Mathematics (Class 11) — Free Notes (CBSE & HBSE)
Free Class 11 Maths notes — Sets, Relations and Functions, Trigonometry, Complex Numbers, Permutations and Combinations, Binomial Theorem, Sequences and Series, Straight Lines, Conic Sections, Limits and Derivatives, Statistics and Probability — with solved examples, MCQs and important questions for CBSE and HBSE. Free Class 11 Mathematics course on SikshaSarovar.
Free, chapter-wise Mathematics notes for Class 11 on Siksha Sarovar, aligned to NCERT and both CBSE and Haryana Board (HBSE). Covers 14 chapters with explanations, worked examples and board-pattern practice questions.
Chapters covered (14)
- Sets — Foundation of all higher mathematics — every later chapter (functions, probability, calculus) speaks the language of sets. CBSE asks 5–6 marks: 1 MCQ + 1 short answer (set…
- Relations and Functions — Builds on sets to introduce relations, functions, domain/range, and special real-valued functions. CBSE expects 6–8 marks: ordered pairs, function types, and graph sketching. HBSE…
- Trigonometric Functions — The most identity-heavy chapter — every formula reappears in calculus and physics. CBSE allocates 8–10 marks across MCQ, identity proofs, equation solving, and graph sketching.…
- Complex Numbers and Quadratic Equations — Introduces i = √(−1), polar form, and quadratic equations with negative discriminant. CBSE expects 6–8 marks; HBSE typically 5–7 marks, focused on modulus-argument and quadratic…
- Linear Inequalities — Compact chapter combining algebra with coordinate geometry. CBSE asks 4–5 marks: one number-line solution and one graphical system. HBSE keeps it at 3–4 marks.
- Permutations and Combinations — Combinatorial reasoning chapter — sets up probability and binomial theorem. CBSE expects 6–8 marks: factorial computation, permutations with restrictions, combinations, and a word…
- Binomial Theorem — Expansion formula and properties of binomial coefficients. CBSE asks 5–6 marks: general/middle term, numerical coefficient finding, identities. HBSE asks 4–5 marks.
- Sequences and Series — Covers Arithmetic Progression (AP), Geometric Progression (GP), and standard summation formulas. CBSE asks 6–8 marks: nth term, sum to n terms, GP word problem, AM-GM inequality.
- Straight Lines — Coordinate geometry workhorse — slopes, line forms, distances. CBSE expects 6–8 marks; HBSE 5–7 marks. Heavy formula chapter — memorise the five forms of line equation.
- Conic Sections — Circle, parabola, ellipse, hyperbola — standard forms and key properties. CBSE expects 6–8 marks across MCQ and short/long questions on equation derivation, foci, vertices,…
- Introduction to Three Dimensional Geometry — Extends Cartesian plane to space: coordinate triple (x, y, z), distance, and section formula in 3D. CBSE expects 4–5 marks; HBSE 3–4 marks. Short, formula-heavy.
- Limits and Derivatives — First taste of calculus — intuitive limits, standard limits, and derivative from first principles. CBSE expects 8–10 marks: 1 MCQ + 1 short limit + 1 long…
- Statistics — Measures of dispersion — range, mean deviation, variance, standard deviation, and coefficient of variation. CBSE asks 5–6 marks; HBSE 4–5 marks. Formula-heavy chapter with…
- Probability — Axiomatic foundation of probability — sample spaces, events, P(A ∪ B), complementary events. CBSE asks 5–7 marks; HBSE 4–6 marks. Builds on the language of sets from Chapter 1.
Sets: Sets — Definition, Notation, Types
What is a Set?
A set is a well-defined collection of distinct objects. "Well-defined" means: given any object, we can decide unambiguously whether it belongs to the set or not.
The collection of "tall students in your class" is not a set (tall is subjective); the collection of "students above 170 cm" is a set.
Notation
- Sets are denoted by capital letters: A, B, C, …
- Elements by lowercase: a, b, x, y, …
- x ∈ A means "x belongs to A"; x ∉ A means "x does not belong to A".
Ways to Represent a Set
| Method | Example |
|---|---|
| Roster (Tabular) | A = {1, 2, 3, 4, 5} |
| Set-builder (Rule) | A = {x : x ∈ ℕ, x ≤ 5} |
| Descriptive | A = first five natural numbers |
In roster form: elements are separated by commas, order does not matter, and repetition is ignored (so {1, 2, 2, 3} = {1, 2, 3}).
Standard Number Sets (must memorise the symbols)
| Symbol | Set |
|---|---|
| ℕ | Natural numbers {1, 2, 3, …} |
| W | Whole numbers {0, 1, 2, …} |
| ℤ | Integers {…, −2, −1, 0, 1, 2, …} |
| ℚ | Rational numbers (p/q form) |
| ℝ | Real numbers |
| ℂ | Complex numbers |
| ℤ⁺, ℝ⁺ | Positive integers / reals |
Types of Sets
Empty / Null Set (∅ or { }) — contains no elements. Caution: {0} is not empty (it contains 0), and {∅} contains one element (the empty set itself).
Singleton set — exactly one element: {7}.
Finite set — countable, finite number of elements. Cardinality n(A) = number of elements.
Infinite set — cannot be exhausted by counting (ℕ, ℝ).
Equal sets — A = B iff every element of A is in B and vice-versa (same elements, in any order).
Equivalent sets — A ~ B iff n(A) = n(B). Equal ⇒ equivalent, but equivalent ⇏ equal.
CBSE Tip: Always specify the universal set when using set-builder notation — "x ∈ ℕ" or "x ∈ ℝ" can change the resulting set entirely.
Frequently asked questions
Are these Mathematics notes free?
Yes — all Mathematics notes on Siksha Sarovar are free to read, no account required.
Do the notes follow CBSE and HBSE?
Yes. Notes are NCERT-aligned and include both CBSE and Haryana Board (HBSE) exam guidance, important questions and MCQs.
Can I prepare for board exams here?
Yes — each chapter includes key concepts, formulas, important questions and practice MCQs for board exam revision.