Maths Formulas for All Competitive Exams 2024 for Class 6th to 12th

Maths Formula for Class 6th,7th,8th,9th,10th,11th,12th & Competitive Exams 2024-2025

Maths Formulas for All Competitive Exams 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, Math Formulae For Grades 6th–12th give in a Better Comprehension of the Material. Many Students Struggle to Solve Arithmetic Problems, yet a solid Foundation in Basic Mathematical Formulae can Significantly Enhance problem-Solving Efficiency. To deal with mathematical Difficulties Efficiently, students Should Focus on Memorizing Basic math formulas based on algebra, Arithmetic, and geometry. Mathematics, unlike many other courses, requires consistent practice. Students can develop a solid understanding of arithmetic formulas by thorough and Consistent practice, Making Them Easily Accessible when Needed. Maths Formulas for Class 6th-12th Pdf Download.

 

 Formulas For Square 2024

1. (a + b) ² = a ² + b ² + 2ab
2. (a − b) ² = a ² + b ² − 2ab
3. a ² − b ² = (a − b) (a + b)
4. (x + a) (x + b) = x ² + (a + b) x + ab
5. (a + b + c) ² = a ² + b ² + c ²  + 2ab + 2bc + 2ca
6. (a + (−b) + (−c)) ² = a ² + (−b) ²  + (−c) ² + 2a (−b) + 2 (−b) (−c) + 2a (−c)
7. (a – b – c) ² = a ² + b ² + c ² − 2ab + 2bc − 2ca

  Formulas for Cube 2024

1. (a + b) ³ = a ³ + b ³ + 3ab(a + b)
2. (a − b) ³ = a ³ – b ³ – 3ab(a – b)
3. a ³ − b ³ = (a − b) (a ² + b ² + ab)
4. a ³ + b ³ = (a + b) (a ² + b ² − ab)
5. (a + b + c) ³ = a ³ + b ³ + c ³ + 3(a + b)(b + c)(c + a)
6. a ³ + b ³ + c ³  − 3abc = (a + b + c) (a ² + b ² + c ² − ab − bc − ac)
7. If (a + b + c) = 0, a ³ + b ³ + c ³ = 3abc

Special Case Formulas for 2024-2025

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  )

1. √a = a ^1/2
2. ∛a = a ^1/3
3. ⁿ √a = a ^1/n
4. a ^p.  a ^q = a ^{p + q}
5. a ^p / a ^q  = a ^{p – q}
6. a ^p.  b ^p = (ab) ^p
7. (a ^p ) ^q.  = a ^pq
8. a ^0 .  = 1
9. a ^–n.  = 1/a ⁿ

Arithmetic Formulas 

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

Trigonometry Formulas

1. sin(90° – A) = cos A
2. cos(90° – A) = sin A
3. tan(90° – A) = cot A
4. cot(90° – A) = tan A
5. sec(90° – A) = cosec A
6. cosec(90° – A) = sec A
7. sin2 θ + cos2 θ = 1 ⇒ sin2 θ = 1 – cos2θ ⇒ cos2θ = 1 – sin2 θ
8. Cosec 2θ – cot2 θ = 1 ⇒ cosec 2θ = 1 + cot2 θ ⇒ cot2 θ = cosec2θ – 1
9. sec2 θ – tan2 θ = 1 ⇒ sec2 θ = 1 + tan2 θ ⇒ tan2 θ = sec2 θ – 1
10. sin θ cosec θ = 1 ⇒ cos θ sec θ = 1 ⇒ tan θ cot θ = 1

Area and Volume Formulas

1. The volume of Sphere = 4/3 ×π r3
2. Lateral Surface Area of Sphere (LSA) = 4π r2
3. Total Surface Area of Sphere (TSA) = 4πr2
4. The volume of the Right Circular Cylinder = πr2h
5. Lateral Surface Area of Right Circular Cylinder (LSA) = 2×(πrh)
6. Total Surface Area of Right Circular Cylinder (TSA) = 2πr×(r + h)
7. The volume of Hemisphere = ⅔ x (πr3)
8. Lateral Surface Area of Hemisphere (LSA) = 2π r2
9. Total Surface Area of Hemisphere (TSA) = 3π r2
10. The volume of Prism = B × h
11. Lateral Surface Area of Prism (LSA) = p × h

Quadratic Formula: The roots of a Quadratic Equation ax² + bx + c = 0 are given by x = [-b ± √(b² – 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

11th Class Maths important Formulas pdf Download 2024

12th Class Maths important Formulas pdf Download 2024

AP 10th Class Model Papers Blueprint

Math Formulas for Basic Algebra

1. (a + b)2 = a2 + 2ab + b2
2. (a – b)2 = a2 – 2ab + b2
3. a2 – b2 = (a – b)(a + b)
4. a2 + b2 = (a + b)2 – 2ab
5. (a – b – c)2 = a2 + b2 + c2 – 2ab + 2bc – 2ca
6. (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
7. (a +b+ c+…)2=a2+b2+c2+⋯+2(ab +ac+ bc +⋯
8. (x+ y+ z)2=x2+y2+z2+2xy+2yz+2xz
9. (x +y−z)2=x2+y2+z2+2xy−2yz−2xz
10. (x− y+ z)2=x2+y2+z2−2xy−2yz+2xz
11. (x−y−z)2=x2+y2+z2−2xy+2yz−2xz
12. (a + b)3 = a3 + 3a2b + 3ab2 + b3 ; (a + b)3 = a3 + b3 + 3ab(a + b)
13. (a – b)3 = a3 – 3a2b + 3ab2 – b3 = a3 – b3 – 3ab(a – b)
14. a3 + b3 = (a + b)(a2 – ab + b2)
15. a3 – b3 = (a – b)(a2 + ab + b2)
16. x3+y3+z3−3xyz=(x+ y+ z)(x2+y2+z2−xy−yz−xz)
17. x3+y3=(x+ y)(x2−xy+y2)
18. x3−y3=(x−y)(x2+xy+y2)
19. (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4
20. (a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4
21. a4 – b4 = (a – b)(a + b)(a2 + b2)
22. a5 – b5 = (a – b)(a4 + a3b + a2b2 + ab3 + b4)
23. x2+y2+z2−xy−yz−zx=1/2[(x−y)2+(y−z)2+(z−x)2]
24. x2+y2=1/2[(x+ y)2+(x−y)2]
25. (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 :

1. Profit of Percentage = (Profit / Cost price) × 100
2. Loss of Percentage = (Loss / Cost price) × 100
3. Simple Interest = (Principal × Rate × Time) / 100
4. Amount = Principal + Interest
5. Percentage Change = (Change / Original Amount) × 100
6. Product of rational numbers = (Product of Numerators) / (Product of Denominators)
7. Multiplication of a rational number by the reciprocal of another rational number.
8. Law of Product : am × an = am+n
9. Law of Quotient : am / an = am-n
10. Law of Zero Exponent : a0 = 1
11. Law of Negative Exponent : a-m = 1 / am
12. Law of Power of a Quotient : (a/b)^m = am / bm
13. Law of Power of a Power : (a^m)^n = a(mn)
14. Law of Power of a Product : (ab)m = am * bm
15. Perimeter of a Rectangle = 2 × (Length + Breadth)
16. Area of Rectangle = Length × Breadth
17. Area of a Square = Side2
18. Area of Triangle = (1/2) × Base × Height
19. Perimeter of a Square = 4 × Side
20. Area of a Parallelogram = Base × Height
21. Area of a Circle = πr2
22. 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

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

Class 9th Maths formulas 2024

Real Numbers 

1. √ab = √a √b
2. √(a/b) = √a / √b
3. (√a + √b) (√a – √b) = a – b
4. (√a + √b)2 = a + 2√ab + b
5. (a + √b) (a – √b) = a2 – b
6. (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 

1. (x + β)² = x² + β² + 2 x β
2. (x – β)² = x² + β² – 2 x β
3. (x + θ) (x – θ) = x² – θ²
4. (x + α)(x + θ) = x² + (α + θ)x + αθ
5. (x + α)(x – θ) = x² + (α – θ)x – αθ
6. (x – α)(x + θ) = x² + (θ – α)x – xθ
7. (x – α)(x – θ) = x² – (α + θ)x + αq
8. (α + θ)³ = α³ + θ³ + 3αθ(α + θ)
9. (α – θ)³ = α³ + θ³ – 3αθ(α – θ)
10. (α + β + θ)² = α² + β² + θ² + 2αβ + 2βθ + 2αθ
11. (α + β – θ)² = α² + β² + θ² + 2αβ – 2βθ – 2αθ
12. (α – β + θ)² = α² + β² + θ²- 2αβ – 2βθ + 2αθ
13. (α – β – θ)² = α² + β² + θ² – 2αβ + 2βθ – 2αθ
14. (x)³ + (β)³ = ( x + β) (x² – xβ + β)
15. (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

1. a × (b + c) = a × b + a × c (Distributive property)
2. a + b = b + a (Commutative Property of Addition)

a × b = b × a (Commutative Property of Multiplication)

1. a + (b + c) = (a + b) + c (Associative Property of Addition)
2. a × (b × c) = (a × b) × c (Associative Property of Multiplication)
3. a + 0 = a (Additive Identity Property)
4. a × 1 = a(Multiplicative Identity Property)
5. a + (-a) = 0 (Additive Inverse Property)
6. a⋅(1/a) = 1 (Multiplicative Inverse Property)
7. a × (0) =0 (Zero Property of Multiplication)

Trigonometry Formulas

1. sin(90° – A) = cos A
2. cos(90° – A) = sin A
3. tan(90° – A) = cot A
4. cot(90° – A) = tan A
5. sec(90° – A) = cosec A
6. cosec(90° – A) = sec A
7. sin2 θ + cos2 θ = 1 ⇒ sin2 θ = 1 – cos 2 θ ⇒ cos 2 θ = 1 – sin2 θ
8. cosec 2θ – cot2 θ = 1 ⇒ cosec 2θ = 1 + cot2 θ ⇒ cot2 θ = cosec 2 θ – 1
9. sec2 θ – tan2 θ = 1 ⇒ sec2 θ = 1 + tan2 θ ⇒ tan2 θ = sec2 θ – 1
10. sin θ cosec θ = 1 ⇒ cos θ sec θ = 1 ⇒ tan θ cot θ = 1

Calculus Formulas

1. d/dx [f(x) + g (x)] = d/dx [f(x)] + d/dx [g(x)]
2. d/dx [f(x) – g (x)] = d/dx [f(x)] – d/dx [g(x)]
3. d/dx [f(x) × g (x)] = d/dx [f(x)] × [g(x)] + [f(x)] × d/dx [g(x)]
4. 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

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

Class 12th Maths formulas 2024

Vector Formulas

1. A + B = B + A (Commutative Law)
2. A + (B + C) = (A + B) + C (Associative Law)
3. (A • B )= |P| |Q| cos θ ( Dot Product )
4. (A × B )= |P| |Q| sin θ (Cross Product)
5. k (A + B )= kA + kB
6. A + 0 = 0 + A (Additive Identity)

Trigonometry Formulas

1. sin-1(-x) = – sin-1x
2. tan-1x + cot-1x = π / 2
3. sin-1x + cos-1 x = π / 2
4. cos-1(-x) = π – cos-1x
5. cot-1(-x) = π – cot-1x

Calculus Formulas

1. ∫ f(x) dx = F(x) + C
2. Power Rule: ∫ xn dx = (xn+1) / (n+1) + C. (Where n ≠ -1)
3. Exponential Rules: ∫ ex dx = ex + C
4. ∫ ax dx = ax / ln(a) + C
5. ∫ ln(x) dx = x ln(x) – x + C
6. Constant Multiplication Rule: ∫ a dx = ax + C, where a is the constant.
7. Reciprocal Rule: ∫ (1/x) dx = ln(x)+ C
8. Sum Rules: ∫ [f(x) + g(x)] dx = ∫f(x) dx + ∫g(x) dx
9. Difference Rules: ∫ [f(x) – g(x)] dx = ∫f(x) dx – ∫g(x) dx
10. ∫k f(x) dx = k ∫f(x) dx, , where k is any real number.
11. Integration by parts: ∫ f(x) g(x) dx = f(x) ∫ g(x) dx – ∫[d/dx f(x) × ∫ g(x) dx]dx
12. ∫cos x dx = sin x + C
13. ∫ sin x dx = -cos x + C
14. ∫ sec2x dx = tan x + C
15. ∫ cosec2x dx = -cot x + C
16. ∫ sec x tan x dx = sec x + C
17. ∫ cosec x cot x dx = – cosec x + C

official website for 10th formulas https://www.bse.ap.gov.in/