Class 11 Mathematics Formulas
1. Sets
- Union: A union B = {x | x belongs to A or x belongs to B}
- Intersection: A intersection B = {x | x belongs to A and x belongs to B}
- Complement: A' = {x in U | x not in A}
- De Morgan's laws: (A union B)' = A' intersection B', (A intersection B)' = A' union B'
2. Relations and Functions
- Domain: Set of first components of ordered pairs
- Range: Set of second components
- Types of functions: One-one, many-one, onto, into, bijective
3. Trigonometric Functions
- sin theta: opposite / hypotenuse
- cos theta: adjacent / hypotenuse
- tan theta: sin theta / cos theta
- Identities: sin^2 theta + cos^2 theta = 1
- Sum and difference formulas: sin(A +/- B) = sin A cos B +/- cos A sin B
- Double angle formula: sin 2theta = 2 sin theta cos theta
4. Principle of Mathematical Induction
Used to prove statements for all natural numbers.
5. Complex Numbers and Quadratic Equations
- Complex number: z = a + bi
- Modulus: |z| = sqrt(a^2 + b^2)
- Argument: arg(z) = tan^-1(b/a)
- Polar form: z = r(cos theta + i sin theta)
6. Linear Inequalities
- Solution set: Values of x satisfying the inequality
- Graphical solution: Shaded regions on a number line
7. Permutations and Combinations
- Permutation: P(n,r) = n! / (n-r)!
- Combination: C(n,r) = n! / [r!(n-r)!]
- Circular permutation: (n-1)!
8. Binomial Theorem
- Expansion: (a + b)^n = sum C(n,k) a^(n-k) b^k
- General term: T_(r+1) = C(n,r) a^(n-r) b^r
- Middle term: For even n, the (n/2 + 1)th term
9. Sequences and Series
- Arithmetic progression: a, a+d, a+2d, ...
- Geometric progression: a, ar, ar^2, ...
- Harmonic progression: 1/a, 1/(a+d), ...
- Sum of AP: S = n/2 [2a + (n-1)d]
- Sum of GP: S = a(1-r^n)/(1-r) for r not equal to 1
10. Straight Lines
- Slope-intercept form: y = mx + c
- Point-slope form: y - y1 = m(x - x1)
- Two-point form: (y - y1)/(x - x1) = (y2 - y1)/(x2 - x1)
- Intercept form: x/a + y/b = 1
- Normal form: x cos alpha + y sin alpha = p
- Distance of point from line: |ax + by + c|/sqrt(a^2 + b^2)
- Angle between lines: tan theta = |(m2 - m1)/(1 + m1m2)|
11. Conic Sections
- Circle: x^2 + y^2 + 2gx + 2fy + c = 0
- Parabola: y^2 = 4ax, x^2 = 4ay
- Ellipse: x^2/a^2 + y^2/b^2 = 1
- Hyperbola: x^2/a^2 - y^2/b^2 = 1
12. Introduction to Three Dimensional Geometry
- Distance between points: sqrt[(x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2]
- Section formula: ((m x2 + n x1)/(m+n), (m y2 + n y1)/(m+n), (m z2 + n z1)/(m+n))
13. Limits and Derivatives
- Limit: lim x->a f(x) = L
- Derivative: f'(x) = lim h->0 [f(x+h) - f(x)]/h
- Power rule: d/dx (x^n) = n x^(n-1)
- Product rule: d/dx (uv) = u'v + uv'
- Quotient rule: d/dx (u/v) = (u'v - uv')/v^2
- Chain rule: d/dx f(g(x)) = f'(g(x)) g'(x)
14. Mathematical Reasoning
Statements, negation, converse, contrapositive, and related logical ideas.
15. Statistics
- Mean: sum(xi) / n
- Variance: sum(xi - mu)^2 / n
- Standard deviation: sqrt(variance)
16. Probability
- Probability axioms: 0 <= P(E) <= 1, P(S) = 1
- Addition theorem: P(A union B) = P(A) + P(B) - P(A intersection B)
- Conditional probability: P(A|B) = P(A intersection B)/P(B)
- Multiplication theorem: P(A intersection B) = P(A) P(B|A)
- Bayes' theorem: P(A|B) = [P(B|A) P(A)] / P(B)