COMEDK UGET Mathematics - Algebra and Trigonometry Syllabus

Mathematics - Algebra and Trigonometry syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Mathematics - Algebra and Trigonometry in COMEDK UGET, not a summary of it.

1. 1

   Sets, Relations, Functions and Logic

   3 topics

   • Sets, Relations and Functions
     • Set operations and Venn diagrams
     • Types of relations and functions
     • Composition and inverse of functions
   • Mathematical Reasoning
     • Statements and logical connectives
     • Validity of statements
   • Principle of Mathematical Induction
     • Statement and method
     • Applications to divisibility and series
2. 2

   Complex Numbers and Quadratic Equations

   3 topics

   • Complex Numbers
     • Algebra of complex numbers and Argand plane
     • Modulus, argument and polar form
     • Cube roots of unity
   • Quadratic Equations
     • Roots and nature of roots
     • Relation between roots and coefficients
   • Linear Inequalities
     • Solution of linear inequalities
     • Graphical representation
3. 3

   Combinatorics and Series

   3 topics

   • Permutations and Combinations
     • Fundamental principle of counting
     • Permutations with restrictions
     • Combinations and applications
   • Binomial Theorem
     • General and middle term
     • Properties of binomial coefficients
   • Sequences and Series
     • Arithmetic and geometric progressions
     • Harmonic progression and means
     • Sum of special series
4. 4

   Matrices and Determinants

   3 topics

   • Matrices
     • Types and operations
     • Transpose, symmetric and skew-symmetric matrices
     • Inverse of a matrix
   • Determinants
     • Properties of determinants
     • Area of triangle and applications
     • Solution of system of linear equations
   • Applications of Matrices and Determinants
     • Cramer's rule
     • Consistency of linear systems
5. 5

   Trigonometry

   4 topics

   • Trigonometric Functions
     • Trigonometric ratios and identities
     • Compound and multiple angle formulae
     • Transformation formulae
   • Trigonometric Equations
     • General solutions
     • Principal solutions
   • Inverse Trigonometric Functions
     • Domains and ranges
     • Properties and identities
   • Properties of Triangles and Heights and Distances
     • Sine and cosine rules
     • Heights and distances

Mathematics - Algebra and Trigonometry flashcards for COMEDK UGET

18 of 50 cards from the Mathematics - Algebra and Trigonometry deck — real questions with worked answers.

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

   2^n subsets (including the empty set and the set itself); the number of proper subsets is 2^n - 1.

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

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

3. For finite sets, what is the formula for n(A ∪ B)?

   n(A ∪ B) = n(A) + n(B) − n(A ∩ B).

4. Define a function as a special type of relation.

   A relation f from set A to set B is a function if every element of A has exactly one image in B.

5. What conditions make a function one-one (injective), onto (surjective), and bijective?

   One-one: distinct elements have distinct images. Onto: range equals codomain. Bijective: both one-one and onto.

6. If f: A→B and g: B→C, what is the composite (g∘f)(x)?

   (g∘f)(x) = g(f(x)). Composition exists when the range of f is a subset of the domain of g.

7. What is the domain and range of f(x) = 1/x?

   Domain: all real numbers except 0 (R − {0}); Range: all real numbers except 0 (R − {0}).

8. In mathematical reasoning, what is the negation of "p and q"?

   ~(p ∧ q) = ~p ∨ ~q (not p or not q), by De Morgan's law for statements.

9. What is the contrapositive of the statement "if p then q"?

   "If ~q then ~p." A conditional and its contrapositive are logically equivalent.

10. State the converse and inverse of "if p then q".

    Converse: "if q then p"; Inverse: "if ~p then ~q." These two are equivalent to each other but not to the original.

11. What does the quantifier "there exists" (∃) become when negated?

    Negation of "there exists x such that p(x)" is "for all x, ~p(x)" (∀ x, ~p(x)).

12. State the Principle of Mathematical Induction.

    A statement P(n) is true for all natural numbers n if (1) P(1) is true (base step), and (2) P(k) true implies P(k+1) true (inductive step).

13. Using induction, what is the sum 1 + 2 + 3 + ... + n?

    n(n+1)/2.

14. What is the sum of squares 1² + 2² + ... + n²?

    n(n+1)(2n+1)/6.

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

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

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

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

17. State the polar (modulus-argument) form of a complex number.

    z = r(cos θ + i sin θ), where r = |z| and θ = arg(z) = tan⁻¹(b/a).

18. State De Moivre's theorem.

    (cos θ + i sin θ)ⁿ = cos nθ + i sin nθ, for all integer n.

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