Memorizing Class 10 Maths formulas becomes a challenge when students try to understand every chapter without seeing how these formulas actually support real problem-solving. Each formula strengthens core CBSE concepts and trains the brain to work with numbers, shapes, angles, and data in a precise way. When students build this foundation early, they handle board exam questions with more confidence and solve multi-step problems much faster.

The value of these formulas also stretches far beyond schoolwork. Trigonometry helps in measurement and design, statistics supports data-driven fields, probability guides risk analysis, and algebra forms the base of countless technical applications. From engineering and architecture to finance, coding, and medical research, the ideas students learn in Class 10 appear in many modern careers.

To help students prepare smarter and revise with clarity, every important Class 10 Maths formula is organized chapter-wise with simple explanations and quick examples in this blog.

Important Class 10 Math Formulas 

• (a + b)³ = a³ + b³ + 3ab(a + b)
• (a – b)³ = a³ – b³ – 3ab(a – b)
• (x + y + z)² = x² + y² + z² + 2xy + 2yz + 2xz
• aₙ = a + (n – 1)d
• Sₙ = n/2 [2a + (n – 1)d]
• sin²θ + cos²θ = 1
• sin²θ = 1 – cos²θ
• cos²θ = 1 – sin²θ
• cosec²θ – cot²θ = 1
• cosec²θ = 1 + cot²θ
• cot²θ = cosec²θ – 1
• sec²θ – tan²θ = 1
• sec²θ = 1 + tan²θ
• tan²θ = sec²θ – 1
• sin θ × cosec θ = 1
• cos θ × sec θ = 1
• tan θ × cot θ = 1
• Volume of a sphere = (4/3)πr³
• Surface area of a sphere = 4πr²

Class 10 Maths Formulas Chapter-Wise

Class 10 Algebra Formulas

Algebra helps students convert real-life situations into mathematical expressions. Understanding these identities makes it easier to simplify expressions, solve equations, and identify patterns quickly.

Important Algebra Formulas

• (a + b)² = a² + 2ab + b²
• (a – b)² = a² – 2ab + b²
• (a + b)(a – b) = a² – b²
• (x + a)(x + b) = x² + (a + b)x + ab
• (x + a)(x – b) = x² + (a – b)x – ab
• (x – a)(x + b) = x² + (b – a)x – ab
• (x – a)(x – b) = x² – (a + b)x + ab
• (a + b)³ = a³ + b³ + 3ab(a + b)
• (a – b)³ = a³ – b³ – 3ab(a – b)
• (x + y + z)² = x² + y² + z² + 2xy + 2yz + 2xz
• (x + y – z)² = x² + y² + z² + 2xy – 2yz – 2xz
• (x – y + z)² = x² + y² + z² – 2xy – 2yz + 2xz
• (x – y – z)² = x² + y² + z² – 2xy + 2yz – 2xz
• x³ + y³ + z³ – 3xyz = (x + y + z)(x² + y² + z² – xy – yz – xz

Class 10 Arithmetic Progression Formulas

Arithmetic Progression (AP) introduces the idea of number patterns where the difference between terms stays constant. These formulas help compute missing terms and total sums quickly.

Important AP Formulas

• aₙ = a + (n – 1)d
• Sₙ = n/2 [2a + (n – 1)d]

Class 10 Trigonometry Formulas

Trigonometry studies the relationships between angles and sides of right-angled triangles. These formulas help calculate heights, distances, and angle-based measurements.

Important Trigonometry Formulas

• sin(90° – A) = cos A
• cos(90° – A) = sin A
• tan(90° – A) = cot A
• cot(90° – A) = tan A
• sec(90° – A) = cosec A
• cosec(90° – A) = sec A
• sin²θ + cos²θ = 1
• cosec²θ – cot²θ = 1
• sec²θ – tan²θ = 1
• sin θ cosec θ = 1
• cos θ sec θ = 1
• tan θ cot θ = 1

Class 10 Circle Formulas

Circle concepts revolve around radius, diameter, tangents, and chords. These formulas help solve geometric and coordinate-based problems.

Important Circle Formulas

• Tangent to circle x² + y² = a² for line y = mx + c:
  y = mx ± a√(1 + m²)
• Tangent at (a₁, b₁) for circle x² + y² = a²:
  xa₁ + yb₁ = a²

Class 10 Surface Area and Volume Formulas

These formulas are used to calculate space and surface measurements for 3D shapes like cylinders, spheres, cones, and prisms.

Sphere

• Volume = (4/3)πr³
• Surface Area = 4πr²

Cylinder

• Volume = πr²h
• Curved Surface Area = 2πrh
• Total Surface Area = 2πr(r + h)

Hemisphere

• Volume = (2/3)πr³
• Lateral Surface Area = 2πr²
• Total Surface Area = 3πr²

Prism

• Volume = B × h
• Lateral Surface Area = p × h

Class 10 Statistics Formulas

Statistics focuses on mean, median, and mode for grouped data. These formulas help analyze patterns and numerical trends.

Mean

• Direct method:
  Mean = Σfᵢxᵢ / Σfᵢ
• Assumed mean method:
  Mean = a + (Σfᵢdᵢ / Σfᵢ)
• Step-deviation method:
  Mean = a + (h × Σfᵢuᵢ / Σfᵢ)

Median

Median = l + [(n/2 – cf) / f] × h

Mode

Mode = l + [(f₁ – f₀) / (2f₁ – f₀ – f₂)] × h

Class 10 Probability Formulas

Probability measures how likely an event is to happen. These formulas are essential for predicting outcomes in experiments and real-life situations.

Important Probability Formulas

• P(E) = (Number of favourable outcomes) / (Total outcomes)
• Probability of a sure event = 1
• Probability of an impossible event = 0
• 0 ≤ P(E) ≤ 1

Applications of Class 10 Maths Formulas

Class 10 Maths formulas are practical and widely applicable, helping students solve real-life problems efficiently. Mastering them makes calculations quicker, improves accuracy, and helps spot patterns in numbers and shapes. Here’s how these formulas are used in everyday situations:

Algebra & Quadratic Formulas: Quadratic equations are used to model situations involving motion, optimization, and design. For instance, they can calculate the maximum height of a projectile, estimate profits in business scenarios, or determine dimensions when planning rectangular spaces.

Trigonometry Formulas: Trigonometric formulas are essential in fields like engineering, architecture, and navigation. They help calculate heights, distances, slopes, and angles—important when designing ramps, rooftops, bridges, or positioning satellites.

Statistics & Probability Formulas: These formulas help interpret data and assess risks. They are applied in weather forecasting, quality control, insurance analysis, elections, and market research, enabling informed decisions.

Surface Area & Volume Formulas: Geometry formulas are practical in construction, packaging, and manufacturing. Knowing the volume of a cylinder helps fill tanks, while surface area calculations assist in painting walls or designing containers.

Arithmetic & Sequence Formulas: Arithmetic progression formulas are useful in financial planning, budgeting, and scheduling tasks that involve regular increases or decreases.

Tips to Memorize Class 10 Maths Formulas

Memorizing formulas is easier when understanding is combined with consistent practice. Here are some effective strategies:

1. Understand First: Learn the reasoning behind each formula instead of rote memorization. Knowing why it works makes recall much easier.
2. Visualize Formulas: Use diagrams, sketches, or mental images, especially for geometry, algebra, and trigonometry. Visual memory strengthens recall.
3. Practice Frequently: Solve multiple questions using each formula. Applying formulas in different scenarios reinforces memory and builds confidence.
4. Create Formula Sheets: Keep a notebook or flashcards with all formulas. Review them regularly to keep them fresh.
5. Group Similar Formulas: Organize formulas into categories—like trigonometric identities or surface area formulas. Grouping reduces mental load and speeds up recall.
6. Teach or Explain: Explain formulas to a friend or even aloud to yourself. Teaching strengthens understanding and memory.