AP EAMCET / TS EAMCET Mathematics - Algebra and Trigonometry Syllabus

Mathematics - Algebra and Trigonometry syllabus: all 4 chapters

Expand any chapter to see its topics and sub-topics.

1. 1

   Sets, Relations and Functions

   4 topics

   • Functions
     • One-one, onto and bijective functions
     • Composition and inverse of functions
     • Domain, range and real-valued functions
   • Mathematical Induction
     • Principle of finite mathematical induction
     • Applications to divisibility and series
   • Theory of Equations
     • Relation between roots and coefficients
     • Transformation of equations
   • Quadratic Expressions
     • Nature of roots and discriminant
     • Sign, maximum and minimum of a quadratic
2. 2

   Algebra of Counting and Matrices

   4 topics

   • Permutations and Combinations
     • Linear and circular permutations
     • Combinations and selections
   • Binomial Theorem
     • Binomial theorem for positive integral index
     • Series for rational index and partial fractions
   • Matrices
     • Types of matrices and algebra of matrices
     • Adjoint and inverse of a matrix
     • Solving linear equations: Cramer's rule and matrix inversion
   • Determinants
     • Properties, minors and cofactors
     • Consistency of system of equations
3. 3

   Complex Numbers and Demoivre

   3 topics

   • Complex Numbers
     • Modulus, argument and Argand plane
     • Conjugate and algebraic operations
   • De Moivre's Theorem
     • Powers and roots of complex numbers
     • nth roots of unity
   • Applications of Complex Numbers
     • Geometric interpretation and loci
4. 4

   Trigonometry

   5 topics

   • Trigonometric Ratios and Transformations
     • Compound, multiple and submultiple angles
     • Sum to product and product to sum
   • Trigonometric Equations
     • General solutions
   • Inverse Trigonometric Functions
     • Principal values and properties
   • Hyperbolic Functions
     • Definitions and inverse hyperbolic functions
   • Properties of Triangles
     • Sine, cosine and projection rules
     • In-radius, circumradius and ex-radii

AP EAMCET / TS EAMCET Mathematics - Algebra and Trigonometry flashcards — 50 questions with answers

1. What is a function from set A to set B?

   A relation that assigns to every element of A (the domain) exactly one element of B (the codomain). No element of A is left unassigned and none has two images.

2. Define one-one (injective), onto (surjective), and bijective functions.

   Injective: distinct inputs give distinct outputs (f(a)=f(b) implies a=b). Surjective: every element of the codomain is an image of some input (range = codomain). Bijective: both injective and surjective.

3. What is the condition for a function f to have an inverse, and what is the relation between f and its inverse?

   f must be a bijection. Then f⁻¹ exists with f(f⁻¹(x))=x and f⁻¹(f(x))=x; (f∘g)⁻¹ = g⁻¹∘f⁻¹.

4. State the principle of finite mathematical induction.

   If P(1) is true (base step), and P(k) true implies P(k+1) true for all k≥1 (inductive step), then P(n) is true for every positive integer n.

5. Using induction-style formulas, what are the sums of the first n natural numbers, their squares, and their cubes?

   Σn = n(n+1)/2; Σn² = n(n+1)(2n+1)/6; Σn³ = [n(n+1)/2]².

6. State the Fundamental Theorem of Algebra and the relation between roots and degree.

   Every polynomial equation of degree n (n≥1) with complex coefficients has exactly n roots in the complex numbers, counted with multiplicity.

7. For a cubic ax³+bx²+cx+d=0 with roots α, β, γ, what are the relations between roots and coefficients?

   α+β+γ = −b/a; αβ+βγ+γα = c/a; αβγ = −d/a.

8. For a polynomial with real coefficients, how do complex and irrational (surd) roots occur?

   Complex roots occur in conjugate pairs (a+ib and a−ib); irrational surd roots occur in conjugate pairs (a+√b and a−√b).

9. What is the relationship between repeated (multiple) roots of a polynomial f(x) and its derivative f'(x)?

   If α is a root of multiplicity m, it is a root of f'(x) with multiplicity m−1. A common root of f(x) and f'(x) indicates a repeated root.

10. For a quadratic ax²+bx+c=0, what are the sum and product of its roots?

    Sum of roots = −b/a; Product of roots = c/a.

11. What does the discriminant Δ = b²−4ac tell about the roots of a quadratic with real coefficients?

    Δ>0: real and distinct roots; Δ=0: real and equal roots; Δ<0: complex conjugate roots. Δ a perfect square (with rationals) means rational roots.

12. State the sign and maximum/minimum behavior of the quadratic expression ax²+bx+c.

    It has a minimum at x=−b/2a if a>0 and a maximum there if a<0; the extreme value is (4ac−b²)/4a. If Δ<0, the expression has the same sign as a for all real x.

13. State the quadratic formula for the roots of ax²+bx+c=0.

    x = [−b ± √(b²−4ac)] / 2a.

14. What are the formulas for permutations nPr and combinations nCr?

    nPr = n!/(n−r)! (ordered arrangements); nCr = n!/[r!(n−r)!] (unordered selections). nPr = r!·nCr.

15. State the formula for permutations of n objects when some are identical.

    n!/(p!·q!·r!…), where p, q, r,… are the counts of each set of identical objects.

16. How many ways can n distinct objects be arranged in a circle?

    (n−1)! arrangements; if clockwise and anticlockwise are not distinguished (e.g. a necklace), it is (n−1)!/2.

17. State key properties of combinations: nCr = nC(n−r), and Pascal's rule.

    nCr = nC(n−r); nCr + nC(r−1) = (n+1)Cr; nC0 + nC1 + … + nCn = 2ⁿ.

18. State the Binomial Theorem for a positive integer index n.

    (x+a)ⁿ = Σ_{r=0}^{n} nCr · x^{n−r} · aʳ, giving n+1 terms.

19. What is the general term in the expansion of (x+a)ⁿ?

    T_{r+1} = nCr · x^{n−r} · aʳ (the (r+1)th term).

20. How do you find the term independent of x (constant term) in a binomial expansion?

    Write the general term, simplify the exponent of x to a single expression, set that exponent equal to 0, solve for r, then substitute r into the general term.

AP EAMCET / TS EAMCET Mathematics - Algebra and Trigonometry FAQ