CBSE · Class 11
Maths Formulas for Class 11
Chapter-wise Maths formulas for CBSE Class 11 (2026-27) — Trigonometry, Sets, Complex Numbers, Permutations & Combinations, Binomial Theorem, Conic Sections and more.
For reference only. Always verify formulas and information against your official NCERT textbooks or board-prescribed materials before use in exams. Learnizo does not guarantee absolute accuracy.
Ch 1.Sets
| Formula / Relation | Expression |
|---|---|
| n(A ∪ B) | n(A) + n(B) − n(A ∩ B) |
| n(A ∪ B ∪ C) | n(A)+n(B)+n(C)−n(A∩B)−n(B∩C)−n(A∩C)+n(A∩B∩C) |
| Complement: n(A') | n(U) − n(A) |
| De Morgan's Law 1 | (A ∪ B)' = A' ∩ B' |
| De Morgan's Law 2 | (A ∩ B)' = A' ∪ B' |
Ch 2.Trigonometric Functions
| Formula / Relation | Expression |
|---|---|
| Degree to Radian | θ(rad) = θ(°) × π/180 |
| Arc length | l = rθ |
| sin²x + cos²x | = 1 |
| 1 + tan²x | = sec²x |
| 1 + cot²x | = cosec²x |
| sin(A+B) | = sinA cosB + cosA sinB |
| sin(A−B) | = sinA cosB − cosA sinB |
| cos(A+B) | = cosA cosB − sinA sinB |
| cos(A−B) | = cosA cosB + sinA sinB |
| tan(A+B) | = (tanA+tanB)/(1−tanA tanB) |
| tan(A−B) | = (tanA−tanB)/(1+tanA tanB) |
| sin 2A | = 2 sinA cosA = 2tanA/(1+tan²A) |
| cos 2A | = cos²A − sin²A = 1−2sin²A = 2cos²A−1 |
| tan 2A | = 2tanA/(1−tan²A) |
| sin 3A | = 3sinA − 4sin³A |
| cos 3A | = 4cos³A − 3cosA |
| sinC + sinD | = 2sin[(C+D)/2]cos[(C−D)/2] |
| sinC − sinD | = 2cos[(C+D)/2]sin[(C−D)/2] |
| cosC + cosD | = 2cos[(C+D)/2]cos[(C−D)/2] |
| cosC − cosD | = −2sin[(C+D)/2]sin[(C−D)/2] |
| Sine rule | a/sinA = b/sinB = c/sinC = 2R |
| Cosine rule | a² = b² + c² − 2bc cosA |
Ch 3.Complex Numbers
| Formula / Relation | Expression |
|---|---|
| i² = −1 | i⁴ = 1, i³ = −i |
| Modulus | |z| = √(a²+b²) for z = a+ib |
| Argument | arg(z) = tan⁻¹(b/a) |
| Conjugate | z̄ = a − ib |
| z · z̄ | = |z|² |
| Polar form | z = r(cosθ + i sinθ) = re^(iθ) |
| De Moivre's Theorem | (cosθ + i sinθ)ⁿ = cos(nθ) + i sin(nθ) |
Ch 4.Linear Inequalities
| Formula / Relation | Expression |
|---|---|
| Multiplying by negative | Reverses the inequality sign |
| Solution set | All values satisfying the inequality, shown on number line |
Ch 5.Permutations and Combinations
| Formula / Relation | Expression |
|---|---|
| Factorial | n! = n×(n−1)×…×2×1; 0! = 1 |
| Permutation | ⁿPᵣ = n!/(n−r)! |
| Combination | ⁿCᵣ = n!/[r!(n−r)!] |
| ⁿCᵣ + ⁿCᵣ₋₁ | = ⁿ⁺¹Cᵣ |
| ⁿC₀ = ⁿCₙ | = 1 |
| Permutation with repetition | nʳ |
Ch 6.Binomial Theorem
| Formula / Relation | Expression |
|---|---|
| Binomial Expansion | (a+b)ⁿ = Σᵣ₌₀ⁿ ⁿCᵣ aⁿ⁻ʳ bʳ |
| General Term (Tᵣ₊₁) | Tᵣ₊₁ = ⁿCᵣ · aⁿ⁻ʳ · bʳ |
| Middle term (n even) | T_(n/2 + 1) |
| Middle terms (n odd) | T_((n+1)/2) and T_((n+3)/2) |
| Sum of binomial coefficients | 2ⁿ = ΣⁿCᵣ |
Ch 7.Sequences and Series
| Formula / Relation | Expression |
|---|---|
| AP nth term | aₙ = a + (n−1)d |
| AP sum | Sₙ = n/2[2a+(n−1)d] |
| GP nth term | aₙ = arⁿ⁻¹ |
| GP sum (finite) | Sₙ = a(rⁿ−1)/(r−1), r ≠ 1 |
| GP sum (infinite, |r|<1) | S∞ = a/(1−r) |
| AM-GM inequality | AM ≥ GM; (a+b)/2 ≥ √(ab) |
| Sum of first n natural numbers | Σn = n(n+1)/2 |
| Sum of squares | Σn² = n(n+1)(2n+1)/6 |
| Sum of cubes | Σn³ = [n(n+1)/2]² |
Ch 8.Straight Lines
| Formula / Relation | Expression |
|---|---|
| Slope from two points | m = (y₂−y₁)/(x₂−x₁) |
| Slope-intercept form | y = mx + c |
| Point-slope form | y − y₁ = m(x − x₁) |
| Two-point form | (y−y₁)/(y₂−y₁) = (x−x₁)/(x₂−x₁) |
| Intercept form | x/a + y/b = 1 |
| Distance from point to line | d = |ax₁+by₁+c| / √(a²+b²) |
| Angle between two lines | tan θ = |(m₁−m₂)/(1+m₁m₂)| |
Ch 9.Conic Sections
| Formula / Relation | Expression |
|---|---|
| Circle (standard) | x² + y² = r² |
| Circle (general) | (x−h)² + (y−k)² = r² |
| Parabola (opens right) | y² = 4ax |
| Parabola (opens up) | x² = 4ay |
| Ellipse | x²/a² + y²/b² = 1 (a>b) |
| Hyperbola | x²/a² − y²/b² = 1 |
| Eccentricity (ellipse) | e = c/a < 1 |
Ch 10.Limits
| Formula / Relation | Expression |
|---|---|
| lim(x→0) sin x/x | = 1 |
| lim(x→0) (1−cos x)/x | = 0 |
| lim(x→0) tan x/x | = 1 |
| lim(x→0) (eˣ−1)/x | = 1 |
| lim(x→0) (aˣ−1)/x | = ln a |
| lim(x→∞)(1+1/x)ˣ | = e |
| L'Hôpital's Rule (0/0 or ∞/∞) | lim f(x)/g(x) = lim f'(x)/g'(x) |
Ch 11.Statistics
| Formula / Relation | Expression |
|---|---|
| Mean deviation (mean) | MD = Σ|xᵢ − x̄| / n |
| Variance | σ² = Σ(xᵢ − x̄)² / n |
| Standard Deviation | σ = √[Σ(xᵢ−x̄)²/n] |
| Coefficient of variation | CV = (σ/x̄) × 100 |
Ch 12.Probability
| Formula / Relation | Expression |
|---|---|
| P(E) | = n(E)/n(S) |
| P(A ∪ B) | = P(A)+P(B)−P(A∩B) |
| P(A') | = 1−P(A) |
| Mutually exclusive events | P(A∩B) = 0; P(A∪B) = P(A)+P(B) |
Frequently Asked Questions
Which trigonometry formulas are most important for Class 11 Maths?
The compound angle formulas (sin(A±B), cos(A±B), tan(A±B)), double angle formulas (sin2A, cos2A, tan2A), and the sum-to-product formulas are most frequently tested. Along with the three Pythagorean identities, these form the core of Class 11 Trigonometry.
What is the general term in binomial expansion?
The (r+1)th term is Tᵣ₊₁ = ⁿCᵣ · aⁿ⁻ʳ · bʳ. To find a specific term, set up Tᵣ₊₁ equal to the required term and solve for r. For the term independent of x, set the power of x to zero and solve for r.
How is variance different from standard deviation?
Variance (σ²) = Σ(xᵢ−x̄)²/n is the average squared deviation from the mean. Standard deviation (σ) = √variance. Standard deviation is in the same unit as the data while variance is in squared units, so SD is easier to interpret.
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