α – θ)
- (α + β + θ)² = α² + β² + θ² + 2αβ + 2βθ + 2αθ
- (α + β – θ)² = α² + β² + θ² + 2αβ – 2βθ – 2αθ
- (α – β + θ)² = α² + β² + θ²- 2αβ – 2βθ + 2αθ
- (α – β – θ)² = α² + β² + θ² – 2αβ + 2βθ – 2αθ
- (x)³ + (β)³ = ( x + β) (x² – xβ + β)
- (x)³ – (β)³ = ( x + β) (x² – xβ + β)

**Cuboid**

2 = (lb + bh + hl),

Here, l = length,

b = Breadth, h = height

V = Length x Breadth x Height

**Cube**

A = 6 side²

V = Side³

**Cylinder**

A = 2πr( h + r)

Here,

r = radius of circular cylinder

H = height of a cylinder

V = πr²H

**Cone**

A = πr( L + r)

Here,

l = slant height

r = Radius of base

**Class 11th Maths formulas 2024**

**Algebra Formulas**

- a × (b + c) = a × b + a × c (Distributive property)
- a + b = b + a (Commutative Property of Addition)
- a × b = b × a (Commutative Property of Multiplication)
- a + (b + c) = (a + b) + c (Associative Property of Addition)
- a × (b × c) = (a × b) × c (Associative Property of Multiplication)
- a + 0 = a (Additive Identity Property)
- a × 1 = a(Multiplicative Identity Property)
- a + (-a) = 0 (Additive Inverse Property)
- a⋅(1/a) = 1 (Multiplicative Inverse Property)
- a × (0) =0 (Zero Property of Multiplication)

**Trigonometry Formulas**

- sin(90° – A) = cos A
- cos(90° – A) = sin A
- tan(90° – A) = cot A
- cot(90° – A) = tan A
- sec(90° – A) = cosec A
- cosec(90° – A) = sec A
- sin2 θ + cos2 θ = 1 ⇒ sin2 θ = 1 – cos 2 θ ⇒ cos 2 θ = 1 – sin2 θ
- cosec 2θ – cot2 θ = 1 ⇒ cosec 2θ = 1 + cot2 θ ⇒ cot2 θ = cosec 2 θ – 1
- sec2 θ – tan2 θ = 1 ⇒ sec2 θ = 1 + tan2 θ ⇒ tan2 θ = sec2 θ – 1
- sin θ cosec θ = 1 ⇒ cos θ sec θ = 1 ⇒ tan θ cot θ = 1

**Calculus Formulas**

- d/dx [f(x) + g (x)] = d/dx [f(x)] + d/dx [g(x)]
- d/dx [f(x) – g (x)] = d/dx [f(x)] – d/dx [g(x)]
- d/dx [f(x) × g (x)] = d/dx [f(x)] × [g(x)] + [f(x)] × d/dx [g(x)]
- d/dx [f(x) / g (x)] = {d/dx [f(x)] × [g(x)] – [f(x)] × d/dx [g(x)]} / g(x)2

**Geometry and Lines Formulas**

- Slope m = rise/run = Δy/Δx = y2−y1/x2−x1
- Point-Slope Form y−y1 = m (x−x1)

**Class 12th Maths formulas 2024**

**Vector Formulas**

- A + B = B + A (Commutative Law)
- A + (B + C) = (A + B) + C (Associative Law)
- (A • B )= |P| |Q| cos θ ( Dot Product )
- (A × B )= |P| |Q| sin θ (Cross Product)
- k (A + B )= kA + kB
- A + 0 = 0 + A (Additive Identity)

**Trigonometry Formulas**

- sin-1(-x) = – sin-1x
- tan-1x + cot-1x = π / 2
- sin-1x + cos-1 x = π / 2
- cos-1(-x) = π – cos-1x
- cot-1(-x) = π – cot-1x

**Calculus Formulas**

- ∫ f(x) dx = F(x) + C
- Power Rule: ∫ xn dx = (xn+1) / (n+1) + C. (Where n ≠ -1)
- Exponential Rules: ∫ ex dx = ex + C
- ∫ ax dx = ax / ln(a) + C
- ∫ ln(x) dx = x ln(x) – x + C
- Constant Multiplication Rule: ∫ a dx = ax + C, where a is the constant.
- Reciprocal Rule: ∫ (1/x) dx = ln(x)+ C
- Sum Rules: ∫ [f(x) + g(x)] dx = ∫f(x) dx + ∫g(x) dx
- Difference Rules: ∫ [f(x) – g(x)] dx = ∫f(x) dx – ∫g(x) dx
- ∫k f(x) dx = k ∫f(x) dx, , where k is any real number.
- Integration by parts: ∫ f(x) g(x) dx = f(x) ∫ g(x) dx – ∫[d/dx f(x) × ∫ g(x) dx]dx
- ∫cos x dx = sin x + C
- ∫ sin x dx = -cos x + C
- ∫ sec2x dx = tan x + C
- ∫ cosec2x dx = -cot x + C
- ∫ sec x tan x dx = sec x + C
- ∫ cosec x cot x dx = – cosec x + C

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