10th Class Math Formulas
All 10th Class Math formulas, chapter by chapter, with search and a printable layout.
Algebra (37)
| Formula | Expression |
|---|---|
| Quadratic Formula | x = (-b ± √(b² - 4ac)) / 2a |
| Discriminant | D = b² - 4ac |
| Sum of Roots | α + β = -b/a |
| Product of Roots | αβ = c/a |
| (a + b)² | a² + 2ab + b² |
| (a - b)² | a² - 2ab + b² |
| a² - b² | (a + b)(a - b) |
| (a + b)³ | a³ + 3a²b + 3ab² + b³ |
| a³ + b³ | (a + b)(a² - ab + b²) |
| a³ - b³ | (a - b)(a² + ab + b²) |
| Binomial Theorem | (x + y)ⁿ = Σ ⁿCᵣ xⁿ⁻ʳ yʳ |
| (a+b+c)² | a²+b²+c²+2ab+2bc+2ca |
| Remainder Theorem | f(x) ÷ (x-a): remainder = f(a) |
| Factor Theorem | (x-a) is a factor of f(x) iff f(a)=0 |
| Sum/Product for Cubic | x³+px+q=0: α+β+γ=0 |
| Cube of Trinomial | (a+b+c)³ = a³+b³+c³+3(a+b)(b+c)(c+a) |
| Surds Rationalization | 1/√a = √a/a |
| Componendo-Dividendo | (a+b)/(a-b) = (c+d)/(c-d) |
| a⁴ − b⁴ | (a²+b²)(a+b)(a−b) |
| Sum of First n Natural Numbers | Sₙ = n(n+1)/2 |
| Sum of Squares of First n Numbers | Σn² = n(n+1)(2n+1)/6 |
| Sum of Cubes of First n Numbers | Σn³ = [n(n+1)/2]² |
| Nature of Roots (Discriminant) | D>0 real distinct, D=0 real equal, D<0 complex |
| Formation of Quadratic Equation | x² − (Sum of roots)x + Product of roots = 0 |
| Reciprocal of Roots Equation | cx² + bx + a = 0 |
| Distance from Point to Line | d = |Ax₁+By₁+C|/√(A²+B²) |
| Section Formula (Internal Division) | P = (mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n) |
| Two-Point Form of Line | (y−y₁)/(x−x₁) = (y₂−y₁)/(x₂−x₁) |
| Intercept Form of Line | x/a + y/b = 1 |
| Slope from General Equation | m = −A/B, for Ax+By+C=0 |
| Condition for Parallel Lines | m₁ = m₂ |
| Condition for Perpendicular Lines | m₁ × m₂ = −1 |
| Area of Triangle (Coordinates) | ½|x₁(y₂−y₃)+x₂(y₃−y₁)+x₃(y₁−y₂)| |
| Variation Joint | z = kxy |
| Matrix Addition Condition | Matrices must have same order |
| Scalar Multiplication of Matrix | kA = k·aᵢⱼ |
| Identity Matrix Property | AI = IA = A |
Sets & Functions (12)
| Formula | Expression |
|---|---|
| Union | A∪B = {x: x∈A or x∈B} |
| Intersection | A∩B = {x: x∈A and x∈B} |
| De Morgan's Law | (A∪B)' = A'∩B' |
| Cartesian Product Size | |A×B| = |A|×|B| |
| Complement of Set | A' = U − A |
| Power Set Cardinality | |P(A)| = 2ⁿ |
| De Morgan's Law (Intersection) | (A∩B)' = A'∪B' |
| Composition of Functions | (f∘g)(x) = f(g(x)) |
| Inverse Function Condition | f(f⁻¹(x)) = x |
| Domain and Range (concept) | Domain = set of inputs, Range = set of outputs |
| Even Function | f(−x) = f(x) |
| Odd Function | f(−x) = −f(x) |
Matrices (9)
| Formula | Expression |
|---|---|
| Determinant 3×3 | |A| = a(ei−fh) − b(di−fg) + c(dh−eg) |
| Matrix Multiplication | (AB)ᵢⱼ = Σₖ AᵢₖBₖⱼ |
| Transpose Property | (AB)ᵀ = BᵀAᵀ |
| Adjoint | adj(A) = transpose of cofactor matrix |
| Inverse via Adjoint | A⁻¹ = adj(A)/|A| |
| Singular Matrix Condition | |A| = 0 |
| Symmetric Matrix (10th) | aᵢⱼ = aⱼᵢ |
| Skew-Symmetric Matrix | Aᵀ = −A |
| Inverse Matrix Property | AA⁻¹ = I |
Exponents & Radicals (5)
| Formula | Expression |
|---|---|
| Product of Powers | aᵐ × aⁿ = aᵐ⁺ⁿ |
| Power of Power | (aᵐ)ⁿ = aᵐⁿ |
| Negative Exponent | a⁻ⁿ = 1/aⁿ |
| Fractional Exponent | a^(m/n) = ⁿ√(aᵐ) |
| Zero Exponent | a⁰ = 1 |
Geometry (12)
| Formula | Expression |
|---|---|
| Pythagoras Theorem | a² + b² = c² |
| Area of Triangle (Heron's) | A = √(s(s-a)(s-b)(s-c)) |
| Area of Circle | A = πr² |
| Circumference | C = 2πr |
| Volume of Sphere | V = (4/3)πr³ |
| Volume of Cylinder | V = πr²h |
| Volume of Cone | V = (1/3)πr²h |
| Surface Area of Sphere | SA = 4πr² |
| Area of Trapezium | A = ½(a+b)h |
| Area of Parallelogram | A = base × height |
| Volume of Cube | V = a³ |
| Volume of Cuboid | V = l × w × h |
Trigonometry (18)
| Formula | Expression |
|---|---|
| SOH-CAH-TOA | sinθ=opp/hyp, cosθ=adj/hyp, tanθ=opp/adj |
| Area using Trig | A = ½ab sinC |
| sinθ Definition | sinθ = Opposite/Hypotenuse |
| cosθ Definition | cosθ = Adjacent/Hypotenuse |
| tanθ Definition | tanθ = Opposite/Adjacent = sinθ/cosθ |
| Reciprocal Identity cosecθ | cosecθ = 1/sinθ |
| Reciprocal Identity secθ | secθ = 1/cosθ |
| Reciprocal Identity cotθ | cotθ = 1/tanθ |
| Angle of Elevation/Depression (concept) | angle from horizontal to line of sight |
| sin(A − B) | sinA cosB − cosA sinB |
| Sum to Product sinA+sinB | 2 sin((A+B)/2) cos((A−B)/2) |
| Sum to Product cosA+cosB | 2 cos((A+B)/2) cos((A−B)/2) |
| Product to Sum 2sinAcosB | sin(A+B) + sin(A−B) |
| Area of Triangle (Trig) | Area = ½ab sinC |
| Radian to Degree | θ(deg) = θ(rad) × 180/π |
| Arc Length | s = rθ |
| Area of Circular Sector | A = ½r²θ |
| Period of sin/cos | T = 2π/b for sin(bx) |
Mensuration (11)
| Formula | Expression |
|---|---|
| Area of Triangle (Base-Height) | A = ½ × base × height |
| Heron's Formula | A = √(s(s−a)(s−b)(s−c)) |
| Area of Rhombus | A = ½ × d₁ × d₂ |
| Circumference of Circle | C = 2πr |
| Surface Area of Cube | SA = 6a² |
| Surface Area of Cuboid | SA = 2(lb+bh+hl) |
| Curved Surface Area of Cylinder | CSA = 2πrh |
| Total Surface Area of Cylinder | TSA = 2πr(r+h) |
| Curved Surface Area of Cone | CSA = πrl |
| Volume of Hemisphere | V = 2/3 πr³ |
| Pythagoras' Theorem | c² = a² + b² |
Inequalities (4)
| Formula | Expression |
|---|---|
| Triangle Inequality | |a+b| <= |a|+|b| |
| AM-GM Inequality (n terms) | (a1+a2+...+an)/n >= (a1a2...an)^(1/n) |
| Cauchy-Schwarz Inequality | (Sum aibi)² <= (Sum ai²)(Sum bi²) |
| Absolute Value Inequality | |x-a| < b means a-b < x < a+b |
Set Theory (2)
| Formula | Expression |
|---|---|
| Cardinality of Union (3 Sets) | |A∪B∪C| = |A|+|B|+|C|-|A∩B|-|A∩C|-|B∩C|+|A∩B∩C| |
| Symmetric Difference | A Δ B = (A-B) ∪ (B-A) |
More class-wise formulas
Formulas are for revision. Always follow the notation and rounding used in your own textbook and board papers.
FAQ
How many 10th Class Math formulas are on this page?
110 formulas in 9 chapters.
Can I print the 10th Class Math formulas?
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They follow the usual school and intermediate syllabus, but chapter lists differ between boards. Check your own syllabus for what is included in your exam.