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Math Formulas for Classes 9 and 11, Summaries of Mathematics

Mathematics

A list of math formulas for classes 9 and 11, covering topics such as real numbers, geometry, algebra, trigonometry, and calculus. The formulas are presented in a concise and organized manner, making it a useful reference for students studying these topics.

Typology: Summaries

2022/2023

Available from 11/28/2023

rushindra-gaikwad
rushindra-gaikwad 🇮🇳

3 documents

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Class 9 Math formulas
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
pf3
pf4
pf5

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Download Math Formulas for Classes 9 and 11 and more Summaries Mathematics in PDF only on Docsity!

Class 9 Math formulas

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 – b 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) Surface Area and Volume Shape Surface Area (A) Volume (V) Cuboid 2 = (lb + bh + hl), Here, l = length, b = Breadth, h = height V = Length x Breadth x Height Cube A = 6 side²

S = ( a + b + c)/ Polynomial Formula P (x) = anxn + an- 1xn- 1 – an- 2xn- 1 + …… ax + a Statistics (Measure of Central Tendency) Mean Sum of all the observations/ Total Number of Observations Median For odd observations = ((n+1)/2)th observations For even Observations – ((n/2)th + ((n/2) +1)th)/2 observations Mode The value which occurs most frequently in a data

Class 10 Math formulas

Algebra Formulas

  1. (a + b)2 = a2 + 2ab + b
  2. (a – b)2 = a2 – 2ab + b
  3. (a + b) (a – b) = a2 – b
  4. (x + a)(x + b) = x2 + (a + b)x + ab
  5. (x + a)(x – b) = x2 + (a – b)x – ab
  6. (x – a)(x + b) = x2 + (b – a)x – ab
  7. (x – a)(x – b) = x2 – (a + b)x + ab
  8. (a + b)3 = a3 + b3 + 3ab(a + b)
  9. (a – b)3 = a3 – b3 – 3ab(a – b)
  10. (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2xz
  11. (x + y – z)2 = x2 + y2 + z2 + 2xy – 2yz – 2xz
  12. (x – y + z)2 = x2 + y2 + z2 – 2xy – 2yz + 2xz
  13. (x – y – z)2 = x2 + y2 + z2 – 2xy + 2yz – 2xz
  14. x3 + y3 + z3 – 3xyz = (x + y + z)(x2 + y2 + z2 – xy – yz – xz) Arithmetic Formulas
  15. an = a + (n – 1) d, where an is the nth term.
  16. 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 – cos2 θ ⇒ cos2 θ = 1 – sin2 θ
  8. cosec2 θ – cot2 θ = 1 ⇒ cosec2 θ = 1 + cot2 θ ⇒ cot2 θ = cosec2 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 Circle Formula
  11. The tangent to a circle equation x2 + y2 = a2 for a line y = mx + c is given by the equation y = mx ± a √ [1+ m2].
  12. The tangent to a circle equation x2 + y2 = a2 at (a1,b1) is xa1 + yb1 = a Area and Volume Formulas
  13. The volume of Sphere = 4/3 ×π r
  14. Lateral Surface Area of Sphere (LSA) = 4π r
  15. Total Surface Area of Sphere (TSA) = 4πr
  16. The volume of the Right Circular Cylinder = πr2h
  17. Lateral Surface Area of Right Circular Cylinder (LSA) = 2×(πrh)
  18. Total Surface Area of Right Circular Cylinder (TSA) = 2πr×(r + h)
  19. The volume of Hemisphere = ⅔ x (πr3)
  20. Lateral Surface Area of Hemisphere (LSA) = 2πr
  21. Total Surface Area of Hemisphere (TSA) = 3πr
  22. The volume of Prism = B × h
  23. Lateral Surface Area of Prism (LSA) = p × h

Class 11 Math formulas

Algebra Formulas

  1. a × (b + c) = a × b + a × c (Distributive property)
  2. a + b = b + a (Commutative Property of Addition)
  3. a × b = b × a (Commutative Property of Multiplication)
  4. a + (b + c) = (a + b) + c (Associative Property of Addition)
  5. a × (b × c) = (a × b) × c (Associative Property of Multiplication)
  6. a + 0 = a (Additive Identity Property)
  7. a × 1 = a(Multiplicative Identity Property)
  8. a + (-a) = 0 (Additive Inverse Property)
  9. a⋅(1/a) = 1 (Multiplicative Inverse Property)
  10. a × (0) =0 (Zero Property of Multiplication) Trigonometry Formulas
  11. sin(90° – A) = cos A
  1. Sum Rules: ∫ [f(x) + g(x)] dx = ∫f(x) dx + ∫g(x) dx
  2. Difference Rules: ∫ [f(x) – g(x)] dx = ∫f(x) dx – ∫g(x) dx
  3. ∫k f(x) dx = k ∫f(x) dx, , where k is any real number.
  4. Integration by parts: ∫ f(x) g(x) dx = f(x) ∫ g(x) dx – ∫[d/dx f(x) × ∫ g(x) dx]dx
  5. ∫cos x dx = sin x + C
  6. ∫ sin x dx = -cos x + C
  7. ∫ sec2 x dx = tan x + C
  8. ∫ cosec2 x dx = -cot x + C
  9. ∫ sec x tan x dx = sec x + C
  10. ∫ cosec x cot x dx = – cosec x + C Geometry Formulas
  11. Cartesian equation of a plane: lx + my + nz = d
  12. Distance between two points P(x1, y1, z1) and Q(x2, y2, z2): PQ = √ ((x1 – x2)
  • (y1 – y2)2 + (z1 – z2)2)