Mathematics is often considered the backbone of academic success. Whether you are studying in CBSE, ICSE, or SSC board, mastering mathematical formulae is essential for solving problems quickly and accurately. From basic arithmetic to advanced algebra and geometry, formulas are the building blocks of mathematics. At Dhingra Classes Nashik, we believe that a strong grasp of formulas is key to scoring high marks in board examinations. Our students, including Tejasi Ware (99.2%), Himanshi Dhingra (98.6%), Aavni Shinde (92.00%), and Akshitaa Sonar (91.6%), have consistently excelled in Mathematics by mastering these essential formulas.
In this comprehensive guide, we present the top 100 mathematics formulae for school students from Class 6 to 10. These formulas are categorized by topic for easy reference and revision.
📐 Number Systems & Arithmetic
| Formula | Description |
|---|---|
| (a + b)² = a² + 2ab + b² | Square of a binomial (sum) |
| (a – b)² = a² – 2ab + b² | Square of a binomial (difference) |
| a² – b² = (a + b)(a – b) | Difference of squares |
| (a + b)³ = a³ + 3a²b + 3ab² + b³ | Cube of a binomial (sum) |
| (a – b)³ = a³ – 3a²b + 3ab² – b³ | Cube of a binomial (difference) |
| a³ + b³ = (a + b)(a² – ab + b²) | Sum of cubes |
| a³ – b³ = (a – b)(a² + ab + b²) | Difference of cubes |
| (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca | Square of a trinomial |
| LCM × HCF = Product of two numbers | Relationship between LCM and HCF |
| Percentage = (Part / Whole) × 100 | Percentage formula |
| Profit = SP – CP | Profit calculation |
| Loss = CP – SP | Loss calculation |
| Profit % = (Profit / CP) × 100 | Profit percentage |
| Loss % = (Loss / CP) × 100 | Loss percentage |
| SP = CP × (100 + Profit%) / 100 | Selling price with profit |
| SP = CP × (100 – Loss%) / 100 | Selling price with loss |
| Simple Interest = (P × R × T) / 100 | Simple interest formula |
| Compound Interest = P(1 + R/100)^T – P | Compound interest formula |
| Amount = P(1 + R/100)^T | Amount with compound interest |
📐 Algebra
| Formula | Description |
|---|---|
| Linear Equation: ax + b = 0 | Standard form of linear equation |
| Quadratic Equation: ax² + bx + c = 0 | Standard form of quadratic equation |
| Quadratic Formula: x = [-b ± √(b² – 4ac)] / 2a | Solution of quadratic equation |
| Discriminant: D = b² – 4ac | Determines nature of roots |
| Roots: α + β = -b/a, αβ = c/a | Sum and product of roots |
| Arithmetic Progression: a_n = a + (n – 1)d | nth term of AP |
| Sum of AP: S_n = n/2 [2a + (n – 1)d] | Sum of n terms of AP |
| Geometric Progression: a_n = ar^{n-1} | nth term of GP |
| Sum of GP: S_n = a(1 – r^n) / (1 – r) | Sum of n terms of GP |
| Factorial: n! = n × (n – 1) × … × 1 | Factorial notation |
| Permutation: nPr = n! / (n – r)! | Permutations |
| Combination: nCr = n! / [r!(n – r)!] | Combinations |
| Binomial Theorem: (x + y)^n = Σ nCr x^{n-r} y^r | Binomial expansion |
📐 Geometry
| Formula | Description |
|---|---|
| Area of Rectangle = l × b | Area formula |
| Perimeter of Rectangle = 2(l + b) | Perimeter formula |
| Area of Square = side² | Area formula |
| Perimeter of Square = 4 × side | Perimeter formula |
| Area of Triangle = ½ × b × h | Area formula |
| Heron’s Formula: Area = √[s(s-a)(s-b)(s-c)] | Area of triangle using semi-perimeter |
| Semi-perimeter: s = (a + b + c) / 2 | Semi-perimeter of triangle |
| Area of Parallelogram = b × h | Area formula |
| Area of Rhombus = ½ × d₁ × d₂ | Area using diagonals |
| Area of Trapezium = ½ × (a + b) × h | Area formula |
| Area of Circle = πr² | Area of circle |
| Circumference of Circle = 2πr | Circumference formula |
| Area of Sector = (θ/360) × πr² | Area of sector |
| Length of Arc = (θ/360) × 2πr | Arc length |
| Area of Semicircle = ½ × πr² | Area of semicircle |
| Perimeter of Semicircle = πr + 2r | Perimeter of semicircle |
| Pythagoras Theorem: a² + b² = c² | Right triangle relation |
| Euclid’s Division Lemma: a = bq + r | Division algorithm |
| Angle Sum Property: Sum of angles in triangle = 180° | Triangle angle sum |
| Sum of Exterior Angles = 360° | Polygon exterior angle sum |
| Interior Angle of Regular Polygon = (n – 2) × 180° / n | Interior angle formula |
| Diagonals of Polygon = n(n – 3) / 2 | Number of diagonals |
📐 Mensuration (3D Shapes)
| Formula | Description |
|---|---|
| Volume of Cube = side³ | Volume formula |
| Surface Area of Cube = 6side² | Total surface area |
| Volume of Cuboid = l × b × h | Volume formula |
| Surface Area of Cuboid = 2(lb + bh + hl) | Total surface area |
| Volume of Cylinder = πr²h | Volume formula |
| Curved Surface Area of Cylinder = 2πrh | Lateral surface area |
| Total Surface Area of Cylinder = 2πr(r + h) | Total surface area |
| Volume of Cone = ⅓πr²h | Volume formula |
| Slant Height of Cone: l = √(r² + h²) | Slant height |
| Curved Surface Area of Cone = πrl | Lateral surface area |
| Total Surface Area of Cone = πr(r + l) | Total surface area |
| Volume of Sphere = ⁴/₃πr³ | Volume formula |
| Surface Area of Sphere = 4πr² | Surface area |
| Volume of Hemisphere = ⅔πr³ | Volume formula |
| Curved Surface Area of Hemisphere = 2πr² | Curved surface area |
| Total Surface Area of Hemisphere = 3πr² | Total surface area |
| Volume of Frustum = (πh/3)(R² + r² + Rr) | Frustum volume |
| Curved Surface Area of Frustum = πl(R + r) | Lateral surface area |
📐 Trigonometry
| Formula | Description |
|---|---|
| sin θ = Opposite / Hypotenuse | Sine ratio |
| cos θ = Adjacent / Hypotenuse | Cosine ratio |
| tan θ = Opposite / Adjacent | Tangent ratio |
| cot θ = Adjacent / Opposite | Cotangent ratio |
| sec θ = Hypotenuse / Adjacent | Secant ratio |
| cosec θ = Hypotenuse / Opposite | Cosecant ratio |
| sin²θ + cos²θ = 1 | Pythagorean identity |
| 1 + tan²θ = sec²θ | Pythagorean identity |
| 1 + cot²θ = cosec²θ | Pythagorean identity |
| sin(90° – θ) = cos θ | Complementary angles |
| cos(90° – θ) = sin θ | Complementary angles |
| tan(90° – θ) = cot θ | Complementary angles |
| sin 0° = 0, sin 30° = ½, sin 45° = 1/√2, sin 60° = √3/2, sin 90° = 1 | Standard values |
| cos 0° = 1, cos 30° = √3/2, cos 45° = 1/√2, cos 60° = ½, cos 90° = 0 | Standard values |
| tan 0° = 0, tan 30° = 1/√3, tan 45° = 1, tan 60° = √3 | Standard values |
📐 Statistics & Probability
| Formula | Description |
|---|---|
| Mean (Direct Method) = Σxi / n | Arithmetic mean |
| Mean (Assumed Mean) = a + Σfidi / Σfi | Mean using assumed mean |
| Mean (Step Deviation) = a + h × Σfiui / Σfi | Mean using step deviation |
| Median (Odd n) = (n+1)/2th observation | Median for odd number of observations |
| Median (Even n) = Average of n/2th and (n/2+1)th observations | Median for even number |
| Mode = Value with highest frequency | Mode definition |
| Range = Maximum – Minimum | Range formula |
| Variance = Σ(xi – μ)² / n | Population variance |
| Standard Deviation = √Variance | Standard deviation |
| Probability = Favorable Outcomes / Total Outcomes | Probability formula |
| P(A ∪ B) = P(A) + P(B) – P(A ∩ B) | Union of two events |
| P(A ∩ B) = P(A) × P(B) | Intersection of independent events |
| P(A / B) = P(A ∩ B) / P(B) | Conditional probability |
📐 Coordinate Geometry
| Formula | Description | ||
|---|---|---|---|
| Distance Formula: d = √[(x₂ – x₁)² + (y₂ – y₁)²] | Distance between two points | ||
| Midpoint Formula: M = [(x₁ + x₂)/2, (y₁ + y₂)/2] | Midpoint of a line segment | ||
| Section Formula: (mx₂ + nx₁)/(m+n), (my₂ + ny₁)/(m+n) | Point dividing a line segment | ||
| Slope: m = (y₂ – y₁) / (x₂ – x₁) | Slope of a line | ||
| Equation of Line: y = mx + c | Slope-intercept form | ||
| Equation of Line: y – y₁ = m(x – x₁) | Point-slope form | ||
| Equation of Line: (y – y₁)/(y₂ – y₁) = (x – x₁)/(x₂ – x₁) | Two-point form | ||
| **Distance from Point to Line = | Ax₁ + By₁ + C | / √(A² + B²)** | Perpendicular distance |
📐 Quadratic Equations & Polynomials
| Formula | Description |
|---|---|
| Quadratic Equation: ax² + bx + c = 0 | Standard form |
| Discriminant: D = b² – 4ac | Determines nature of roots |
| Roots: x = (-b ± √D) / 2a | Quadratic formula |
| Sum of Roots: α + β = -b/a | Sum of roots |
| Product of Roots: αβ = c/a | Product of roots |
| Nature of Roots (D > 0): Real & unequal | Discriminant > 0 |
| Nature of Roots (D = 0): Real & equal | Discriminant = 0 |
| Nature of Roots (D < 0): No real roots | Discriminant < 0 |
How Dhingra Classes Helps Students Master Mathematics
At Dhingra Classes Nashik, we help students:
Master mathematical formulas through regular practice.
Apply formulas to solve complex problems.
Develop speed and accuracy through mock tests.
Build conceptual clarity in all topics.
Contact Dhingra Classes
Phone: 98230 62106
Email: dhingraclassesnsk@gmail.com
Website: www.dhingraclassesnashik.com
Address:Plot No 3, XQ3G+H3M Deacon Homes, 301C, opp. Metro Zone, near Guru Govind Sing, Samarth Nagar, Dnyaneshwar Nagar, Pathardi Phata, Nashik, Maharashtra 422009
Conclusion
Mastering the top 100 mathematics formulae for school students is essential for solving problems quickly and scoring high marks in board examinations. By memorizing and practicing these formulas, students can approach mathematics with confidence and ease. At Dhingra Classes Nashik, we are committed to helping students build a strong mathematical foundation and achieve academic excellence.
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