KCET 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 KCET, not a summary of it.

1. 1

   Sets, Relations and Trigonometry

   4 topics

   • Sets
     • Types of sets and operations
     • Venn diagrams and De Morgan's laws
   • Relations and Functions
     • Types of relations and functions
     • Composition and inverse of functions
     • Binary operations
   • Trigonometric Functions
     • Trigonometric identities and equations
     • Sum, difference and multiple angle formulae
     • Sine and cosine rules
   • Inverse Trigonometric Functions
     • Domain, range and principal values
     • Properties and identities
2. 2

   Algebra

   6 topics

   • Complex Numbers and Quadratic Equations
     • Argand plane and polar form
     • Modulus, argument and conjugate
     • Roots of quadratic equations
   • Linear Inequalities
     • Solution of inequalities
     • Graphical representation in two variables
   • Permutations and Combinations
     • Fundamental principle of counting
     • Factorial, nPr and nCr
   • Binomial Theorem
     • General and middle terms
     • Properties of binomial coefficients
   • Sequences and Series
     • Arithmetic and geometric progressions
     • Sum to n terms of special series
   • Mathematical Induction
     • Principle and applications
3. 3

   Coordinate Geometry

   3 topics

   • Straight Lines
     • Slope and forms of line equations
     • Distance and angle between lines
   • Conic Sections
     • Circle, parabola, ellipse and hyperbola
     • Standard equations and properties
   • Three Dimensional Geometry
     • Direction cosines and ratios
     • Equation of line and plane in space
     • Angle and distance measures
4. 4

   Calculus

   5 topics

   • Limits and Continuity
     • Standard limits
     • Continuity and differentiability
   • Differentiation
     • Rules of differentiation
     • Derivatives of implicit and parametric functions
     • Logarithmic and higher order derivatives
   • Applications of Derivatives
     • Rate of change and tangents/normals
     • Maxima, minima and monotonicity
   • Integrals
     • Indefinite integrals and methods
     • Definite integrals and properties
     • Area under curves
   • Differential Equations
     • Order, degree and formation
     • Variable separable and linear equations
5. 5

   Vectors, Probability and Linear Algebra

   4 topics

   • Vector Algebra
     • Addition and scalar multiplication
     • Dot and cross product
     • Scalar and vector triple product
   • Probability
     • Conditional probability and Bayes' theorem
     • Random variables and probability distributions
     • Binomial distribution
   • Statistics
     • Measures of central tendency
     • Mean deviation, variance and standard deviation
   • Matrices and Determinants
     • Types and algebra of matrices
     • Determinants and properties
     • Inverse of matrix and solving linear equations

Mathematics flashcards for KCET

21 of 67 cards from the Mathematics deck — real questions with worked answers.

1. In set theory, 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 (including the empty set and A itself). If |A| = n, then |P(A)| = 2^n.

2. State the formula for the number of elements in the union of two finite sets A and B.

   n(A ∪ B) = n(A) + n(B) − n(A ∩ B).

3. Define the Cartesian product A × B and give its cardinality.

   A × B = {(a, b) : a ∈ A, b ∈ B}, the set of all ordered pairs. If |A| = m and |B| = n, then |A × B| = mn.

4. What conditions make a relation R on a set an equivalence relation?

   R must be reflexive (aRa), symmetric (aRb ⇒ bRa), and transitive (aRb and bRc ⇒ aRc).

5. Distinguish between a one-one (injective), onto (surjective), and bijective function.

   Injective: distinct inputs give distinct outputs. Surjective: every element of the codomain is an image of some input. Bijective: both injective and surjective.

6. What is the maximum number of relations from a set A with m elements to a set B with n elements?

   2^(mn), since each relation is a subset of A × B which has mn elements.

7. Convert: how do degrees relate to radians?

   180° = π radians, so 1 radian = 180/π degrees ≈ 57.3°, and 1° = π/180 radians.

8. State the three Pythagorean trigonometric identities.

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

9. State the sine and cosine addition formulas for sin(A+B) and cos(A+B).

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

10. State the general solution of sin θ = sin α.

    θ = nπ + (−1)^n α, where n ∈ Z.

11. State the general solutions of cos θ = cos α and tan θ = tan α.

    cos θ = cos α ⇒ θ = 2nπ ± α; tan θ = tan α ⇒ θ = nπ + α, n ∈ Z.

12. Give the principal value ranges of sin⁻¹x, cos⁻¹x, and tan⁻¹x.

    sin⁻¹x ∈ [−π/2, π/2]; cos⁻¹x ∈ [0, π]; tan⁻¹x ∈ (−π/2, π/2).

13. What is the value of sin⁻¹x + cos⁻¹x for x ∈ [−1, 1]?

    sin⁻¹x + cos⁻¹x = π/2.

14. State the formula for tan⁻¹x + tan⁻¹y when xy < 1.

    tan⁻¹x + tan⁻¹y = tan⁻¹((x + y)/(1 − xy)), valid when xy < 1.

15. For a complex number z = a + ib, define its modulus and conjugate.

    Modulus |z| = √(a² + b²); conjugate z̄ = a − ib.

16. State the quadratic formula and the nature of roots based on the discriminant D = b² − 4ac.

    x = (−b ± √(b²−4ac))/(2a). If D > 0: real and distinct; D = 0: real and equal; D < 0: complex conjugate roots.

17. For a complex number, what is the relation between modulus, argument, and the polar form?

    z = r(cos θ + i sin θ) where r = |z| is the modulus and θ = arg(z) is the argument (angle with positive real axis).

18. State De Moivre's theorem.

    (cos θ + i sin θ)^n = cos(nθ) + i sin(nθ) for any integer n.

19. How does multiplying or dividing both sides of an inequality by a negative number affect it?

    The inequality sign reverses (e.g., a < b becomes −a > −b when multiplied by −1).

20. State the formula for the number of permutations of n distinct objects taken r at a time.

    P(n, r) = nPr = n!/(n − r)!.

21. State the formula for the number of combinations of n distinct objects taken r at a time.

    C(n, r) = nCr = n!/(r!(n − r)!).

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