IPU CET Mathematics Syllabus

Mathematics syllabus: all 5 chapters

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

1. 1

   Algebra

   6 topics

   • Sets, Relations and Functions
     • Types of relations and functions
     • Composition and inverse of functions
   • Complex Numbers
     • Algebra of complex numbers
     • Modulus, argument and polar form
     • De Moivre's theorem
   • Quadratic Equations and Theory of Equations
     • Nature of roots
     • Relation between roots and coefficients
   • Sequences and Series
     • Arithmetic and geometric progressions
     • Sum of special series
   • Permutations, Combinations and Binomial Theorem
     • Counting principles
     • Binomial theorem and general term
   • Matrices and Determinants
     • Algebra of matrices and inverse
     • Properties of determinants
     • Solution of linear equations
2. 2

   Trigonometry

   4 topics

   • Trigonometric Functions and Identities
     • Trigonometric ratios and identities
     • Sum, difference and multiple angle formulae
   • Trigonometric Equations
     • General solutions
     • Principal solutions
   • Inverse Trigonometric Functions
     • Domain, range and principal values
     • Properties and identities
   • Properties of Triangles
     • Sine and cosine rules
     • Heights and distances
3. 3

   Coordinate Geometry

   4 topics

   • Straight Lines
     • Slope and various forms of line equation
     • Distance, angle and family of lines
   • Circles
     • Equation of a circle
     • Tangents and normals
   • Conic Sections
     • Parabola
     • Ellipse
     • Hyperbola
   • Three-Dimensional Geometry
     • Direction cosines and ratios
     • Equations of line and plane
     • Distance between lines and planes
4. 4

   Calculus

   6 topics

   • Limits, Continuity and Differentiability
     • Evaluation of limits
     • Continuity and differentiability conditions
   • Differentiation
     • Rules and chain rule
     • Derivatives of implicit and parametric functions
   • Applications of Derivatives
     • Tangents, normals and rate of change
     • Maxima, minima and monotonicity
   • Indefinite and Definite Integration
     • Methods of integration
     • Definite integral properties
   • Applications of Integrals
     • Area under curves
     • Area between two curves
   • Differential Equations
     • Order, degree and formation
     • Variable separable and linear equations
5. 5

   Vectors, Probability and Statistics

   4 topics

   • Vector Algebra
     • Addition and scalar product
     • Vector product and scalar triple product
   • Probability
     • Conditional probability and Bayes' theorem
     • Random variable and binomial distribution
   • Statistics
     • Measures of central tendency
     • Mean deviation, variance and standard deviation
   • Mathematical Reasoning
     • Statements and logical connectives
     • Tautology and contradiction

IPU CET Mathematics flashcards — 57 questions with answers

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

   n(A ∪ B) = n(A) + n(B) − n(A ∩ B).

2. If a set has n elements, how many subsets and how many proper subsets does it have?

   It has 2^n subsets and 2^n − 1 proper subsets.

3. What is the number of elements in the Cartesian product A × B, and how is a relation from A to B defined?

   n(A × B) = n(A)·n(B); a relation from A to B is any subset of A × B.

4. Define a one-one (injective) and an onto (surjective) function.

   Injective: distinct inputs give distinct outputs (f(a)=f(b) ⟹ a=b). Surjective: every element of the codomain is an image of some input (range = codomain).

5. For complex number z = a + bi, give its modulus and the value of i².

   |z| = √(a² + b²) and i² = −1.

6. State the polar (Euler) form of a complex number and De Moivre's theorem.

   z = r(cos θ + i sin θ) = r·e^{iθ}; De Moivre: (cos θ + i sin θ)^n = cos nθ + i sin nθ.

7. What are the n distinct nth roots of unity and their sum?

   The nth roots of unity are e^{2πik/n} = cos(2πk/n)+i sin(2πk/n), k = 0,…,n−1; their sum is 0.

8. For az² + bz + c = 0, what is the relation between conjugate complex roots and the coefficients?

   With real coefficients, complex roots occur in conjugate pairs; sum of roots = −b/a, product = c/a.

9. State the quadratic formula and the discriminant for ax² + bx + c = 0.

   x = [−b ± √(b² − 4ac)] / (2a); discriminant D = b² − 4ac.

10. How does the discriminant D determine the nature of roots of a real quadratic?

    D > 0: two distinct real roots; D = 0: equal (repeated) real roots; D < 0: two complex conjugate roots.

11. For a cubic ax³ + bx² + cx + d = 0 with roots α, β, γ, state Vieta's relations.

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

12. Give the nth term and sum of n terms of an arithmetic progression (AP).

    aₙ = a + (n−1)d; Sₙ = n/2 [2a + (n−1)d] = n/2 (a + l).

13. Give the nth term and sum of n terms of a geometric progression (GP), and the sum to infinity.

    aₙ = a·r^{n−1}; Sₙ = a(rⁿ−1)/(r−1) (r≠1); S∞ = a/(1−r) for |r| < 1.

14. State the formulas for Σn, Σn², and Σn³ for the first n natural numbers.

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

15. State the relationship (inequality) between AM, GM and HM of positive numbers.

    AM ≥ GM ≥ HM, with equality iff all numbers are equal; also GM² = AM·HM for two numbers.

16. Give the formulas for permutations nPr and combinations nCr.

    nPr = n!/(n−r)!; nCr = n!/[r!(n−r)!].

17. State the binomial theorem for (a + b)ⁿ and the general (r+1)th term.

    (a+b)ⁿ = Σ_{r=0}^{n} nCr a^{n−r} bʳ; T_{r+1} = nCr a^{n−r} bʳ.

18. State two key properties of binomial coefficients: symmetry and Pascal's rule.

    Symmetry: nCr = nC(n−r); Pascal's rule: nCr + nC(r−1) = (n+1)Cr; also Σ nCr = 2ⁿ.

19. How many arrangements of n objects are there when p, q, … are alike?

    n! / (p! q! …), dividing by the factorials of the counts of identical objects.

20. For a 2×2 matrix A = [[a,b],[c,d]], give det(A) and A⁻¹.

    det(A) = ad − bc; A⁻¹ = (1/det A)·[[d, −b], [−c, a]], provided ad − bc ≠ 0.

IPU CET Mathematics FAQ