Class 11 Maths Formula Poster (Printable PDF, Free) — All 53 Formulas

Trigonometric Identities & Functions

Addition formulas: sin(A + B) = sin A cos B + cos A sin B; sin(A - B) = sin A cos B - cos A sin BSimilarly for cos and tan
Cosine addition: cos(A + B) = cos A cos B - sin A sin B; cos(A - B) = cos A cos B + sin A sin B
Tangent addition: tan(A + B) = (tan A + tan B)/(1 - tan A tan B); tan(A - B) = (tan A - tan B)/(1 + tan A tan B)
Double angle formulas: sin 2A = 2 sin A cos A; cos 2A = cos² A - sin² A = 2cos² A - 1 = 1 - 2sin² A; tan 2A = 2tan A/(1 - tan² A)
Triple angle formulas: sin 3A = 3 sin A - 4 sin³ A; cos 3A = 4 cos³ A - 3 cos A; tan 3A = (3tan A - tan³ A)/(1 - 3tan² A)
Sum to product: sin C + sin D = 2 sin((C + D)/2) cos((C - D)/2); cos C + cos D = 2 cos((C + D)/2) cos((C - D)/2)Useful for simplifying trigonometric expressions
Product to sum: 2 sin A cos B = sin(A + B) + sin(A - B); 2 cos A cos B = cos(A + B) + cos(A - B)

Complex number definition: z = a + ib, where i² = -1a = real part, b = imaginary part
Modulus (absolute value): |z| = √(a² + b²)For z = a + ib
Conjugate: z* = a - ibFor z = a + ib; z × z* = |z|²
Argument (angle): arg(z) = tan⁻¹(b/a)Angle made with positive real axis; consider quadrant
Polar form: z = r(cos θ + i sin θ) = r e^(iθ)where r = |z|, θ = arg(z)
De Moivre's Theorem: (cos θ + i sin θ)ⁿ = cos nθ + i sin nθFor integer n; also applies to zⁿ = rⁿ(cos nθ + i sin nθ)
nth roots of unity: 1^(1/n) = e^(2πik/n), k = 0, 1, 2, ..., n-1Sum of nth roots of unity = 0

Factorial: n! = n × (n - 1) × (n - 2) × ... × 2 × 1; 0! = 1Product of all positive integers up to n
Permutation (nPr): ⁿPᵣ = n!/(n - r)!Number of ways to arrange r objects from n distinct objects
Combination (nCr): ⁿCᵣ = n!/(r!(n - r)!) = ⁿPᵣ/r!Number of ways to choose r objects from n distinct objects; order doesn't matter
Properties of combinations: ⁿC₀ = 1, ⁿCₙ = 1, ⁿCᵣ = ⁿCₙ₋ᵣ, ⁿCᵣ + ⁿCᵣ₋₁ = ⁿ⁺¹CᵣPascal's identity: ⁿCᵣ + ⁿCᵣ₋₁ = ⁿ⁺¹Cᵣ
Circular permutations: (n - 1)!Arrangements of n distinct objects in a circle
Permutations with repetition: nʳr selections from n objects with replacement

Binomial expansion: (x + y)ⁿ = Σ ⁿCᵣ xⁿ⁻ʳ yʳ (r = 0 to n)Expansion of (x + y)ⁿ using binomial coefficients
General term: Tᵣ₊₁ = ⁿCᵣ xⁿ⁻ʳ yʳ(r + 1)th term in binomial expansion
Middle term: If n is even: T₍ₙ/₂₎₊₁; If n is odd: T₍ₙ₊₁₎/₂ and T₍ₙ₊₃₎/₂There are two middle terms if n is odd
Sum of binomial coefficients: ⁿC₀ + ⁿC₁ + ⁿC₂ + ... + ⁿCₙ = 2ⁿSum of all binomial coefficients
Binomial series: (1 + x)ⁿ = 1 + nx + n(n-1)/2! x² + n(n-1)(n-2)/3! x³ + ...For |x| < 1; used for fractional and negative exponents

Arithmetic Progression (AP): aₙ = a + (n - 1)d; Sₙ = n/2[2a + (n - 1)d]a = first term, d = common difference
Geometric Progression (GP): aₙ = ar^(n-1); Sₙ = a(1 - rⁿ)/(1 - r) if r ≠ 1a = first term, r = common ratio
Sum of infinite GP: S∞ = a/(1 - r) if |r| < 1Only converges if |r| < 1
Arithmetic Mean (AM): A = (a + b)/2Mean of two numbers
Geometric Mean (GM): G = √(ab)For two positive numbers a and b
Harmonic Mean (HM): H = 2ab/(a + b)Reciprocal of AM of reciprocals
AM-GM-HM inequality: A ≥ G ≥ H, with equality iff a = bUseful inequality for two positive numbers

Slope of line: m = tan θ = (y₂ - y₁)/(x₂ - x₁)θ = angle with positive x-axis
Point-slope form: y - y₁ = m(x - x₁)Line passing through (x₁, y₁) with slope m
Slope-intercept form: y = mx + cm = slope, c = y-intercept
Two-point form: (y - y₁)/(y₂ - y₁) = (x - x₁)/(x₂ - x₁)Line through points (x₁, y₁) and (x₂, y₂)
Intercept form: x/a + y/b = 1a = x-intercept, b = y-intercept
Distance from point to line: d = |ax₀ + by₀ + c|/√(a² + b²)Distance from (x₀, y₀) to line ax + by + c = 0
Angle between two lines: tan θ = |m₁ - m₂|/(1 + m₁m₂)Slopes m₁ and m₂; parallel if m₁ = m₂, perpendicular if m₁m₂ = -1

Circle: Standard: (x - h)² + (y - k)² = r²; General: x² + y² + 2gx + 2fy + c = 0Center: (h, k) or (-g, -f), Radius: r or √(g² + f² - c)
Parabola: Standard: y² = 4ax (focus at (a, 0)), x² = 4ay (focus at (0, a))Vertex at origin; directrix x = -a or y = -a
Ellipse: Standard: x²/a² + y²/b² = 1 (a > b); eccentricity e = √(1 - b²/a²)Foci at (±c, 0) where c² = a² - b²
Hyperbola: Standard: x²/a² - y²/b² = 1; eccentricity e = √(1 + b²/a²)Foci at (±c, 0) where c² = a² + b²; asymptotes: y = ±(b/a)x

Distance formula in 3D: d = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]Distance between points P₁(x₁, y₁, z₁) and P₂(x₂, y₂, z₂)
Section formula in 3D: P = ((mx₂ + nx₁)/(m + n), (my₂ + ny₁)/(m + n), (mz₂ + nz₁)/(m + n))Point dividing line segment in ratio m:n
Direction cosines: If line makes angles α, β, γ with x, y, z axes, then l = cos α, m = cos β, n = cos γ; l² + m² + n² = 1Direction cosines satisfy l² + m² + n² = 1
Equation of plane: Ax + By + Cz + D = 0General form; normal vector: (A, B, C)
Distance from point to plane: d = |Ax₀ + By₀ + Cz₀ + D|/√(A² + B² + C²)Distance from point (x₀, y₀, z₀) to plane

Limit definition: lim(x→a) f(x) = L means for every ε > 0, ∃ δ > 0 such that |f(x) - L| < ε whenever |x - a| < δFormal definition of limit
Limit laws: lim[f(x) + g(x)] = lim f(x) + lim g(x); lim[f(x) × g(x)] = lim f(x) × lim g(x); lim[f(x)/g(x)] = lim f(x)/lim g(x) if lim g(x) ≠ 0Assuming individual limits exist
Standard limits: lim(x→0) sin x/x = 1; lim(x→0) (1 - cos x)/x² = 1/2; lim(x→∞) (1 + 1/x)ˣ = eImportant limits to memorize
L'Hôpital's Rule: lim(x→a) f(x)/g(x) = lim(x→a) f'(x)/g'(x)If 0/0 or ∞/∞ form
Continuity at a point: f is continuous at x = a if lim(x→a) f(x) = f(a)Left limit = Right limit = Function value