9th Class Math Formulas
All 9th Class Math formulas, chapter by chapter, with search and a printable layout.
Chapters: Algebra · Sets & Functions · Basic Arithmetic · Exponents & Radicals · Geometry · Trigonometry · Mensuration · Inequalities · Financial Mathematics · Set Theory
Algebra (33)
| 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) |
| Laws of Exponents - Product | aᵐ × aⁿ = aᵐ⁺ⁿ |
| Laws of Exponents - Quotient | aᵐ ÷ aⁿ = aᵐ⁻ⁿ |
| Laws of Exponents - Power of Power | (aᵐ)ⁿ = aᵐⁿ |
| Surds - Rationalizing | 1/√a = √a/a |
| HCF and LCM Relation | HCF × LCM = Product of two numbers |
| Percentage Change | % change = (New − Old)/Old × 100 |
| Ratio and Proportion | a:b = c:d ⇒ ad = bc |
| a² + b² (from sum/product) | (a+b)² − 2ab |
| Linear Equation Slope-Intercept | y = mx + c |
| Simple Interest | SI = PRT/100 |
| Compound Interest | A = P(1 + r/100)ⁿ |
| Arithmetic Mean of Two Numbers | AM = (a+b)/2 |
| Geometric Mean of Two Numbers | GM = √(ab) |
| Speed Distance Time | Speed = Distance/Time |
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) |
Basic Arithmetic (5)
| Formula | Expression |
|---|
| Ratio & Proportion | a:b = c:d ⇒ ad = bc |
| Compound Proportion | a/b = (c×e)/(d×f) |
| Direct Variation | y = kx |
| Inverse Variation | y = k/x |
| Percentage Formula | % = (Part/Whole) × 100 |
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 (2)
| Formula | Expression |
|---|
| SOH-CAH-TOA | sinθ=opp/hyp, cosθ=adj/hyp, tanθ=opp/adj |
| Area using Trig | A = ½ab sinC |
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 |
Financial Mathematics (8)
| Formula | Expression |
|---|
| Profit Percentage | Profit% = (SP-CP)/CP × 100 |
| Loss Percentage | Loss% = (CP-SP)/CP × 100 |
| Markup Price | MP = CP + Markup |
| Discount Amount | Discount = MP - SP |
| Zakat Calculation | Zakat = 2.5% of Nisab-exceeding wealth |
| Present Value | PV = FV / (1+r)^n |
| Future Value of Annuity | FV = P × [((1+r)^n - 1)/r] |
| Effective Annual Rate | EAR = (1+r/n)^n - 1 |
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 9th Class Math formulas are on this page?
94 formulas in 10 chapters.
Can I print the 9th Class Math formulas?
Yes. Press Print / Save as PDF. The page switches to a clean black-on-white layout without menus.
How do I find one formula quickly?
Type a word such as velocity, area or mole in the search box. Only matching formulas stay visible.
Do the formulas follow my board syllabus?
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.
More Calvo tools
Open the full Calvo Scientific Calculator