VITEEE 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 VITEEE, not a summary of it.

1. 1

   Algebra

   4 topics

   • Complex Numbers and Quadratic Equations
     • Algebra of complex numbers and Argand plane
     • Modulus, argument and De Moivre's theorem
     • Nature of roots and relations between roots and coefficients
   • Matrices and Determinants
     • Types of matrices and algebra of matrices
     • Determinants, adjoint and inverse
     • Solution of linear equations by Cramer's rule and matrix method
   • Permutations, Combinations and Binomial Theorem
     • Fundamental principle of counting
     • Binomial theorem for positive integral index and general term
   • Sequences and Series
     • Arithmetic, geometric and harmonic progressions
     • Sum of special series
2. 2

   Trigonometry and Vector Algebra

   3 topics

   • Trigonometric Ratios and Identities
     • Trigonometric ratios and compound angle formulae
     • Multiple and sub-multiple angles
   • Trigonometric Equations and Inverse Functions
     • General solutions of trigonometric equations
     • Inverse trigonometric functions and properties of triangles
   • Vector Algebra
     • Addition of vectors and scalar/vector products
     • Scalar and vector triple products
     • Application to geometry
3. 3

   Analytical Geometry

   3 topics

   • Straight Lines and Pair of Lines
     • Various forms of equation of a line
     • Angle between lines and distance formulae
   • Circles and Conic Sections
     • Equation of a circle and tangents
     • Parabola, ellipse and hyperbola: standard equations and properties
   • Three Dimensional Geometry
     • Direction cosines and ratios
     • Equation of a line and plane in space
     • Shortest distance between lines
4. 4

   Calculus

   4 topics

   • Limits, Continuity and Differentiability
     • Evaluation of limits and standard limits
     • Continuity and differentiability of functions
   • Differentiation and Applications
     • Derivatives of standard, implicit and parametric functions
     • Tangents, normals, maxima and minima
     • Rate of change and approximations
   • Integral Calculus
     • Indefinite integrals: substitution, parts and partial fractions
     • Definite integrals and properties
     • Area under curves
   • Differential Equations
     • Order, degree and formation
     • Variable separable and linear differential equations
5. 5

   Probability, Statistics and Discrete Mathematics

   4 topics

   • Probability Distributions
     • Conditional probability and Bayes' theorem
     • Random variables and binomial distribution
   • Statistics
     • Measures of central tendency and dispersion
     • Mean deviation, variance and standard deviation
   • Discrete Mathematics
     • Mathematical logic and statements
     • Groups, semigroups and basic algebraic structures
   • Correlation and Regression
     • Rank correlation
     • Lines of regression

Mathematics flashcards for VITEEE

21 of 59 cards from the Mathematics deck — real questions with worked answers.

1. What is the modulus and argument of a complex number z = a + bi?

   Modulus |z| = sqrt(a^2 + b^2); argument theta = arctan(b/a), measured from the positive real axis (adjusted for quadrant).

2. State De Moivre's Theorem for a complex number in polar form.

   (cos theta + i sin theta)^n = cos(n theta) + i sin(n theta), for integer n.

3. For the quadratic ax^2 + bx + c = 0, what are the sum and product of its roots?

   Sum of roots = -b/a; product of roots = c/a.

4. What does the discriminant D = b^2 - 4ac tell you about the roots of a quadratic equation?

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

5. What is the formula for the cube roots of unity, and what is their sum?

   The roots are 1, omega, omega^2 where omega = (-1 + i sqrt(3))/2; their sum is 1 + omega + omega^2 = 0, and omega^3 = 1.

6. How is the determinant of a 2x2 matrix [[a, b], [c, d]] calculated?

   Determinant = ad - bc.

7. What is the formula for the inverse of a non-singular matrix A?

   A^(-1) = (1/|A|) * adj(A), where adj(A) is the adjoint (transpose of the cofactor matrix) and |A| != 0.

8. When does a square matrix A have an inverse?

   A is invertible if and only if it is non-singular, i.e., its determinant |A| != 0.

9. State the property of determinants when two rows (or columns) are interchanged.

   The sign of the determinant changes (it is multiplied by -1).

10. What is the relationship between |adj(A)| and |A| for an n x n matrix?

    |adj(A)| = |A|^(n-1).

11. What is the formula for the number of permutations of n distinct objects taken r at a time?

    P(n, r) = n! / (n - r)!

12. What is the formula for combinations C(n, r), and how does it relate to permutations?

    C(n, r) = n! / (r!(n - r)!) = P(n, r) / r!

13. State the Binomial Theorem for (a + b)^n.

    (a + b)^n = sum from r=0 to n of C(n, r) * a^(n-r) * b^r.

14. What is the general (r+1)th term in the expansion of (a + b)^n?

    T_(r+1) = C(n, r) * a^(n-r) * b^r.

15. What is the value of C(n, 0) + C(n, 1) + ... + C(n, n)?

    2^n (the sum of all binomial coefficients in (1+1)^n).

16. What is the formula for the nth term of an arithmetic progression (AP)?

    a_n = a + (n - 1)d, where a is the first term and d is the common difference.

17. What is the sum of the first n terms of an AP?

    S_n = (n/2)[2a + (n - 1)d] = (n/2)(a + l), where l is the last term.

18. What is the sum of the first n terms of a geometric progression (GP)?

    S_n = a(r^n - 1)/(r - 1) for r != 1; the sum to infinity (|r| < 1) is a/(1 - r).

19. What is the formula for the sum of squares of the first n natural numbers?

    sum of k^2 = n(n + 1)(2n + 1)/6.

20. Define the arithmetic mean (AM) and geometric mean (GM) of two positive numbers a and b, and state the AM-GM inequality.

    AM = (a + b)/2, GM = sqrt(ab); the inequality states AM >= GM.

21. State the Pythagorean trigonometric identity and its two derived forms.

    sin^2 x + cos^2 x = 1; derived: 1 + tan^2 x = sec^2 x and 1 + cot^2 x = cosec^2 x.

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