ISC 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 ISC Class 11, not a summary of it.

1. 1

   Sets and Functions

   3 topics

   • Sets
   • Relations and 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

   Statistics and Probability

   2 topics

   • Statistics
   • Probability

Mathematics flashcards for ISC Class 11

21 of 51 cards from the Mathematics deck — real questions with worked answers.

1. What is the formula for the number of subsets of a set with n elements?

   2^n. Of these, 2^n − 1 are proper subsets.

2. State De Morgan's laws for two sets A and B.

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

3. What is the formula relating the cardinalities of A ∪ B for finite sets?

   n(A ∪ B) = n(A) + n(B) − n(A ∩ B).

4. Define the power set of a set A.

   The set of all subsets of A, denoted P(A). If n(A) = n, then n(P(A)) = 2^n.

5. If n(A) = p and n(B) = q, how many relations exist from A to B?

   2^(pq), since A × B has pq elements and each subset is a relation.

6. Define a function (mapping) from set A to set B.

   A relation in which every element of A is associated with exactly one element of B.

7. What are the domain and range of the function f(x) = √x (real-valued)?

   Domain: x ≥ 0 (i.e. [0, ∞)); Range: [0, ∞).

8. Distinguish between a relation and a function.

   Every function is a relation, but a relation is a function only if each domain element maps to exactly one range element.

9. Convert the angle radian measure to degrees: what is 180° in radians?

   π radians. So 1 radian = 180/π degrees ≈ 57°16'.

10. State the Pythagorean trigonometric identities.

    sin²θ + cos²θ = 1; 1 + tan²θ = sec²θ; 1 + cot²θ = cosec²θ.

11. State the formula for sin(A + B) and cos(A + B).

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

12. What is the general solution of sin θ = 0?

    θ = nπ, where n is any integer.

13. What is the general solution of cos θ = 0?

    θ = (2n+1)π/2, where n is any integer.

14. State the double-angle formula for cos 2θ in three forms.

    cos 2θ = cos²θ − sin²θ = 2cos²θ − 1 = 1 − 2sin²θ.

15. What is the value of sin 2θ in terms of sin θ and cos θ?

    sin 2θ = 2 sin θ cos θ.

16. What are the three steps of proof by the Principle of Mathematical Induction?

    1) Base step: verify P(1) is true. 2) Inductive hypothesis: assume P(k) is true. 3) Inductive step: prove P(k+1) is true; conclude P(n) holds for all n.

17. Define the imaginary unit i and state the value of i².

    i = √(−1), and i² = −1.

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

    |z| = √(a² + b²).

19. What is the conjugate of z = a + bi, and what is z·z̄?

    z̄ = a − bi; and z·z̄ = a² + b² = |z|².

20. State the quadratic formula for ax² + bx + c = 0.

    x = (−b ± √(b² − 4ac)) / (2a).

21. What does the discriminant b² − 4ac tell you about the roots of a quadratic?

    > 0: two distinct real roots; = 0: equal (repeated) real roots; < 0: two complex conjugate roots.

See more Mathematics flashcards →

Planning Mathematics for ISC Class 11

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