CBSE Class 11 Mathematics Syllabus

Mathematics syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Mathematics in CBSE Class 11, not a summary of it.

1. 1

   Sets and Functions

   3 topics

   • Sets
   • Relations & Functions
   • Trigonometric Functions
2. 2

   Algebra

   6 topics

   • Principle of Mathematical Induction
   • Complex Numbers and Quadratic Equations
   • Linear Inequalities
   • Permutations and Combinations
   • Binomial Theorem
   • Sequence and Series
3. 3

   Coordinate Geometry

   3 topics

   • Straight Lines
   • Conic Sections
   • Introduction to Three-dimensional Geometry
4. 4

   Calculus

   1 topic

   • Limits and Derivatives
5. 5

   Mathematical Reasoning

   1 topic

   • Mathematical Reasoning
6. 6

   Statistics and Probability

   2 topics

   • Statistics
   • Probability

Mathematics flashcards for CBSE Class 11

21 of 50 cards from the Mathematics deck — real questions with worked answers.

1. What is the definition of a set?

   A well-defined collection of distinct objects (elements). 'Well-defined' means it is unambiguous whether any given object belongs to the collection.

2. What is the power set of a set A, and how many elements does it have if A has n elements?

   The power set P(A) is the set of all subsets of A. It has 2^n elements.

3. State the formula for the number of elements in the union of two sets: n(A ∪ B).

   n(A ∪ B) = n(A) + n(B) − n(A ∩ B).

4. State the inclusion-exclusion formula for n(A ∪ B ∪ C).

   n(A∪B∪C) = n(A)+n(B)+n(C) − n(A∩B) − n(B∩C) − n(A∩C) + n(A∩B∩C).

5. State De Morgan's laws for sets.

   (A ∪ B)' = A' ∩ B' and (A ∩ B)' = A' ∪ B'.

6. How many elements are in the Cartesian product A × B if n(A)=p and n(B)=q?

   p × q elements.

7. What is the difference between a relation and a function?

   A relation is any subset of A × B. A function is a special relation where every element of the domain A is related to exactly one element of B.

8. Define the domain, codomain, and range of a function.

   Domain = set of all inputs (set A). Codomain = set B into which the function maps. Range = set of actual output values, a subset of the codomain.

9. What is the domain and range of the identity function f(x)=x and the modulus function f(x)=|x|?

   Identity: domain R, range R. Modulus: domain R, range [0, ∞).

10. State the relations between degree and radian measure of angles.

    π radians = 180°. So 1 radian = (180/π)° ≈ 57°16′, and 1° = (π/180) radians.

11. State the three fundamental Pythagorean trigonometric identities.

    sin²x + cos²x = 1; 1 + tan²x = sec²x; 1 + cot²x = cosec²x.

12. State the formulas for sin(A+B) and cos(A+B).

    sin(A+B) = sinA cosB + cosA sinB; cos(A+B) = cosA cosB − sinA sinB.

13. State the double-angle formulas for sin 2x and cos 2x.

    sin 2x = 2 sinx cosx; cos 2x = cos²x − sin²x = 2cos²x − 1 = 1 − 2sin²x.

14. State the formula for tan(A+B).

    tan(A+B) = (tanA + tanB) / (1 − tanA tanB).

15. What is the general solution of sin x = 0 and cos x = 0?

    sin x = 0 ⇒ x = nπ, n ∈ Z. cos x = 0 ⇒ x = (2n+1)π/2, n ∈ Z.

16. What are the four steps of the Principle of Mathematical Induction?

    1) Base step: prove P(1) is true. 2) Assume P(k) is true (inductive hypothesis). 3) Prove P(k+1) is true using the hypothesis. 4) Conclude P(n) holds for all n ∈ N.

17. Define the imaginary unit i and give the values of i², i³, and i⁴.

    i = √(−1). i² = −1, i³ = −i, i⁴ = 1.

18. What is the modulus and conjugate of the complex number z = a + bi?

    Modulus |z| = √(a² + b²). Conjugate z̄ = a − bi.

19. How do you find the multiplicative inverse of z = a + bi?

    z⁻¹ = z̄ / |z|² = (a − bi)/(a² + b²).

20. State the quadratic formula and the roots of ax² + bx + c = 0 when the discriminant is negative.

    x = (−b ± √(b²−4ac)) / 2a. If b²−4ac < 0, the roots are complex: x = (−b ± i√(4ac−b²)) / 2a.

21. How does the inequality sign behave when multiplying or dividing both sides by a negative number?

    The inequality sign reverses (flips direction).

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