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By rohit.pandey1
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Updated on 26 May 2026, 16:06 IST
Mathematics in Class 11 forms the foundation for higher studies, competitive exams, and problem-solving skills required in engineering, science, economics, and technology. Whether you are preparing for CBSE Board Exams, JEE Main 2027, school tests, or Olympiads, learning formulas is one of the most important steps toward scoring high marks.
| Chapter No. | CBSE Class 11 Maths Formula Chapter | Formula Resource |
| Chapter 1 | Sets Formulas Class 11 | View Formulas |
| Chapter 2 | Relations and Functions Formulas Class 11 | View Formulas |
| Chapter 3 | Trigonometric Functions Formulas Class 11 | View Formulas |
| Chapter 4 | Principle of Mathematical Induction Formulas | View Formulas |
| Chapter 5 | Complex Numbers and Quadratic Equations Formulas | View Formulas |
| Chapter 7 | Permutations and Combinations Formulas Class 11 | View Formulas |
| Chapter 8 | Binomial Theorem Formulas Class 11 | View Formulas |
| Chapter 10 | Straight Lines Formulas Class 11 | View Formulas |
| Chapter 12 | Three Dimensional Geometry Formulas Class 11 | View Formulas |
| Chapter 13 | Limits and Derivatives Formulas Class 11 | View Formulas |
| Chapter 14 | Mathematical Reasoning Formulas Class 11 | View Formulas |
| Chapter 15 | Statistics Formulas Class 11 | View Formulas |
| Chapter 16 | Probability Formulas Class 11 | View Formulas |
Sets form the foundation of Class 11 Maths. Here are all essential formulas:
| Formula | Description |
| n(A ∪ B) = n(A) + n(B) - n(A ∩ B) | Union of two sets |
| n(A ∪ B ∪ C) = n(A) + n(B) + n(C) - n(A ∩ B) - n(B ∩ C) - n(A ∩ C) + n(A ∩ B ∩ C) | Union of three sets |
| n(A - B) = n(A) - n(A ∩ B) | Difference of sets |
| n(A') = n(U) - n(A) | Complement of a set |
| n(A ⊕ B) = n(A - B) + n(B - A) | Symmetric difference |
Memory Tip: Remember "Union adds, Intersection subtracts" for the n(A ∪ B) formula.
Common Mistake to Avoid: Don't forget to subtract n(A ∩ B) when calculating n(A ∪ B).
| Relation Type | Definition |
| Reflexive | (a, a) ∈ R for all a ∈ A |
| Symmetric | (a, b) ∈ R ⟹ (b, a) ∈ R |
| Transitive | (a, b) ∈ R and (b, c) ∈ R ⟹ (a, c) ∈ R |
| Equivalence | Reflexive + Symmetric + Transitive |
Trigonometry is crucial for both boards and JEE. Master these formulas for scoring high.
| Function | Definition | Range |
| sin θ | Opposite/Hypotenuse | [-1, 1] |
| cos θ | Adjacent/Hypotenuse | [-1, 1] |
| tan θ | Opposite/Adjacent | (-∞, ∞) |
| cot θ | Adjacent/Opposite | (-∞, ∞) |
| sec θ | Hypotenuse/Adjacent | (-∞, -1] ∪ [1, ∞) |
| cosec θ | Hypotenuse/Opposite | (-∞, -1] ∪ [1, ∞) |
Mnemonic for sin(A+B): "Sine Add: Same Different" (sin cos + cos sin)
Mnemonic for cos(A+B): "Cosine Add: Cosines Sines Subtract" (cos cos - sin sin)
JEE Tip: Double and triple angle formulas appear frequently in competitive exams.
For a statement P(n) to be true for all natural numbers n ≥ 1:
| Formula | Description |
| 1 + 2 + 3 + ... + n = n(n+1)/2 | Sum of first n natural numbers |
| 1² + 2² + 3² + ... + n² = n(n+1)(2n+1)/6 | Sum of squares |
| 1³ + 2³ + 3³ + ... + n³ = [n(n+1)/2]² | Sum of cubes |
| Formula | Description |
| z = a + ib | Standard form (a = real part, b = imaginary part) |
| i² = -1 | Definition of iota |
| i³ = -i, i⁴ = 1 | Powers of i (cycle repeats every 4) |
| z̄ = a - ib | Conjugate of z |
| |z| = √(a² + b²) | Modulus/Absolute value |
| arg(z) = tan⁻¹(b/a) | Argument of z |
For ax² + bx + c = 0:
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| Rule | Example |
| Adding/Subtracting same number to both sides doesn't change inequality | If a < b, then a + c < b + c |
| Multiplying/Dividing by positive number doesn't change inequality | If a < b and c > 0, then ac < bc |
| Multiplying/Dividing by negative number reverses inequality | If a < b and c < 0, then ac > bc |
This chapter is highly scoring for both CBSE and JEE. Master these formulas.
| Formula | Description | When to Use |
| ⁿPᵣ = n!/(n-r)! | Permutations of n things taken r at a time | Arrangement matters |
| ⁿPₙ = n! | Permutations of n distinct objects | All objects arranged |
| n! = n × (n-1) × (n-2) × ... × 2 × 1 | Factorial | Basic calculation |
| 0! = 1 | Zero factorial | By convention |
| Formula | Description | When to Use |
| ⁿCᵣ = n!/[r!(n-r)!] | Combinations of n things taken r at a time | Selection, order doesn't matter |
| ⁿCᵣ = ⁿCₙ₋ᵣ | Symmetry property | Simplification |
| ⁿCᵣ + ⁿCᵣ₋₁ = ⁿ⁺¹Cᵣ | Pascal's identity | Building combinations |
| ⁿC₀ = ⁿCₙ = 1 | Boundary conditions | Edge cases |
(a + b)ⁿ = ⁿC₀aⁿ + ⁿC₁aⁿ⁻¹b + ⁿC₂aⁿ⁻²b² + ... + ⁿCₙbⁿ
| Formula | Result |
| (1 + x)ⁿ | ⁿC₀ + ⁿC₁x + ⁿC₂x² + ... + ⁿCₙxⁿ |
| (1 - x)ⁿ | ⁿC₀ - ⁿC₁x + ⁿC₂x² - ... + (-1)ⁿ ⁿCₙxⁿ |
| Coefficient of xʳ in (a + bx)ⁿ | ⁿCᵣ aⁿ⁻ʳ bʳ |
JEE Important:
| Formula | Description | Example |
| aₙ = a + (n-1)d | nth term | a=2, d=3: a₅=2+4(3)=14 |
| Sₙ = n/2[2a + (n-1)d] | Sum of n terms (Form 1) | For above: S₅=5/2[4+12]=40 |
| Sₙ = n/2[a + l] | Sum of n terms (Form 2) | l = last term |
| d = aₙ - aₙ₋₁ | Common difference | Constant difference |
| Formula | Description | When to Use |
| aₙ = arⁿ⁻¹ | nth term | r = common ratio |
| Sₙ = a(rⁿ - 1)/(r - 1) | Sum of n terms (r > 1) | Finite GP |
| Sₙ = a(1 - rⁿ)/(1 - r) | Sum of n terms (r < 1) | Finite GP |
| S∞ = a/(1-r) | Sum to infinity | |r| < 1 only |
| Series | Sum Formula |
| 1 + 2 + 3 + ... + n | n(n+1)/2 |
| 1² + 2² + 3² + ... + n² | n(n+1)(2n+1)/6 |
| 1³ + 2³ + 3³ + ... + n³ | [n(n+1)/2]² |
💡 Memory Trick for GP Sum:
| Formula | Description | Application |
| d = √[(x₂-x₁)² + (y₂-y₁)²] | Distance between two points | Finding length |
| ((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n)) | Section formula (internal) | Dividing line in ratio m:n |
| ((mx₂-nx₁)/(m-n), (my₂-ny₁)/(m-n)) | Section formula (external) | External division |
| ((x₁+x₂)/2, (y₁+y₂)/2) | Midpoint formula | Center of line segment |
| Formula | Description |
| m = (y₂-y₁)/(x₂-x₁) | Slope through two points |
| m = tan θ | Slope and angle of inclination |
| m₁ × m₂ = -1 | Perpendicular lines |
| m₁ = m₂ | Parallel lines |
| Form | Equation | When to Use |
| Slope-intercept | y = mx + c | Slope m, y-intercept c known |
| Point-slope | y - y₁ = m(x - x₁) | Slope and one point known |
| Two-point | (y-y₁)/(y₂-y₁) = (x-x₁)/(x₂-x₁) | Two points known |
| Intercept form | x/a + y/b = 1 | x-intercept a, y-intercept b |
| Normal form | x cos α + y sin α = p | Perpendicular distance from origin |
| General form | Ax + By + C = 0 | Standard form |
Distance from (x₁, y₁) to Ax + By + C = 0:
d = |Ax₁ + By₁ + C|/√(A² + B²)
💡 Quick Recall:
Conic Sections carry significant weightage in JEE. These formulas are essential.
| Equation | Description | Parameters |
| (x-h)² + (y-k)² = r² | Standard form | Center (h,k), radius r |
| x² + y² = r² | Circle at origin | Center (0,0), radius r |
| x² + y² + 2gx + 2fy + c = 0 | General form | Center (-g,-f), radius √(g²+f²-c) |
| Standard Form | Vertex | Focus | Directrix | Axis | Latus Rectum |
| y² = 4ax | (0,0) | (a,0) | x = -a | x-axis | 4a |
| y² = -4ax | (0,0) | (-a,0) | x = a | x-axis | 4a |
| x² = 4ay | (0,0) | (0,a) | y = -a | y-axis | 4a |
| x² = -4ay | (0,0) | (0,-a) | y = a | y-axis | 4a |
| Standard Form | Center | Foci | Major Axis | Eccentricity |
| x²/a² + y²/b² = 1 (a>b) | (0,0) | (±c,0) | 2a | e = c/a = √(1-b²/a²) |
| x²/b² + y²/a² = 1 (a>b) | (0,0) | (0,±c) | 2a | e = c/a = √(1-b²/a²) |
Where: c² = a² - b²
Latus Rectum of Ellipse: 2b²/a
| Standard Form | Center | Foci | Transverse Axis | Eccentricity |
| x²/a² - y²/b² = 1 | (0,0) | (±c,0) | 2a | e = c/a = √(1+b²/a²) |
| y²/a² - x²/b² = 1 | (0,0) | (0,±c) | 2a | e = c/a = √(1+b²/a²) |
Where: c² = a² + b²
Latus Rectum of Hyperbola: 2b²/a
Asymptotes: y = ±(b/a)x
JEE Tip: Remember "a² - b² for ellipse, a² + b² for hyperbola" when finding c.
Distance between A(x₁, y₁, z₁) and B(x₂, y₂, z₂):
d = √[(x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²]
Point dividing line joining (x₁, y₁, z₁) and (x₂, y₂, z₂) in ratio m:n:
((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n), (mz₂+nz₁)/(m+n))
For vertices A(x₁,y₁,z₁), B(x₂,y₂,z₂), C(x₃,y₃,z₃):
G = ((x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3, (z₁+z₂+z₃)/3)
Calculus is the foundation for Class 12 and engineering. Master these basics.
| Limit | Value | Application |
| lim(x→0) (sin x)/x | 1 | Trigonometric limits |
| lim(x→0) (1 - cos x)/x | 0 | Trigonometric limits |
| lim(x→0) (tan x)/x | 1 | Trigonometric limits |
| lim(x→0) (eˣ - 1)/x | 1 | Exponential limits |
| lim(x→0) (aˣ - 1)/x | log a | Exponential limits |
| lim(x→0) (log(1+x))/x | 1 | Logarithmic limits |
| lim(x→∞) (1 + 1/x)ˣ | e | Euler's number |
| lim(x→0) (1 + x)^(1/x) | e | Euler's number |
| Function | Derivative | Function | Derivative |
| xⁿ | nxⁿ⁻¹ | c (constant) | 0 |
| sin x | cos x | cos x | -sin x |
| tan x | sec²x | cot x | -cosec²x |
| sec x | sec x tan x | cosec x | -cosec x cot x |
| eˣ | eˣ | aˣ | aˣ log a |
| log x | 1/x | √x | 1/(2√x) |
| Rule | Formula |
| Sum/Difference | d/dx[f(x) ± g(x)] = f'(x) ± g'(x) |
| Product Rule | d/dx[f(x)g(x)] = f'(x)g(x) + f(x)g'(x) |
| Quotient Rule | d/dx[f(x)/g(x)] = [g(x)f'(x) - f(x)g'(x)]/[g(x)]² |
| Chain Rule | d/dx[f(g(x))] = f'(g(x)) × g'(x) |
| Constant Multiple | d/dx[cf(x)] = c f'(x) |
Memory Trick:
| Connective | Symbol | Example |
| AND (Conjunction) | ∧ | p ∧ q |
| OR (Disjunction) | ∨ | p ∨ q |
| NOT (Negation) | ~ or ¬ | ~p |
| Implies (Conditional) | → or ⇒ | p → q |
| If and only if (Biconditional) | ↔ or ⇔ | p ↔ q |
Truth Tables: Covered in detail in NCERT with standard results.
| Measure | Formula (Ungrouped) | Formula (Grouped) |
| Mean (x̄) | Σx/n | Σfx/Σf |
| Median | Middle value when arranged | L + [(n/2 - cf)/f] × h |
| Mode | Most frequent value | L + [(f₁-f₀)/(2f₁-f₀-f₂)] × h |
| Measure | Formula |
| Range | Largest value - Smallest value |
| Mean Deviation (MD) | Σ|x - x̄|/n |
| Variance (σ²) | Σ(x - x̄)²/n |
| Standard Deviation (σ) | √[Σ(x - x̄)²/n] |
| Coefficient of Variation | (σ/x̄) × 100 |
| Rule | Formula | Condition |
| Mutually Exclusive | P(A ∪ B) = P(A) + P(B) | A ∩ B = φ |
| General Addition | P(A ∪ B) = P(A) + P(B) - P(A ∩ B) | Any events |
| Three Events | P(A∪B∪C) = P(A)+P(B)+P(C)-P(A∩B)-P(B∩C)-P(A∩C)+P(A∩B∩C) | Any events |
Create flashcards for each chapter with:
Understanding derivation = better retention. Derive at least once:
Set your phone wallpaper to a formula sheet. You'll see it 50+ times daily!
| Chapter | CBSE Marks |
| Trigonometric Functions | 12-15 |
| Limits and Derivatives | 10-12 |
| Permutations & Combinations | 8-10 |
| Binomial Theorem | 6-8 |
| Sequences and Series | 8-10 |
| Conic Sections | 8-10 |
| Straight Lines | 6-8 |
| Complex Numbers | 6-8 |
| Probability | 6-8 |
| Statistics | 6-8 |
| Sets | 4-6 |
| 3D Geometry | 4-6 |
Many students lose marks in CBSE board exams and JEE Main because they apply formulas incorrectly. Here are the most common Class 11 Maths formula mistakes and the correct methods to avoid them.
Students often confuse trigonometric identities with normal algebraic addition.
sin(A+B) = sin A + sin B
sin(A+B) = sin A cos B + cos A sin B
Why this mistake happens: Many students forget that trigonometric angle formulas are identities, not simple algebraic expansions.
Quick Revision Tip: Sine addition always contains both sin and cos, and two terms are always present.
This is one of the most common mistakes in Class 11 Maths.
Using permutation formulas for selection-based questions.
| Situation | Formula Type |
| Arranging students in a row | Permutation |
| Selecting students for a team | Combination |
Quick Memory Trick: P = Position, C = Choose.
Students often use the same GP formula in every question without checking the value of the common ratio.
Sn = a(rn - 1) / (r - 1)
If r > 1:
Sn = a(rn - 1) / (r - 1)
If r < 1:
Sn = a(1 - rn) / (1 - r)
Important Tip: Always check whether r > 1 or r < 1 before applying the GP sum formula.
Students frequently forget that:
i2 = -1
(a + ib)(c + id) = ac + bd + i(ad + bc)
(a + ib)(c + id) = (ac - bd) + i(ad + bc)
Why this happens: The negative sign generated by i2 = -1 is often ignored.
Stopping immediately after getting:
0 / 0
Exam Tip: Whenever you get an indeterminate form, simplify first and substitute later.
Thinking perpendicular slopes are simply negative reciprocals without checking the condition.
m1 × m2 = -1
| Line Type | Condition |
| Parallel Lines | m1 = m2 |
| Perpendicular Lines | m1m2 = -1 |
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There are approximately 150-200 important formulas across all 16 chapters. However, focus on mastering 80-100 most frequently used formulas first. Trigonometry alone has 40+ formulas, followed by Calculus and Coordinate Geometry.
Trigonometric Functions (Chapter 3) has the maximum formulas, including basic ratios, identities, sum/difference formulas, double/triple angles, and product-to-sum conversions. Conic Sections and Limits/Derivatives also have extensive formula lists.
Class 11 formulas form the foundation (40% of JEE syllabus), but you'll need Class 12 formulas and advanced problem-solving for JEE. However, mastering Class 11 thoroughly is crucial as concepts build upon each other.
No. Focus on understanding and memorizing high-frequency formulas. Some complex formulas can be derived from basic ones during exams if you understand the concepts.
Infinity Learn provide free downloadable PDFs including a complete formula book, one-page cheat sheet, chapter-wise PDFs, and handwritten notes. Links are available in the download section above.
NCERT contains all essential CBSE formulas. Reference books may include additional shortcuts and variations, but NCERT formulas are sufficient for CBSE boards. For JEE, you might need a few extra formulas and techniques.