Examius
🇮🇳 COMEDK UGET · subject
COMEDK UGET Mathematics - Algebra and Trigonometry Syllabus
The Mathematics - Algebra and Trigonometry syllabus for COMEDK UGET in full: 5 chapters, 16 topics and 39 sub-topics, every one listed below, plus 50 Mathematics - Algebra and Trigonometry flashcards with answers.
Mathematics - Algebra and Trigonometry syllabus: all 5 chapters
Expand any chapter to see its topics and sub-topics.
-
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
- Sets, Relations and Functions
-
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
- Complex Numbers
-
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
- Permutations and Combinations
-
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
- Matrices
-
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
- Trigonometric Functions
COMEDK UGET Mathematics - Algebra and Trigonometry flashcards — 50 questions with answers
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.
State De Morgan's laws for sets A and B.
(A ∪ B)' = A' ∩ B' and (A ∩ B)' = A' ∪ B'.
For finite sets, what is the formula for n(A ∪ B)?
n(A ∪ B) = n(A) + n(B) − n(A ∩ B).
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.
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.
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.
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}).
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.
What is the contrapositive of the statement "if p then q"?
"If ~q then ~p." A conditional and its contrapositive are logically equivalent.
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.
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)).
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).
Using induction, what is the sum 1 + 2 + 3 + ... + n?
n(n+1)/2.
What is the sum of squares 1² + 2² + ... + n²?
n(n+1)(2n+1)/6.
Define the imaginary unit i and state the value of i².
i = √(−1), and i² = −1. Also i³ = −i and i⁴ = 1.
What is the modulus and conjugate of the complex number z = a + bi?
Modulus |z| = √(a² + b²); Conjugate z̄ = a − bi.
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).
State De Moivre's theorem.
(cos θ + i sin θ)ⁿ = cos nθ + i sin nθ, for all integer n.
What is the multiplicative inverse of z = a + bi?
z⁻¹ = z̄/|z|² = (a − bi)/(a² + b²).
State the quadratic formula for ax² + bx + c = 0.
x = [−b ± √(b² − 4ac)] / (2a).
Show the other 30 Mathematics - Algebra and Trigonometry flashcards
What does the discriminant D = b² − 4ac tell you about the roots of a quadratic?
D > 0: real and distinct roots; D = 0: real and equal roots; D < 0: complex conjugate roots.
For ax² + bx + c = 0 with roots α and β, give the sum and product of roots.
Sum α + β = −b/a; Product αβ = c/a.
How do you form a quadratic equation given roots α and β?
x² − (α + β)x + αβ = 0.
When solving a linear inequality, when must you reverse the inequality sign?
When multiplying or dividing both sides by a negative number.
What is the formula for the number of permutations of n distinct objects taken r at a time?
ⁿPᵣ = n! / (n − r)!
What is the formula for combinations of n objects taken r at a time?
ⁿCᵣ = n! / [r!(n − r)!]
State the relationship between ⁿPᵣ and ⁿCᵣ.
ⁿPᵣ = ⁿCᵣ × r! (permutations equal combinations times the arrangements of r items).
What is the number of permutations of n objects where p are alike of one kind and q alike of another?
n! / (p! q!).
State the Binomial Theorem for (a + b)ⁿ.
(a + b)ⁿ = Σ_{r=0}^{n} ⁿCᵣ a^{n−r} b^r.
What is the general (r+1)th term in the expansion of (a + b)ⁿ?
T_{r+1} = ⁿCᵣ a^{n−r} b^r.
How many terms are there in the expansion of (a + b)ⁿ?
n + 1 terms.
What is the nth term of an arithmetic progression (AP)?
aₙ = a + (n − 1)d, where a is the first term and d the common difference.
What is the sum of the first n terms of an AP?
Sₙ = n/2 [2a + (n − 1)d] = n/2 (a + l), where l is the last term.
What is the nth term and the sum of n terms of a geometric progression (GP)?
nth term: aₙ = arⁿ⁻¹; Sum Sₙ = a(rⁿ − 1)/(r − 1), r ≠ 1.
What is the sum of an infinite GP when |r| < 1?
S∞ = a / (1 − r).
What is the arithmetic mean (AM) and geometric mean (GM) of two numbers a and b?
AM = (a + b)/2; GM = √(ab). Also AM ≥ GM.
What is the condition for two matrices to be conformable for multiplication?
The number of columns of the first matrix must equal the number of rows of the second.
Define a symmetric and a skew-symmetric matrix.
Symmetric: A' = A (a_ij = a_ji); Skew-symmetric: A' = −A (a_ij = −a_ji, so diagonal entries are 0).
What is an identity matrix and a scalar matrix?
Identity matrix: diagonal matrix with all diagonal entries 1. Scalar matrix: diagonal matrix with all diagonal entries equal.
How do you compute the determinant of a 2×2 matrix [[a,b],[c,d]]?
det = ad − bc.
What is the relationship det(AB) and det(A)·det(B)?
det(AB) = det(A) × det(B).
What is the formula for the inverse of a matrix A using its adjoint?
A⁻¹ = (1/det A) · adj(A), provided det A ≠ 0.
When does a system of linear equations have a unique solution (Cramer's rule / matrix method)?
When the coefficient determinant Δ ≠ 0 (matrix is non-singular/invertible).
In Cramer's rule for two equations, how is x found?
x = Δ₁/Δ, where Δ is the coefficient determinant and Δ₁ replaces the x-column with the constants.
What is the formula for the area of a triangle with vertices (x₁,y₁), (x₂,y₂), (x₃,y₃) using a determinant?
Area = ½ |x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂)|.
State the basic Pythagorean trigonometric identities.
sin²θ + cos²θ = 1; 1 + tan²θ = sec²θ; 1 + cot²θ = cosec²θ.
State the sum formulas for sin(A+B) and cos(A+B).
sin(A+B) = sinA cosB + cosA sinB; cos(A+B) = cosA cosB − sinA sinB.
What is the general solution of sin θ = sin α?
θ = nπ + (−1)ⁿ α, where n ∈ Z.
What are the principal value ranges of sin⁻¹x and cos⁻¹x?
sin⁻¹x ∈ [−π/2, π/2]; cos⁻¹x ∈ [0, π].
State the Sine Rule and the Cosine Rule for a triangle.
Sine Rule: a/sinA = b/sinB = c/sinC = 2R. Cosine Rule: a² = b² + c² − 2bc·cosA.
COMEDK UGET Mathematics - Algebra and Trigonometry FAQ
What is in the COMEDK UGET Mathematics - Algebra and Trigonometry syllabus?
COMEDK UGET Mathematics - Algebra and Trigonometry is split into 5 chapters: Sets, Relations, Functions and Logic, Complex Numbers and Quadratic Equations, Combinatorics and Series, Matrices and Determinants and Trigonometry. Together they contain 16 topics and 39 sub-topics.
How many chapters are in COMEDK UGET Mathematics - Algebra and Trigonometry?
5 chapters, containing 16 topics and 39 sub-topics. The largest chapter is Trigonometry, with 4 topics.
Are there flashcards for COMEDK UGET Mathematics - Algebra and Trigonometry?
Yes — a 50-card Mathematics - Algebra and Trigonometry deck, printed in full in the flashcards section of this page and available in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.