JEE Maths Formulas Chapter-Wise: Calculus, Algebra & Coordinate Geometry

Dedication is not enough when you are preparing for JEE Main and JEE Advanced. It requires more than just solving problems, which demands quick recall of important formulas, practice, and concentration. Therefore, students must follow a well-organized JEE Maths formulas chapter-wise sheet. It helps students revise faster, reduce mistakes, and improve speed during exams.

Calculus, Algebra, and Coordinate Geometry are the three highest-scoring sections in JEE Mathematics. Each chapter contains several formulas that students should remember and apply confidently. Therefore, learn some tricks for memorizing the formulas randomly and practice regularly to strengthen retention.

Here you can explore the most important formulas chapter-wise:

Calculus Formulas

Calculus is one of the most vital parts of JEE, making formula revision essential.

Limits

Important standard results include:

• lim (sin x)/x = 1 as x → 0
• lim (1 + 1/n)^n = e
• lim (e^x – 1)/x = 1

L'Hôpital's Rule applies only to indeterminate forms like 0/0 or ∞/∞.

Memory Trick: Always identify the indeterminate form before applying L'Hôpital's Rule.

Differentiation

Important derivative formulas include:

• d/dx (xⁿ) = nxⁿ⁻¹
• d/dx (sin x) = cos x
• d/dx (cos x) = –sin x
• d/dx (eˣ) = eˣ
• d/dx (ln x) = 1/x

Important rules:

• Product Rule: (uv)' = u'v + uv'
• Quotient Rule: (u/v)' = (vu' − uv')/v²
• Chain Rule: Differentiate the outer function first, then multiply by the derivative of the inner function.

Memory Trick: Think "Outside first, inside next" for the chain rule.

Integration

Standard integrals include:

• ∫xⁿ dx = xⁿ⁺¹/(n+1)
• ∫1/x dx = ln|x|
• ∫eˣ dx = eˣ
• ∫sin x dx = –cos x
• ∫cos x dx = sin x

Reduction formulas help simplify repeated integrations involving powers of trigonometric functions.

Memory Trick: Differentiation and integration are inverse operations.

Definite Integrals

Key properties include:

• ∫₀ᵃ f(x) dx = ∫₀ᵃ f(a−x) dx
• Even function:
  ∫₋ₐᵃ f(x) dx = 2∫₀ᵃ f(x) dx
• Odd function:
  ∫₋ₐᵃ f(x) dx = 0

Memory Trick: Even doubles, odd disappears.

Differential Equations

Common forms include:

• dy/dx = ky
• Solution:
  y = Ce^(kx)

Memory Trick: Whenever the derivative is proportional to the function, exponential solutions appear.

Algebra Formulas

Again, algebra contributes heavily to JEE, whether you are appearing for mains or advanced. It requires a strong conceptual understanding.

Quadratic Equations

For ax² + bx + c = 0:

• Discriminant:
  D = b² − 4ac
• Sum of roots:
  −b/a
• Product of roots:
  c/a

Memory Trick: "Minus, Plus"—sum has minus; product has plus.

Complex Numbers

Euler's Formula:

e^(iθ) = cos θ + i sin θ

De Moivre's Theorem:

(cos θ + i sin θ)ⁿ = cos(nθ) + i sin(nθ)

Memory Trick: Multiply the angle; raise the modulus.

Permutations and Combinations

Important formulas:

• nPr = n!/(n−r)!
• nCr = n!/[r!(n−r)!]

Identity:

nCr = nC(n−r)

Memory Trick: Permutations arrange; combinations choose.

Binomial Theorem

General term:

Tᵣ₊₁ = nCr aⁿ⁻ʳ bʳ

The middle term depends on whether n is even or odd.

Memory Trick: Position determines the exponent.

Matrices and Determinants

For a 2×2 matrix:

|A| = ad − bc

Inverse:

A⁻¹ = Adj(A)/|A|

Cramer's Rule helps solve systems of linear equations.

Memory Trick: Determinant first, inverse later.

Sequences and Series

Arithmetic Progression (AP):

• nth term:
  a + (n−1)d
• Sum:
  n/2 [2a + (n−1)d]

Geometric Progression (GP):

• nth term:
  arⁿ⁻¹
• Sum:
  a(rⁿ−1)/(r−1)

Harmonic Progression (HP):

Terms are reciprocals of an AP.

Memory Trick: AP adds; GP multiplies.

Coordinate Geometry Formulas

Coordinate geometry combines algebra with visualization.

Straight Lines

Slope:

m = (y₂−y₁)/(x₂−x₁)

Equation:

y = mx + c

Distance Formula:

√[(x₂−x₁)² + (y₂−y₁)²]

Angle between two lines:

tan θ = |(m₂−m₁)/(1+m₁m₂)|

Memory Trick: Slope controls direction.

Circles

General equation:

x² + y² + 2gx + 2fy + c = 0

Center:

(−g, −f)

Radius:

√(g² + f² − c)

Memory Trick: Negative coefficients give the center.

Conic Sections

Parabola:

y² = 4ax

Ellipse:

x²/a² + y²/b² = 1

Hyperbola:

x²/a² − y²/b² = 1

Eccentricity:

• Parabola = 1
• Ellipse < 1
• Hyperbola > 1

Memory Trick: Eccentricity tells the shape.

3D Geometry

Direction cosines:

l² + m² + n² = 1

Plane equation:

Ax + By + Cz + D = 0

Line equation:

(x−x₁)/a = (y−y₁)/b = (z−z₁)/c

Memory Trick: Direction ratios become direction cosines after normalization.

Downloadable Cheat Sheet

Whenever you are looking for the best revision resource that can be the savior for the mock test, a one-page JEE Maths formulas chapter-wise cheat sheet can be the solution. It can be your best friend before the final exam. Infinity Learn also organizes separate pages for Calculus, Algebra, and Coordinate Geometry in a print-friendly PDF format. You can keep the sheets near your study table for quick daily revision. It is also a great helping hand for last-minute practice.

How Infinity Learn Helps with JEE Maths Formulas

Infinity Learn creates structured learning resources that make formula revision more effective and easier, specifically designed for JEE aspirants.

Students can access:

• Formula revision videos for every chapter
• Flashcard-based revision tools for quick memorisation
• Practice questions linked directly to each formula
• Chapter-wise mock tests to strengthen formula application
• Regular revision sessions guided by expert faculty

Therefore, students can expect to understand not only what the formulas are but also their applications. So, also keep these formulas at hand and know when and how to use them correctly.

Conclusion

Mastering JEE Maths formulas chapter-wise is one of the smartest ways to improve speed and accuracy in the exam. Focus on Calculus, Algebra, and Coordinate Geometry, revise formulas every day, and apply memory tricks to strengthen recall. Better if you spend 20–30 minutes daily revising your formula sheet. Try to solve a few practice questions from each chapter. Consistent revision is the key to students remembering formulas naturally and performing confidently in JEE Main and JEE Advanced.