Basic Maths Formulas for Class 6 to 12
Mathematics forms the foundation of scientific thinking and problem-solving skills. A strong grasp of basic maths formulas is essential for students to progress through their academic journey. This comprehensive guide presents key mathematical formulas students encounter from class 6 through class 12, arranged in a structured format for easy reference and revision.
Whether you’re struggling with basic arithmetic, exploring the depths of calculus, or anywhere in between, this collection of basic maths formulas will serve as a valuable resource to support your mathematical development and build confidence in tackling complex problems.
- ▪ Basic Maths Formulas for Class 6 to 12
- ▪ BODMAS Mathematics Formula
- ▪ Algebra Formulas
- ▪ Geometry Formulas
- ▪ Trigonometry Formulas
- ▪ Calculus Formulas
- ▪ Statistics Formulas
- ▪ Miscellaneous Formulas
- ▪ Important Math Formulas Table
- ▪ Importance of Learning Basic Formulas of Maths
- ▪ Tips to Remember Important Maths Formulas
- ▪ Conclusion
- ▪ Basic Maths Formulas for Class 6 to 12 FAQs
Must Buy: Oswal Publishers Books for CBSE Class 9 to 12
Basic Maths Formulas for Class 6 to 12
Class 6 Formulas
| Topic | Formula | Description |
| Arithmetic Operations | a + b = b + a | Commutative property of addition |
| (a + b) + c = a + (b + c) | Associative property of addition | |
| a × b = b × a | Commutative property of multiplication | |
| (a × b) × c = a × (b × c) | Associative property of multiplication | |
| a × (b + c) = a × b + a × c | Distributive property | |
| Fractions | a/b + c/d = (ad + bc)/bd | Addition of fractions |
| a/b – c/d = (ad – bc)/bd | Subtraction of fractions | |
| (a/b) × (c/d) = (a×c)/(b×d) | Multiplication of fractions | |
| (a/b) ÷ (c/d) = (a×d)/(b×c) | Division of fractions | |
| Perimeter | P = 2(l + w) | Perimeter of a rectangle |
| P = 4s | Perimeter of a square | |
| P = a + b + c | Perimeter of a triangle | |
| Area | A = l × w | Area of the rectangle |
| A = s² | Area of a square | |
| A = ½ × b × h | Area of the triangle | |
| Percentage | Percentage = (Value/Total Value) × 100 | Converting to a percentage |
| Value = (Percentage × Total Value)/100 | Finding value from a percentage | |
| Ratio & Proportion | a : b :: c : d → a/b = c/d | Proportion equality |
| Simple Interest | SI = (P × R × T)/100 | P = Principal, R = Rate, T = Time |
Class 6 introduces fundamental concepts of measurement, including perimeter and area calculations for basic shapes. Students also encounter introductory concepts of percentage, ratio, and simple interest calculations. These basic maths formulas form the foundation for more complex mathematical concepts in higher classes.
Class 7 Formulas
| Topic | Formula | Description |
| Circle | A = πr² | Area of a circle |
| C = 2πr | Circumference of a circle | |
| Parallelogram | A = b × h | Area of parallelogram |
| P = 2(a + b) | Perimeter of parallelogram | |
| Rhombus | A = ½ × d₁ × d₂ | Area using diagonals |
| A = b × h | Area using base and height | |
| Trapezium | A = ½ × (a + c) × h | Area of trapezium |
| P = a + b + c + d | Perimeter of trapezium | |
| Simple Interest | SI = (P × R × T)/100 | Where SI = Simple Interest |
| Compound Interest | A = P(1 + R/100)^T | Where A = Amount, P = Principal |
| CI = A – P | Compound Interest | |
| Exponents | a^m × a^n = a^(m+n) | Product rule |
| a^m ÷ a^n = a^(m-n) | Quotient rule | |
| (a^m)^n = a^(m×n) | Power rule | |
| a^0 = 1 | Zero exponent rule |
Class 7 builds upon previous knowledge and introduces circular measurements, exponents, and more complex percentage applications. Learning these basic maths formulas helps students develop stronger mathematical intuition and problem-solving abilities.
Also Learn: Squares 1 to 30
Class 8 Formulas
| Topic | Formula | Description |
| Pythagoras Theorem | a² + b² = c² | In a right-angled triangle |
| Volume | V = l × w × h | Volume of a cuboid |
| V = a³ | Volume of a cube | |
| V = πr²h | Volume of a cylinder | |
| Surface Area | SA = 6a² | Surface area of a cube |
| SA = 2(lb + bh + hl) | Surface area of cuboid | |
| SA = 2πr(r + h) | Surface area of a cylinder | |
| Proportion | Direct: a/b = c/d | Direct proportion |
| Inverse: a/b = d/c | Inverse proportion | |
| Algebraic Identities | (a + b)² = a² + 2ab + b² | Square of sum |
| (a-b)² = a² – 2ab + b² | Square of difference | |
| a² – b² = (a + b)(a – b) | Difference of squares | |
| Data Handling | Mean = Sum of all values/Number of values | Arithmetic mean |
| Median = Middle value(s) | When data is arranged in order | |
| Mode = Most frequently occurring value. | Highest frequency |
In Class 8, students begin to explore three-dimensional geometry and the Pythagorean theorem, which serves as a foundation for later trigonometric concepts. These basic maths formulas are frequently used in solving complex geometrical problems.
Also Learn: Cubes 1 to 30
Class 9 Formulas
| Topic | Formula | Description |
| Quadratic Formula | x = [-b ± √(b² – 4ac)]/2a | For equation ax² + bx + c = 0 |
| Coordinate Geometry | d = √[(x₂ – x₁)² + (y₂ – y₁)²] | Distance between two points |
| m = (y₂ – y₁)/(x₂ – x₁) | Slope of a line | |
| y – y₁ = m(x – x₁) | Point-slope form of a line | |
| Triangles | Area = √[s(s-a)(s-b)(s-c)] | Heron’s formula, s = (a+b+c)/2 |
| Circles | Area = πr² | Area of a circle |
| Circumference = 2πr | Circumference of a circle | |
| Arc length = (θ/360) × 2πr | Where θ is in degrees | |
| Area of sector = (θ/360) × πr² | Where θ is in degrees | |
| Surface Area and Volume | SA = 4πr² | Surface area of a sphere |
| V = (4/3)πr³ | Volume of a sphere | |
| SA = πr(r + l) | Surface area of a cone | |
| V = (1/3)πr²h | Volume of a cone | |
| Statistics | Range = Maximum value – Minimum value | Measure of dispersion |
| Mean Deviation = Σ | x – x̄ |
Class 9 introduces coordinate geometry and more advanced formulas for solving algebraic equations and calculating areas and volumes of complex shapes. These basic maths formulas provide students with tools for solving increasingly challenging problems.
Class 10 Formulas
| Topic | Formula | Description |
| Quadratic Equations | a² – b² = (a+b)(a-b) | Difference of squares |
| (a+b)² = a² + 2ab + b² | Square of sum | |
| (a-b)² = a² – 2ab + b² | Square of difference | |
| (a+b+c)² = a² + b² + c² + 2ab + 2bc + 2ca | Square of trinomial | |
| Arithmetic Progression | a_n = a + (n-1)d | nth term |
| S_n = n/2[2a + (n-1)d] | Sum of n terms | |
| S_n = n/2(a + l) | Where l is the last term | |
| Circle | Area of sector = (θ/360) × πr² | Where θ is in degrees |
| Length of arc = (θ/360) × 2πr | Where θ is in degrees | |
| Trigonometry | sin θ = Opposite/Hypotenuse | Basic ratio |
| cos θ = Adjacent/Hypotenuse | Basic ratio | |
| tan θ = Opposite/Adjacent | Basic ratio | |
| sin θ = 1/cosec θ | Reciprocal relationship | |
| cos θ = 1/sec θ | Reciprocal relationship | |
| tan θ = 1/cot θ | Reciprocal relationship | |
| Surface Area of Solids | SA of cone = πr(r + l) | L is the slant height |
| SA of frustum = π(r₁ + r₂)l + πr₁² + πr₂² | L is the slant height | |
| Volume of Solids | V of sphere = (4/3)πr³ | Volume of sphere |
| V of cone = (1/3)πr²h | Volume of a cone | |
| V of frustum = (1/3)πh(r₁² + r₂² + r₁r₂) | Volume of frustum of cone | |
| Statistics | Mean = Σx/n | Arithmetic mean |
| Median = (n+1)/2th term | For odd n | |
| Median = Average of n/2th and (n/2+1)th terms | For even n | |
| Mode = l + h × (f₁ – f₀)/(2f₁ – f₀ – f₂) | For grouped data |
Class 10 delves deeper into patterns with arithmetic progressions and introduces trigonometric concepts that will be essential in higher classes. Learning these basic maths formulas thoroughly helps in building a solid foundation for future mathematical concepts.
Also Learn: Algebra Formulas Class 10
Class 11 Formulas
| Topic | Formula | Description |
| Sets | n(A ∪ B) = n(A) + n(B) – n(A ∩ B) | Number of elements in the union |
| n(A ∪ B ∪ C) = n(A) + n(B) + n(C) – n(A ∩ B) – n(B ∩ C) – n(C ∩ A) + n(A ∩ B ∩ C) | Union of three sets | |
| Binomial Theorem | (a+b)^n = Σ(k=0 to n) (nCk)a^(n-k)b^k | Binomial expansion |
| nCr = n!/(r!(n-r)!) | Combination formula | |
| Sequences & Series | a_n = ar^(n-1) | nth term of GP |
| S_n = a(1-r^n)/(1-r) | Sum of n terms of GP | |
| S_∞ = a/(1-r) | Sum of infinite GP, | |
| Straight Lines | y – y₁ = m(x – x₁) | Point-slope form |
| ax + by + c = 0 | General form | |
| y = mx + c | Slope-intercept form | |
| Circles | (x-h)² + (y-k)² = r² | Standard form of a circle |
| x² + y² + 2gx + 2fy + c = 0 | General form of a circle | |
| r = √(g² + f² – c) | Radius of circle | |
| Centre = (-g, -f) | From general form | |
| Permutations | nPr = n!/(n-r)! | Permutation formula |
| Combinations | nCr = n!/(r!(n-r)!) | Combination formula |
| nCr = nC(n-r) | Complementary property | |
| Probability | P(E) = Number of favourable outcomes/Total number of possible outcomes | Basic probability |
| P(A’) = 1 – P(A) | Complement rule | |
| P(A ∪ B) = P(A) + P(B) – P(A ∩ B) | Addition rule |
Class 11 marks the transition to more abstract mathematical concepts, introducing combinatorics, sequences, and advanced coordinate geometry. The basic maths formulas taught at this level require deeper understanding and analytical thinking.
Class 12 Formulas
| Topic | Formula | Description |
| Relations & Functions | f: X → Y, f(x) = y | Function definition |
| f⁻¹(y) = x | Inverse function | |
| (f ∘ g)(x) = f(g(x)) | Composite function | |
| Differential Calculus | d/dx(x^n) = nx^(n-1) | Power rule |
| d/dx(e^x) = e^x | Exponential function | |
| d/dx(ln x) = 1/x | Natural logarithm | |
| d/dx(sin x) = cos x | Sine function | |
| d/dx(cos x) = -sin x | Cosine function | |
| d/dx(tan x) = sec²x | Tangent function | |
| Integral Calculus | ∫x^n dx = x^(n+1)/(n+1) + C | Power rule, n ≠ -1 |
| ∫e^x dx = e^x + C | Exponential function | |
| ∫(1/x) dx = ln | x | |
| ∫sin x dx = -cos x + C | Sine function | |
| ∫cos x dx = sin x + C | Cosine function | |
| ∫tan x dx = -ln | cos x | |
| Vectors | a | |
| a·b = | a | |
| a×b = | a | |
| 3D Geometry | d = √[(x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²] | Distance formula |
| r = (x₀, y₀, z₀) + t(a, b, c) | The vector form of a line | |
| ax + by + cz + d = 0 | General form of a plane | |
| Linear Programming | Z = ax + by | Objective function |
| Subject to: ax + by ≤ c | Constraints | |
| Probability | P(A | B) = P(A ∩ B)/P(B) |
| P(A ∩ B) = P(A) × P(B | A) | |
| Bayes’ Theorem | P(A | B) = [P(B |
Class 12 introduces calculus concepts, advanced algebra with matrices, and probability theory, preparing students for university-level mathematics. Mastering these basic maths formulas is crucial for students planning to pursue higher education in mathematics, engineering, or the sciences.
BODMAS Mathematics Formula
BODMAS (or BIDMAS) is a crucial rule that establishes the order of operations when evaluating mathematical expressions. It stands for:
- Brackets: First, solve all expressions within brackets.
- Orders (or Indices): Next, calculate all powers and roots.
- Division and Multiplication: Perform all divisions and multiplications from left to right.
- Addition and Subtraction: Finally, perform all additions and subtractions from left to right.
| BODMAS Step | Operation | Example |
| Brackets | ( ) | (3 + 4) × 2 = 7 × 2 = 14 |
| Orders/Indices | Powers, roots | 2³ + 4 = 8 + 4 = 12 |
| Division | ÷ | 10 ÷ 5 × 2 = 2 × 2 = 4 |
| Multiplication | × | 2 × 3 + 4 = 6 + 4 = 10 |
| Addition | + | 5 + 3 – 2 = 8 – 2 = 6 |
| Subtraction | – | 7 – 3 + 1 = 4 + 1 = 5 |
For example, when evaluating 2 + 3 × 4², follow BODMAS by first calculating 4² = 16, then 3 × 16 = 48, and finally 2 + 48 = 50.
Common mistakes occur when students fail to apply this order correctly. Consider 8 ÷ 2(2+2): First, solve the brackets (2+2) = 4, then proceed with division and multiplication from left to right: 8 ÷ 2 = 4, and 4 × 4 = 16. Remember that BODMAS ensures consistent and correct evaluation of mathematical expressions across all branches of mathematics. Every student should memorise these basic maths formulas and operations to avoid common calculation errors.
Algebra Formulas
Algebraic formulas form the foundation of mathematical problem-solving. These identities help simplify complex expressions and solve equations efficiently. Students should regularly practice applying these basic maths formulas to strengthen their algebraic skills.
Basic Algebraic Identities
| Identity | Formula |
| Square of sum | (a + b)² = a² + 2ab + b² |
| Square of difference | (a-b)² = a² – 2ab + b² |
| Difference of squares | a² – b² = (a + b)(a – b) |
| Cube of sum | (a + b)³ = a³ + 3a²b + 3ab² + b³ |
| Cube of difference | (a-b)³ = a³ – 3a²b + 3ab² – b³ |
| Sum of cubes | a³ + b³ = (a + b)(a² – ab + b²) |
| Difference of cubes | a³ – b³ = (a – b)(a² + ab + b²) |
| a⁴ – b⁴ | (a² + b²)(a + b)(a – b) |
| (a + b + c)² | a² + b² + c² + 2ab + 2bc + 2ca |
| (a + b)⁴ | a⁴ + 4a³b + 6a²b² + 4ab³ + b⁴ |
Quadratic Equations
| Formula | Description |
| ax² + bx + c = 0 | Standard form |
| x = [-b ± √(b² – 4ac)]/2a | Quadratic formula |
| x = -b/2a ± √(b² – 4ac)/2a | Alternative form |
| x = (-b ± √D)/2a | Where D = b² – 4ac |
| Sum of roots = -b/a | Vieta’s formula |
| Product of roots = c/a | Vieta’s formula |
Discriminant (D) = b² – 4ac
- If D > 0: Two distinct real roots
- If D = 0: One real root (repeated)
- If D < 0: No real roots (two complex conjugate roots)
Polynomial Division
For polynomial P(x) divided by divisor D(x): P(x) = D(x) · Q(x) + R(x), where Q(x) is the quotient and R(x) is the remainder.
Remainder Theorem: If a polynomial P(x) is divided by (x-a), the remainder equals P(a).
Factor Theorem: (x-a) is a factor of P(x) if and only if P(a) = 0.
These formulas are essential for algebraic manipulations and provide the building blocks for more advanced mathematical concepts. Understanding these basic maths formulas thoroughly helps in solving complex equations with ease.
Geometry Formulas
Geometry deals with the properties and relationships of points, lines, angles, surfaces, and solids. The general mathematics formula listed here will help students solve a wide range of geometric problems effectively.
2D Shapes
| Shape | Area | Perimeter |
| Square | A = a² | P = 4a |
| Rectangle | A = l × w | P = 2(l + w) |
| Triangle | A = ½ × b × h | P = a + b + c |
| A = √[s(s-a)(s-b)(s-c)] | s = (a+b+c)/2 | |
| A = ½ × ab × sin C | Using two sides and the included angle | |
| Circle | A = πr² | C = 2πr |
| Parallelogram | A = b × h | P = 2(a + b) |
| Rhombus | A = ½ × d₁ × d₂ | P = 4a |
| A = a² × sin A | Using side and angle | |
| Trapezoid/Trapezium | A = ½ × (a + c) × h | P = a + b + c + d |
| Regular Polygon (n sides) | A = (n × s²)/(4 × tan(π/n)) | P = n × s |
| Sector of Circle | A = (θ/360) × πr² | Arc length = (θ/360) × 2πr |
| Ellipse | A = πab | P ≈ 2π√[(a² + b²)/2] |
3D Shapes
| Shape | Volume | Surface Area |
| Cube | V = a³ | SA = 6a² |
| Cuboid/Rectangular Prism | V = l × w × h | SA = 2(lw + wh + hl) |
| Sphere | V = (4/3)πr³ | SA = 4πr² |
| Cylinder | V = πr²h | SA = 2πr(r + h) |
| Cone | V = (1/3)πr²h | SA = πr(r + l) |
| l = √(r² + h²) | ||
| Pyramid | V = (1/3) × Base Area × Height | Varies by base shape |
| Frustum of a Cone | V = (1/3)πh(r₁² + r₂² + r₁r₂) | SA = π(r₁ + r₂)l + πr₁² + πr₂² |
| Prism | V = Base Area × Height | SA = 2 × Base Area + Perimeter × Height |
| Torus | V = 2π²r²R | SA = 4π²rR |
Circle Properties
| Property | Formula |
| Area | A = πr² |
| Circumference | C = 2πr |
| Diameter | d = 2r |
| Arc length | s = rθ (θ in radians) |
| s = (θ/360) × 2πr (θ in degrees) | |
| Area of sector | A = ½r²θ (θ in radians) |
| A = (θ/360) × πr² (θ in degrees) |
Heron’s formula is particularly useful for finding the area of a triangle when only the sides are known: Area = √[s(s-a)(s-b)(s-c)], where s = (a+b+c)/2. These geometric basic maths formulas are crucial for solving problems involving various shapes and figures.
Trigonometry Formulas
Trigonometry connects angles and sides of triangles through ratios and functions. Some basic formula of maths in trigonometry are fundamental in various scientific fields:
Basic Ratios
| Ratio | Formula | Reciprocal |
| Sine | sin θ = Opposite/Hypotenuse | cosec θ = 1/sin θ |
| Cosine | cos θ = Adjacent/Hypotenuse | sec θ = 1/cos θ |
| Tangent | tan θ = Opposite/Adjacent = sin θ/cos θ | cot θ = 1/tan θ |
Fundamental Identities
| Identity | Formula |
| Pythagorean | sin²θ + cos²θ = 1 |
| 1 + tan²θ = sec²θ | |
| 1 + cot²θ = cosec²θ | |
| Ratio | tan θ = sin θ/cos θ |
| cot θ = cos θ/sin θ |
Angle Formulas
| Formula Type | Sine | Cosine | Tangent |
| Addition | sin(A+B) = sinA·cosB + cosA·sinB | cos(A+B) = cosA·cosB – sinA·sinB | tan(A+B) = (tanA + tanB)/(1 – tanA·tanB) |
| Subtraction | sin(A-B) = sinA·cosB – cosA·sinB | cos(A-B) = cosA·cosB + sinA·sinB | tan(A-B) = (tanA – tanB)/(1 + tanA·tanB) |
| Double Angle | sin(2A) = 2sinA·cosA | cos(2A) = cos²A – sin²A | tan(2A) = 2tanA/(1 – tan²A) |
| = 2cos²A – 1 | |||
| = 1 – 2sin²A | |||
| Triple Angle | sin(3A) = 3sinA – 4sin³A | cos(3A) = 4cos³A – 3cosA | tan(3A) = (3tanA – tan³A)/(1 – 3tan²A) |
| Half Angle | sin(A/2) = ±√[(1 – cosA)/2] | cos(A/2) = ±√[(1 + cosA)/2] | tan(A/2) = (1 – cosA)/sinA |
Product to Sum Formulas
| Formula | Expression |
| sinA·sinB | ½[cos(A-B) – cos(A+B)] |
| cosA·cosB | ½[cos(A-B) + cos(A+B)] |
| sinA·cosB | ½[sin(A+B) + sin(A-B)] |
Sum to Product Formulas
| Formula | Expression |
| sinA + sinB | 2sin[(A+B)/2]·cos[(A-B)/2] |
| sinA – sinB | 2cos[(A+B)/2]·sin[(A-B)/2] |
| cosA + cosB | 2cos[(A+B)/2]·cos[(A-B)/2] |
| cosA – cosB | -2sin[(A+B)/2]·sin[(A-B)/2] |
Special Angles Table
| Angle | sin | cos | tan |
| 0° | 0 | 1 | 0 |
| 30° | ½ | √3/2 | 1/√3 |
| 45° | 1/√2 | 1/√2 | 1 |
| 60° | √3/2 | ½ | √3 |
| 90° | 1 | 0 | Undefined |
Understanding these relationships allows students to analyse periodic phenomena and solve complex geometric problems involving angles and distances. These trigonometric basic maths formulas are essential for many applications in physics and engineering.
Calculus Formulas
Calculus explores change and accumulation through differentiation and integration. The basic math formulas chart below presents the fundamental tools of calculus:
Differentiation Rules
| Function | Derivative |
| c (constant) | 0 |
| x^n | nx^(n-1) |
| e^x | e^x |
| ln x | 1/x |
| sin x | cos x |
| cos x | -sin x |
| tan x | sec²x |
| cot x | -cosec²x |
| sec x | sec x · tan x |
| cosec x | -cosec x · cot x |
| a^x | a^x · ln a |
| log_a x | 1/(x · ln a) |
Rules of Differentiation
| Rule | Formula |
| Chain Rule | d/dx[f(g(x))] = f'(g(x)) × g'(x) |
| Product Rule | d/dx[f(x)·g(x)] = f'(x)·g(x) + f(x)·g'(x) |
| Quotient Rule | d/dx[f(x)/g(x)] = [f'(x)·g(x) – f(x)·g'(x)]/[g(x)]² |
| Sum Rule | d/dx[f(x) + g(x)] = f'(x) + g'(x) |
| Difference Rule | d/dx[f(x) – g(x)] = f'(x) – g'(x) |
Integration Formulas
| Function | Integral |
| x^n (n ≠ -1) | x^(n+1)/(n+1) + C |
| 1/x | ln |
| e^x | e^x + C |
| sin x | -cos x + C |
| cos x | sin x + C |
| tan x | -ln |
| sec²x | tan x + C |
| 1/√(1-x²) | sin^(-1)(x) + C |
| 1/(1+x²) | tan^(-1)(x) + C |
| 1/(x²-1) | ½ ln |
Integration Rules
| Rule | Formula |
| Linearity | ∫[af(x) + bg(x)]dx = a∫f(x)dx + b∫g(x)dx |
| Substitution | ∫f(g(x))g'(x)dx = ∫f(u)du, where u = g(x) |
| Integration by Parts | ∫u·v’dx = u·v – ∫v·u’dx |
| Partial Fractions | Decompose rational functions into simpler fractions |
Definite Integration
| Property | Formula |
| Basic Formula | ∫[a to b] f(x)dx = F(b) – F(a) |
| Properties | ∫[a to b] f(x)dx = -∫[b to a] f(x)dx |
| ∫[a to b] [f(x) ± g(x)]dx = ∫[a to b] f(x)dx ± ∫[a to b] g(x)dx | |
| ∫[a to b] c·f(x)dx = c·∫[a to b] f(x)dx | |
| ∫[a to c] f(x)dx + ∫[c to b] f(x)dx = ∫[a to b] f(x)dx |
Calculus connects mathematics to real-world applications, allowing us to calculate rates of change and accumulation in various contexts.
Statistics Formulas
Statistics provides tools to analyse, interpret, and present data effectively. These formulas are essential for data analysis:
| Measure | Formula | Description |
| Mean (Arithmetic) | μ = (Σx)/n | The sum of all values divided by the number of values |
| Median | The middle value when the data is arranged in order | For even n, the average of the two middle values |
| Mode | Value that occurs most frequently | May have multiple modes or none |
| Range | Max(x) – Min(x) | Difference between the highest and lowest values |
| Variance | σ² = Σ(x – μ)²/n | Average squared deviation from the mean |
| Standard Deviation | σ = √[Σ(x – μ)²/n] | Square root of variance |
| Sample Variance | s² = Σ(x – x̄)²/(n-1) | Using n-1 for unbiased estimation |
| Sample Standard Deviation | s = √[Σ(x – x̄)²/(n-1)] | Square root of sample variance |
| Coefficient of Variation | CV = (σ/μ) × 100% | Relative measure of dispersion |
| Z-score | z = (x – μ)/σ | Number of standard deviations from the mean |
| Correlation Coefficient | r = Σ[(x-x̄)(y-ȳ)]/[√Σ(x-x̄)²√Σ(y-ȳ)²] | Measures relationship strength (-1 to +1) |
| Probability | P(A) = n(A)/n(S) | Favourable outcomes divided by total outcomes |
| Binomial Probability | P(X=k) = ⁿCₖ × p^k × (1-p)^(n-k) | Probability of k successes in n trials |
| Normal Distribution | f(x) = (1/(σ√2π)) × e^(-(x-μ)²/2σ²) | Probability density function |
For grouped data, the weighted mean is calculated as μ = Σ(f×x)/Σf, where f represents frequency. Quartiles divide data into four equal parts: Q₁ (25th percentile), Q₂ (median), and Q₃ (75th percentile). The interquartile range (IQR = Q₃ – Q₁) measures dispersion while minimising outlier effects.
Miscellaneous Formulas
These additional formulas are crucial across various mathematical applications:
| Category | Formula | Description |
| Logarithms | ||
| Logarithm Properties | log₍ₐ₎(xy) = log₍ₐ₎(x) + log₍ₐ₎(y) | Product rule |
| log₍ₐ₎(x/y) = log₍ₐ₎(x) – log₍ₐ₎(y) | Quotient rule | |
| log₍ₐ₎(x^n) = n·log₍ₐ₎(x) | Power rule | |
| log₍ₐ₎(a) = 1 | Identity rule | |
| log₍ₐ₎(1) = 0 | Zero rule | |
| log₍ₐ₎(x) = log₍ᵦ₎(x)/log₍ᵦ₎(a) | Change of base formula | |
| Sequences & Series | ||
| Arithmetic Sequence | aₙ = a₁ + (n-1)d | nth term with first term a₁ and difference d |
| Arithmetic Series Sum | Sₙ = n/2·[2a₁ + (n-1)d] = n/2·(a₁ + aₙ) | Sum of n terms |
| Geometric Sequence | aₙ = a₁·r^(n-1) | nth term with first term a₁ and ratio r |
| Geometric Series Sum | Sₙ = a₁·(1-r^n)/(1-r) [r≠1] | Sum of n terms |
| S∞ = a₁/(1-r) [ | ||
| Special Shapes | ||
| Equilateral Triangle | A = (√3/4)·a² | Area with side length a |
| h = (√3/2)·a | Height | |
| Regular Hexagon | A = (3√3/2)·a² | Area with side length a |
| P = 6a | Perimeter | |
| Number Theory | ||
| Factorial | n! = n·(n-1)·(n-2)·…·2·1 | Product of all positive integers ≤ n |
| Combinations | ⁿCᵣ = n!/(r!·(n-r)!) | Number of ways to choose r from n |
| Permutations | ⁿPᵣ = n!/(n-r)! | Number of arrangements of r from n |
Exponential functions and compound interest follow A = P(1+r/n)^(nt) or A = Pe^(rt), where P is principal, r is rate, t is time, and n is compounding frequency. The golden ratio φ = (1+√5)/2 ≈ 1.618 appears in nature, art, and architecture.
Important Math Formulas Table
This reference table consolidates important math formulas across mathematical domains:
| Domain | Key Formulas |
| Algebra | (a+b)² = a² + 2ab + b² |
| (a-b)² = a² – 2ab + b² | |
| (a+b)³ = a³ + 3a²b + 3ab² + b³ | |
| a² – b² = (a+b)(a-b) | |
| Quadratic formula: x = [-b ± √(b² – 4ac)]/2a | |
| Geometry | Circle area: A = πr² |
| Triangle area: A = ½bh | |
| Pythagorean theorem: a² + b² = c² | |
| Sphere volume: V = (4/3)πr³ | |
| Cylinder volume: V = πr²h | |
| Trigonometry | sin²θ + cos²θ = 1 |
| sin(A±B) = sinA·cosB ± cosA·sinB | |
| cos(A±B) = cosA·cosB ∓ sinA·sinB | |
| Law of sines: a/sinA = b/sinB = c/sinC | |
| Law of cosines: c² = a² + b² – 2ab·cosC | |
| Calculus | f'(x) = lim[h→0] [f(x+h) – f(x)]/h |
| ∫f(x)dx = F(x) + C where F'(x) = f(x) | |
| Statistics | μ = (Σx)/n |
| σ = √[Σ(x – μ)²/n] |
Importance of Learning Basic Formulas of Maths
Mathematical formulas serve as essential tools for problem-solving and critical thinking development. Here’s why they matter:
- Foundation for advanced learning: Mastering simple math formulas creates a solid foundation upon which more complex concepts can be built. Just as you need to learn the alphabet before writing essays, you need to know fundamental formulas before tackling advanced mathematics.
- Efficiency in problem-solving: Knowing formulas allows you to approach problems systematically and efficiently. Rather than deriving relationships each time, formulas provide ready-made solutions to common mathematical scenarios.
- Development of pattern recognition: Working with formulas helps you recognise patterns in mathematical relationships. This pattern recognition extends beyond mathematics to everyday life, enhancing your analytical abilities.
- Real-world applications: From calculating discounts while shopping to understanding mortgage payments, mathematical formulas have direct applications in daily life. They enable you to make informed decisions based on quantitative reasoning.
- Exam readiness: Familiarity with formulas reduces exam anxiety and improves performance. When formulas are second nature, you can focus on applying them rather than trying to remember them during tests and save time.
- Career opportunities: Many fields, including science, engineering, finance, data analysis, and technology, require mathematical fluency. A strong command of mathematical formulas opens doors to numerous career paths.
Tips to Remember Important Maths Formulas
Memorising numerous basic maths formulas can be challenging, but these effective strategies can help:
- Understand, don’t just memorise: When you understand how a formula is derived and what it means, remembering it becomes easier. Try to work through the derivation of important formulas to grasp their significance.
- Use mnemonic devices: Create memorable phrases or acronyms where the first letter of each word corresponds to elements in the formula. For trigonometric functions, “SOH-CAH-TOA” helps remember that Sin = Opposite/Hypotenuse, Cos = Adjacent/Hypotenuse, and Tan = Opposite/Adjacent.
- Practice regularly: Regular application reinforces memory. Solve a variety of problems that require using different basic maths formulas. The more you apply a formula, the better you’ll remember it.
- Create formula cards: Write formulas on index cards with examples on the reverse side. Review these cards regularly, especially before exams.
- Group related formulas: Organise all basic formulas of maths by topic or relationship. Understanding how formulas connect helps remember them as part of a logical system rather than isolated facts.
- Create personalised shortcuts: Develop your shortcuts or tricks for remembering complex formulas. Personal associations are often the most memorable.
- Use technology wisely: While calculators and computers can apply basic maths formulas for you, use them to check your work rather than replace understanding.
- Review before sleep: Studies show that reviewing material before sleeping improves retention. Spend a few minutes going through key formulas before bed.
Conclusion
Mathematics is a cumulative subject where each concept builds upon previous knowledge. The maths formulas list in this guide serves as an essential tools that enable students to solve a wide range of problems across various mathematical domains. Remember that basic maths formulas are not merely items to be memorised but relationships to be understood. The deepest learning occurs when you grasp why a formula works, not just how to apply it. Regular practice is key, so apply these formulas to diverse problems to cement your understanding and develop mathematical intuition.
Basic Maths Formulas for Class 6 to 12 FAQs
Q1. How do I calculate the area of a rectangle?
Ans – Formula: Area = length × breadth (A = l × b).
Q2. I struggle with remembering trigonometric formulas. Any specific tips?
Ans – Start with the basic mathematics formula(sin²θ + cos²θ = 1) and derive others when needed. Create visual aids like the unit circle, and practice regularly with different problems that use these formulas.
Q3. How can I tell which formula to use for a particular problem?
Ans – Identify what the problem is asking for and what information is provided. With practice, you’ll recognise patterns in problems that indicate which formulas are applicable. Always start by understanding the core concepts.
Q4. Are there any online resources for practising all maths formulas?
Ans – Yes, our website offers interactive exercises that help you apply formulas in various contexts. We also provide explanations and step-by-step solutions.
It’s great to see such a structured list of math formulas all in one place—really helpful for quick revision before exams. It would be even more useful if there were a few examples showing how to apply some of the formulas in real problems.