NEET / State Class 12 Board (e.g. ISC) 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 NEET / State Class 12 Board (e.g. ISC), not a summary of it.

1. 1

   Relations and Functions

   3 topics

   • Types of Relations and Functions
     • Reflexive, symmetric, transitive and equivalence relations
     • One-one, onto and bijective functions
     • Composition of functions and invertible functions
   • Inverse Trigonometric Functions
     • Domain, range and principal value branches
     • Properties and identities of inverse trigonometric functions
   • Binary Operations and Algebra of Functions
     • Binary operations and their properties
2. 2

   Algebra and Calculus I

   3 topics

   • Matrices and Determinants
     • Operations on matrices; symmetric and skew-symmetric
     • Determinants, minors, cofactors and properties
     • Adjoint, inverse and solution of linear equations
   • Continuity and Differentiability
     • Continuity, differentiability and chain rule
     • Derivatives of implicit, parametric and logarithmic functions
     • Rolle's and Lagrange's mean value theorems
   • Applications of Derivatives
     • Rate of change and approximations
     • Increasing and decreasing functions; tangents and normals
     • Maxima and minima
3. 3

   Integral Calculus

   4 topics

   • Indefinite Integrals
     • Integration by substitution and partial fractions
     • Integration by parts and special integrals
   • Definite Integrals
     • Fundamental theorem and properties of definite integrals
     • Definite integral as limit of a sum
   • Applications of Integrals
     • Area under simple curves and between curves
   • Differential Equations
     • Order, degree and formation of differential equations
     • Variable separable and homogeneous equations
     • Linear differential equations
4. 4

   Vectors, 3D Geometry and Probability

   4 topics

   • Vectors
     • Scalar and vector products
     • Scalar triple product and applications
   • Three-Dimensional Geometry
     • Direction cosines and equation of a line
     • Equation of a plane; angle between lines and planes
     • Shortest distance between two lines
   • Probability
     • Conditional probability and multiplication theorem
     • Bayes' theorem and total probability
     • Random variables and binomial distribution
   • Linear Programming
     • Formulation of LPP and graphical solution
     • Feasible region, optimal solution and constraints

Mathematics flashcards for NEET / State Class 12 Board (e.g. ISC)

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

1. What is a reflexive relation on a set A?

   A relation R on A is reflexive if (a, a) belongs to R for every element a in A.

2. Define a symmetric relation.

   A relation R on A is symmetric if (a, b) in R implies (b, a) in R for all a, b in A.

3. Define a transitive relation.

   A relation R on A is transitive if (a, b) in R and (b, c) in R together imply (a, c) in R.

4. What is an equivalence relation?

   A relation that is reflexive, symmetric, and transitive simultaneously.

5. When is a function f: A to B called one-one (injective)?

   When f(x1) = f(x2) implies x1 = x2; distinct elements of A have distinct images.

6. When is a function called onto (surjective)?

   When every element of the codomain B has at least one pre-image in A, i.e. range = codomain.

7. What is a bijective function?

   A function that is both one-one (injective) and onto (surjective); it has an inverse.

8. What is the principal value range of sin inverse x?

   [-pi/2, pi/2], with domain [-1, 1].

9. What is the principal value range of cos inverse x?

   [0, pi], with domain [-1, 1].

10. What is the principal value range of tan inverse x?

    (-pi/2, pi/2), with domain all real numbers.

11. State the identity relating sin inverse x and cos inverse x.

    sin inverse x + cos inverse x = pi/2, for x in [-1, 1].

12. What is tan inverse x + cot inverse x equal to?

    pi/2, for all real x.

13. Define a binary operation on a set A.

    A binary operation * on A is a function from A x A to A, assigning to each ordered pair (a, b) a unique element a * b in A.

14. When is a binary operation * commutative?

    When a * b = b * a for all a, b in the set.

15. What is the identity element for a binary operation *?

    An element e such that a * e = e * a = a for every a in the set.

16. What is the inverse of an element a under operation * with identity e?

    An element b such that a * b = b * a = e.

17. When is a binary operation * associative?

    When (a * b) * c = a * (b * c) for all a, b, c in the set.

18. What is a symmetric matrix?

    A square matrix A for which A transpose = A, i.e. a_ij = a_ji.

19. What is a skew-symmetric matrix?

    A square matrix A for which A transpose = -A; its diagonal elements are all zero.

20. State the condition for two matrices to be multipliable (A times B).

    The number of columns of A must equal the number of rows of B.

21. What is the property (AB) transpose in terms of A transpose and B transpose?

    (AB) transpose = B transpose times A transpose.

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