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VITEEE Mathematics Syllabus

The Mathematics syllabus for VITEEE in full: 5 chapters, 18 topics and 42 sub-topics, every one listed below, plus 59 Mathematics flashcards with answers.

5Chapters
18Topics
42Sub-topics
59Flashcards

Mathematics syllabus: all 5 chapters

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

  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. 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. 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. 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. 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

VITEEE Mathematics flashcards — 59 questions with 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.

Show the other 39 Mathematics flashcards

  1. 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.

  2. What is the expansion of sin(A + B) and cos(A + B)?

    sin(A + B) = sin A cos B + cos A sin B; cos(A + B) = cos A cos B - sin A sin B.

  3. State the double-angle formula for cos(2A) in three forms.

    cos 2A = cos^2 A - sin^2 A = 2cos^2 A - 1 = 1 - 2sin^2 A.

  4. What is the formula for sin(2A) and tan(2A)?

    sin 2A = 2 sin A cos A; tan 2A = 2 tan A / (1 - tan^2 A).

  5. What is the general solution of sin x = sin alpha?

    x = n*pi + (-1)^n * alpha, where n is any integer.

  6. What is the general solution of cos x = cos alpha and tan x = tan alpha?

    cos x = cos alpha: x = 2n*pi +/- alpha; tan x = tan alpha: x = n*pi + alpha, n an integer.

  7. What are the principal value ranges of arcsin(x), arccos(x), and arctan(x)?

    arcsin: [-pi/2, pi/2]; arccos: [0, pi]; arctan: (-pi/2, pi/2).

  8. What is the formula for the dot (scalar) product of two vectors a and b?

    a . b = |a||b| cos theta = a1*b1 + a2*b2 + a3*b3; it gives a scalar.

  9. What is the cross (vector) product of two vectors, and what is its geometric meaning?

    a x b = |a||b| sin theta * n_hat; its magnitude equals the area of the parallelogram formed by a and b, and it is perpendicular to both.

  10. What is the scalar triple product [a b c], and what does its value represent geometrically?

    [a b c] = a . (b x c); its absolute value equals the volume of the parallelepiped formed by a, b, c. If zero, the vectors are coplanar.

  11. How do you find the angle between two lines with slopes m1 and m2?

    tan theta = |(m1 - m2)/(1 + m1*m2)|; lines are parallel if m1 = m2 and perpendicular if m1*m2 = -1.

  12. What is the perpendicular distance from a point (x1, y1) to the line ax + by + c = 0?

    Distance = |a*x1 + b*y1 + c| / sqrt(a^2 + b^2).

  13. When does the pair of lines ax^2 + 2hxy + by^2 = 0 represent two real and distinct lines?

    When h^2 > ab (the lines are real and distinct; equal if h^2 = ab; imaginary if h^2 < ab).

  14. What is the equation of a circle with center (h, k) and radius r?

    (x - h)^2 + (y - k)^2 = r^2.

  15. For the general circle x^2 + y^2 + 2gx + 2fy + c = 0, what are its center and radius?

    Center = (-g, -f); radius = sqrt(g^2 + f^2 - c).

  16. What is the eccentricity of an ellipse, a parabola, and a hyperbola?

    Ellipse: 0 < e < 1; parabola: e = 1; hyperbola: e > 1.

  17. For the parabola y^2 = 4ax, what are the focus, directrix, and length of the latus rectum?

    Focus = (a, 0); directrix x = -a; length of latus rectum = 4a.

  18. For an ellipse x^2/a^2 + y^2/b^2 = 1 (a > b), what is the relationship between a, b, and eccentricity e?

    b^2 = a^2(1 - e^2), so e = sqrt(1 - b^2/a^2).

  19. What is the distance formula between two points (x1, y1, z1) and (x2, y2, z2) in 3D?

    Distance = sqrt((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2).

  20. What are direction cosines of a line, and what relation do they satisfy?

    Direction cosines l, m, n are the cosines of the angles the line makes with the x, y, z axes; they satisfy l^2 + m^2 + n^2 = 1.

  21. What is the equation of a plane in normal form, and what does it represent?

    lx + my + nz = p, where (l, m, n) are direction cosines of the normal and p is the perpendicular distance from the origin to the plane.

  22. State the definition of continuity of a function f at a point x = a.

    f is continuous at a if the limit of f(x) as x approaches a equals f(a) (limit exists, f(a) defined, and they are equal).

  23. What is the standard limit of (sin x)/x as x approaches 0?

    It equals 1.

  24. What is the relationship between differentiability and continuity of a function?

    If a function is differentiable at a point, it is continuous there; but continuity does not imply differentiability.

  25. State the product rule and quotient rule for differentiation.

    Product: (uv)' = u'v + uv'; Quotient: (u/v)' = (u'v - uv')/v^2.

  26. What is the derivative of f(x) used to find, and what condition gives a local maximum?

    f'(x) gives the slope/rate of change; a local maximum occurs where f'(x) = 0 and f''(x) < 0.

  27. State the fundamental integral of x^n (power rule) for n != -1.

    Integral of x^n dx = x^(n+1)/(n+1) + C.

  28. State the Fundamental Theorem of Calculus for evaluating a definite integral.

    Integral from a to b of f(x) dx = F(b) - F(a), where F is an antiderivative of f.

  29. What is the integration by parts formula?

    Integral of u dv = uv - integral of v du.

  30. What is the order and degree of a differential equation?

    Order is the highest derivative present; degree is the power of the highest-order derivative (when the equation is polynomial in derivatives).

  31. What is the standard form and integrating factor of a linear first-order differential equation?

    Form: dy/dx + P(x)y = Q(x); integrating factor (IF) = e^(integral of P dx), and solution is y*(IF) = integral of Q*(IF) dx + C.

  32. For a binomial distribution with n trials and success probability p, what are the mean and variance?

    Mean = np; variance = npq, where q = 1 - p.

  33. State Bayes' Theorem for events A and B.

    P(A|B) = P(B|A) * P(A) / P(B), provided P(B) != 0.

  34. What is the formula for variance in terms of the mean of squares and square of the mean?

    Variance = E(X^2) - [E(X)]^2 (or mean of squares minus square of the mean).

  35. In statistics, what is the relationship between mean, median, and mode for a moderately skewed distribution?

    Mode = 3*Median - 2*Mean (the empirical relationship).

  36. What is the range of the Karl Pearson correlation coefficient r, and what do its extreme values mean?

    r lies between -1 and +1; r = +1 means perfect positive correlation, r = -1 perfect negative, and r = 0 no linear correlation.

  37. What is the relationship between the correlation coefficient r and the two regression coefficients b_yx and b_xy?

    r = sqrt(b_yx * b_xy), and r has the same sign as both regression coefficients.

  38. In discrete mathematics, state De Morgan's Laws for sets.

    (A union B)' = A' intersect B'; (A intersect B)' = A' union B'.

  39. In Boolean/logic algebra, what is the truth value of a conditional p -> q, and when is it false?

    p -> q is true except when p is true and q is false; it is false only in the case T -> F.

VITEEE Mathematics FAQ

What is in the VITEEE Mathematics syllabus?

VITEEE Mathematics is split into 5 chapters: Algebra, Trigonometry and Vector Algebra, Analytical Geometry, Calculus and Probability, Statistics and Discrete Mathematics. Together they contain 18 topics and 42 sub-topics.

How many chapters are in VITEEE Mathematics?

5 chapters, containing 18 topics and 42 sub-topics. The largest chapter is Algebra, with 4 topics.

Are there flashcards for VITEEE Mathematics?

Yes — a 59-card Mathematics 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.