Pupils! We are familiar with the typical minds. Since school, we have been studying their accounts in depth. The sea is similar to mathematics. Shouldn’t we advance to the next mathematical level? Are you interested in learning mathematics? Keep in mind the following formulas. Rich mathematics will be taught to you as quickly as feasible.
Basic Math Formulas: Mathematics is separated into different branches based on the topics they cover and the methods of computation involved. Each branch has its own set of formulas that are used to solve different types of mathematical issues. Geometry, algebra, arithmetic, percentages, exponentials, and so on are among the branches. All of the fundamental formulas for many mathematical topics, such as trigonometry, geometry, algebra, probability, coordinate geometry, etc., are included in this page.
List of Maths Formulas
1. Algebra Formula
2. Algebraic Expressions Formula
3. Angle Formula
4. Area Formula of Quadrilaterals
5. Area Formula
6. Area of a Pentagon Formula
7. Area of an Octagon Formula
8. Area Under the Curve Formula
9. Arithmetic Sequence Explicit Formula
10. Arithmetic Sequence Recursive Formula
11. Binary Formula
12. Calculus Formula
13. Change of Base Formula
14. Cofactor Formula
15. Complex Number Division Formula
16. Complex Number Power Formula
17. Conditional Probability Formula
18. Cos Inverse Formula
19. Cosine Formula
20. Cube Formula
21. Cubic Equation Formula
22. Daily Compound Interest Formula
23. Decay Formula
24. Decimal to Fraction Formula
25. Derivative Formula
26. Diagonal Formula
27. Equation Formula
28. Exponential Formula
29. Factorial Formula
30. Function Formulas
31. Geometric Distribution Formula
32. Graphs of Trigonometric Formula
33. HYPERBOLA FORMULA
34. Integral Formula
35. Lateral Area Formula
36. Limit Formula
37. LCM Formula
38. Newton’s Method Formula
39. Parabola Formula
40. Parallelogram Formula
41. Percentile Formula
42. Perimeter Formulas
43. Probability Distribution Formulas
44. Proportion Formula
45. Pythagorean Triples Formulas
46. Radius Formula
47. Ratio Formula
48. Rhombus Formula
49. Sequence Formula
50. Sin Tan Formula
51. Sin Cos Formula
52. Surface Areas Formula
53. Statistics Formulas
54. Tangent Formula
55. Tan Theta Formula
56. Volume Charge Density Formula
57. The volume of a Cone Formula
58. The volume of a Cylinder Formula
59. The volume of a Rectangular Prism Formula
60. The volume of a Square Pyramid Formula
61. The volume of A Triangular Prism Formula
62. 30-60-90 Formulas
63. Vertex Formula
64. X and Y Intercept Formula
65. Z Score Formula
Algebra
Algebra is the most crucial concept in mathematics. You need to learn its formulas because of its usage in mathematics in all the classes.
1.a2 – b2 = (a + b) (a – b)
2.(a + b)2 = a2 + 2ab + b2
3.(a – b)2 = a2 – 2ab + b2
4.a2 + b2 = (a – b)2 + 2ab
5.(a+b+c) 2 = a2 + b2+ c2 + 2ab+2bc + 2ac
6.(a-b-c) 2 = a2 + b2+ c2 – 2ab + 2bc – 2ac
7.(a + b)3 = a3+3a2b + 3ab2 + b3
8.(a – b)3 = a3-3a2b + 3ab2 – b3
9. a3-b3 = (a – b)(a2+ ab + b2)
10. a3 + b3 = (a + b)(a2 – ab+b2)
11. (a + b)4 = a4 + 4a3b+ 6a2b2 + 4ab3 + b4
12. (a – b)4 = a4 – 4a3b+ 6a2b2-4ab3 + b4
13. a4 – b4 = (a – b)(a + b)(a2 +b2)
14. a5 – b5 = (a – b) (a4 + a3b+ a2b2+ ab3 + b4)
15. (a+b+c)2=a2+b2+c2+2ab+2bc+2ca
16. (a+b+c+…)2=a2+b2+c2++2(ab +ac+ bc +…
17. (x+y+ z)2=x2+y2+z2+2xy+2yz+2xz
18. (x+y-z)2=x2+y2+z2+2xy-2yz-2xz
19. (x-y+ z)2=x2+y2+z2-2xy-2yz+2xz
20. (x-y-z)2=x2+y2+z2-2xy+2yz-2xz
21.x3+y3+z3-3xyz=(x+y+ z) (x2+y2+z2-xy-yz-xz)
22. x2+y2=1/2[(x+y)2+(x-y)2]
23. (x +a)(x+b)(x+c)=x3+(a+b+c)x2+(ab +bc+ ca)x+ abc
24. x3+y3=(x+y) (x2-xy+y2)
25. x3-y3=(x-y) (x2+xy+y2)
26.x2+y2+z2-xy-yz-zx=1/2[(x-y)2+(y-z)2+(z-x)2]
Geometry
Geometry includes the calculation of surface area, perimeter, volumes, etc. Here is the list of basic geometry formulas:
Area of square = a2
Perimeter of square = 4a
Perimeter of rectangle = 2(l+b)
Area of rectangle = length* breadth
Area of circle = П* r2
Circumference of circle = 2πr
Area of triangle = 1/2 * base * height
Area of cube = 6a2
Surface area of cylinder = 2πr2+2πrh
Surface area of sphere = 4πr2
BODMAS Formula
B = Bracket
O = Of
D = Division
M = Multiplication
A = Addition
S = Subtraction
Class 6 Maths formulas
1. 1,000,000,000 is called one billion.
2. Anything divided by zero is called ‘undefined’.
3. A number is divisible by 2 if it has 0, 2, 4, 6 or 8 in one place.
4. A number is divisible by 3 if the sum of the digits is a multiple of 3.
5. A simple closed figure formed by line segments is a polygon. Triangle is a three-sided Polygon. Quadrilaterals are four-sided polygons.
6. An equation is a condition represented on a variable. An equation is composed of two sides, known as the Left-Hand Side and Right Hand Side, separated by an equal (=) sign.
7. The perimeter of a Square = 4 × Length of its side
8. Perimeter of a Rectangle = 2 × (Length + Breadth)
9. The perimeter of an Equilateral triangle = 3 × Length of a side
10. Area of a Rectangle = length x breadth
11. Variable refers to a value that is not fixed. It can take different values.
12. An equation is a condition represented on a variable.
13. An equation is composed of two sides, known as the Left-Hand Side and Right Hand Side, separated by an equal (=) sign.
Class 7 Maths formulas
1. Product of rational numbers = (Product of Numerators) / (Product of Denominators)
2. First Rational Number * (Reciprocal of other Rational Number)
3. Area of a Square = Side2
4. Perimeter of a Square = 4 × Side
5. Area of Rectangle = Length x Breadth
6. Perimeter of a Rectangle = 2 × (Length + Breadth)
7. Area of a Parallelogram = Base x Height
8. Area of Triangle = 1/2 × Base x Height
9. Circumference of a Circle = πd, where ‘d’ is the diameter of a circle and π = 22/7 or 3.14
10. Area of a Circle = πr2
11. Law of Product: am an = am+n
12. Law of Quotient: am/an = am-n
13. Law of Zero Exponent: a0 = 1
14. Law of Negative Exponent: a-m = 1/am
15. Law of Power of a Power: (am)n = amn
16. Law of Power of a Product: (ab)m = ambm
17. Law of Power of a Quotient: (a/b)m = am/bm
18. (a-b) 2 = a2 – 2ab+b2
19. (a-b-c)2 = a2 +b2+ c2 – 2ab+2bc – 2ac
If their two ratios are equivalent for any four quantities, those four quantities are said to be proportionate.
⇒ Increase in Percentage (Change / Original Amount) x 100
⇒ Profit Percentage = (Profit / Cost price) × 100
⇒ Simple Interest = (Principal x Rate x Time) / 100
⇒ Amount = Principal + Interest
Class 8 Math formulas
1. Additive inverse of rational number: a/b = -b/a
2. Multiplicative Inverse of a/b = c/d, if a/b xc/d=1
3. Distributives a(b-c) = ab – ac
4. Probability of the occurrence of an event = Number of outcomes that comprise an event/ Total number of outcomes
5. Compound Interest formula = Amount – Principal, Amount in case the interest is calculated annually = Principal (1+ Rate/100)n, where ‘n’ is the period.
6. (a – b)2=a2-2ab+b2
7. (a + b) (a – b) = a2 – b2
8. Euler’s Formula: For any polyhedron, Number of faces + Number of vertices – Number of edges = 2
9. Volume of a Cone = (1/3)πr2h
10. Volume of a Sphere = (4/3) π r3
Class 9 Math formulas
1. Real Numbers
1. Vab = √a √b
2. √(a/b) = √a / √b
3. (va + vb) (va – √b) = a – b
4. (va + √b)2 = a + 2√ab + b
5. (a + vb) (a – √b) = a2 – b
6. (a + b) (a – b) = a2 – b2
Maths Formulas For Class 10
1. Algebra Formulas For Class 10
1.(a+b)2= a2 + b2+2ab
2.(a-b)2=a2+ b2 – 2ab
3.(a+b) (a-b) = a2-b2
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)
15.x2+ y2 = [(x + y)2 + (x − y)2]
16.(x+a) (x + b) (x + c) = x3 + (a+b+c)x2+(ab + bc + ca)x + abc
17.x3 + y3= (x + y) (x2 – xy + y2)
18.x3-y3 = (x – y) (x2 + xy + y2)
19.x2 + y2+ z2 -xy – yz – zx = 1⁄2 [(x-y)2+(y-z)2 + (z-x)2]
2. Basic Formulas For Powers For Class 10
1.pmxpn = pm+n
2.{pm}/{pn} = pm-n
3.(pm)n = pmn
4.p-m = 1/pm
5.p1 = p
6.p0 = 1
3. Arithmetic Formulas For Class 10
1. an = a + (n-1) d, where an is the nth term.
2. Sn=n/2 [2a + (n-1)d]
4. Trigonometry Formulas For Class 10
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 Ø + + cos2 Ø =1 ⇒sin2 Ø = 1- cos2 Ø ⇒ cos2 Ø = 1-sin2 Ø
8. cosec2 Ø – cot2 Ø = 1⇒ cosec2 Ø =1+ cot2 Ø ⇒ cot2 Ø = cosec2 Ø – 1
9. sec2 Ø -tan2 Ø = 1⇒ sec2 Ø =1+ tan2 Ø ⇒tan2 Ø = sec2 Ø -1
10. sin Ø cosec Ø = 1⇒ cos Ø sec Ø = 1 ⇒ tan Ø cot Ø = 1
Circle Formula
1. 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].
2. The tangent to a circle equation x2 + y2 = a2 at (al,bl) is xal + yb1 = a2
Area and Volume Formulas
1. Volume of Sphere = 4/3 xπ r3
2. Lateral Surface Area of Sphere (LSA) = 4π г2
3. Total Surface Area of Sphere (TSA) = 4πг2
4. The volume of the Right Circular Cylinder = πr2h
5. Lateral Surface Area of Right Circular Cylinder (LSA) = 2×(лrh)
6. Total Surface Area of Right Circular Cylinder (TSA) = 2πrx (r + h)
7. Volume of Hemisphere = 2/3 x (πr3)
8. Lateral Surface Area of Hemisphere (LSA) = 2πг2
9. Total Surface Area of Hemisphere (TSA) = 3πг2
10. Volume of Prism = B x h
11. Lateral Surface Area of Prism (LSA) = px h
Class 11 Math formulas
Algebra Formulas
1.ax (b+c) = axb+a x c (Distributive property)
2. a + b = b + a (Commutative Property of Addition)
3. a x b = b x a (Commutative Property of Multiplication)
4. a + (b + c) = (a + b) + c (Associative Property of Addition)
5.a x (bx c) = (a x b) x 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
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 Ø + cos2 Ø = 1 ⇒ sin20=1-cos2 Ø cos2 Ø = 1-sin2 Ø
8. cosec2 Ø -cot2 Ø = 1⇒ cosec2 Ø = 1+ cot2 Ø ⇒ cot2 Ø = cosec2 Ø – 1
9. sec2 Ø -tan2 Ø = 1 ⇒ sec2 Ø = 1 + tan2 Ø ⇒ tan2 Ø = sec2 Ø – 1
10. sin Ø cosec Ø = 1⇒ cos Ø sec Ø = 1⇒tan Ø cot Ø = 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) 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-yl = m (x-x1)
Class 12 Math Formulas
Vector Formulas
1. A + B = B+ A (Commutative Law)
2. A+ (B+C) = (A + B) + C (Associative Law)
3. (AB)= IPI IQI cos + ( Dot Product)
4. (A x B)= IPI IQI sin + (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-1x = π/2
4. cos-1(-x) = – cos-lx
5. cot-1(x) = – cot-lx
Calculus Formulas
1. ʃ f(x) dx = F(x) + C
2. Power Rule: ʃ xn dx = (xn+1)/ (n+1)+ C. (Where n ≠ -1)
3. Exponential Rules: [ex dx = ex + C
4. ʃ dx = ax / In (a) + C
5. ʃ In(x) dx = x In(x) = x + C
6. Constant Multiplication Rule: ʃ a dx = ax + C, where a is the constant.
7. Reciprocal Rule: ʃ (1/x) dx = In(x)+ C
8. Sum Rules: ʃ [f(x) + g(x)] dx = ʃ f(x) dx + ʃ g(x) dx
9. Difference Rules: ʃ [f(x) − g(x)] dx = ʃ f(x) dx – ʃ g(x) dx
10. ʃ 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. ʃ cos x dx = sin x + C
13. ʃ sin x dx = -cos x + C
14. ʃ sec2 x dx = tan x + C
15. ʃ cosec2 x dx = -cot x + C
16. ʃ sec x tan x dx = sec x + C
17. ʃ cosec x cot x dx = – cosec x + C
Geometry Formulas
1. Cartesian equation of a plane: Ix + my + nz = d
2. Distance between two points P(x1,y1, z1) and Q(x2, y2, z2): PQ = √((x1 − x2)2 + (y1 – y2)2 + (z1- z2)2)
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