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SRMJEEE Mathematics Syllabus

The Mathematics syllabus for SRMJEEE in full: 5 chapters, 22 topics and 47 sub-topics, every one listed below, plus 50 Mathematics flashcards with answers.

5Chapters
22Topics
47Sub-topics
50Flashcards

Mathematics syllabus: all 5 chapters

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

  1. Algebra

     6 topics
    • Sets, Relations and Functions
      • Types of relations and functions
      • Composition and inverse of functions
    • Complex Numbers
      • Algebra of complex numbers
      • Argand plane and polar form
      • De Moivre's theorem and roots of unity
    • Quadratic Equations and Theory of Equations
      • Nature of roots and discriminant
      • Relation between roots and coefficients
    • Matrices and Determinants
      • Algebra of matrices and inverse
      • Properties of determinants
      • Solution of linear equations
    • Sequences, Series and Binomial Theorem
      • AP, GP and HP
      • Binomial theorem and applications
    • Permutations, Combinations and Probability
      • Counting principles
      • Conditional probability and Bayes' theorem

  2. Trigonometry

     4 topics
    • Trigonometric Functions and Identities
      • Compound and multiple angle formulae
      • Transformation formulae
    • Trigonometric Equations
      • General solutions
    • Inverse Trigonometric Functions
      • Domain, range and principal values
      • Properties and identities
    • Properties of Triangles
      • Sine and cosine rules
      • Heights and distances

  3. Coordinate Geometry

     4 topics
    • Straight Lines and Pair of Lines
      • Various forms of line equations
      • Angle between lines and distance formulae
    • Circles
      • Equation of circle and tangents
      • Family of circles
    • Conic Sections
      • Parabola
      • Ellipse
      • Hyperbola
    • Three Dimensional Geometry
      • Direction cosines and ratios
      • Lines and planes in space

  4. Calculus

     5 topics
    • Limits, Continuity and Differentiability
      • Evaluation of limits
      • Continuity and differentiability conditions
    • Differentiation
      • Rules and chain rule
      • Implicit and parametric differentiation
    • Applications of Derivatives
      • Tangents, normals and rate of change
      • Maxima, minima and monotonicity
    • Integration
      • Indefinite integrals and methods
      • Definite integrals and properties
      • Area under curves
    • Differential Equations
      • Order, degree and formation
      • Variable separable and linear equations

  5. Vectors and Statistics

     3 topics
    • Vector Algebra
      • Addition and scalar product
      • Vector product and scalar triple product
    • Statistics
      • Measures of central tendency
      • Variance and standard deviation
    • Mathematical Reasoning
      • Statements and logical connectives
      • Tautology and contradiction

SRMJEEE Mathematics flashcards — 50 questions with answers

  1. Define a relation $R$ from set $A$ to set $B$.

    A relation $R$ from $A$ to $B$ is any subset of the Cartesian product $A \times B$. Each element is an ordered pair $(a,b)$ with $a \in A$ and $b \in B$.

  2. What are the three properties that define an equivalence relation?

    A relation $R$ on a set is an equivalence relation if it is reflexive ($aRa$), symmetric ($aRb \Rightarrow bRa$), and transitive ($aRb$ and $bRc \Rightarrow aRc$).

  3. When is a function $f: A \to B$ called one-one (injective)?

    $f$ is injective if distinct elements have distinct images: $f(x_1) = f(x_2) \Rightarrow x_1 = x_2$ for all $x_1, x_2 \in A$.

  4. When is a function $f: A \to B$ called onto (surjective)?

    $f$ is surjective if every element of $B$ is the image of at least one element of $A$, i.e. range of $f$ equals $B$.

  5. What condition makes a function $f: A \to B$ bijective and invertible?

    $f$ is bijective if it is both injective and surjective. A function is invertible if and only if it is bijective.

  6. Define the composition of functions $f: A \to B$ and $g: B \to C$.

    The composition $g \circ f : A \to C$ is defined by $(g \circ f)(x) = g(f(x))$ for all $x \in A$.

  7. If $f$ is invertible, what is the relationship between $f \circ f^{-1}$ and $f^{-1} \circ f$?

    $f \circ f^{-1} = I_B$ (identity on $B$) and $f^{-1} \circ f = I_A$ (identity on $A$), where $I$ denotes the identity function.

  8. How many relations can be defined from a set $A$ with $m$ elements to a set $B$ with $n$ elements?

    The number of relations is $2^{mn}$, since a relation is any subset of $A \times B$, which has $mn$ elements.

  9. Define the imaginary unit $i$ and state the values of $i^2, i^3, i^4$.

    $i = \sqrt{-1}$, so $i^2 = -1$, $i^3 = -i$, and $i^4 = 1$. Powers of $i$ cycle with period 4.

  10. How do you find the modulus and conjugate of $z = a + bi$?

    Modulus: $|z| = \sqrt{a^2 + b^2}$. Conjugate: $\bar{z} = a - bi$.

  11. Express the multiplicative inverse of a non-zero complex number $z = a + bi$.

    $z^{-1} = \frac{\bar{z}}{|z|^2} = \frac{a - bi}{a^2 + b^2}$.

  12. State the key property relating $z$, $\bar{z}$ and $|z|$.

    $z \cdot \bar{z} = |z|^2 = a^2 + b^2$, a non-negative real number.

  13. What is the polar (trigonometric) form of a complex number $z = a + bi$?

    $z = r(\cos\theta + i\sin\theta)$, where $r = |z| = \sqrt{a^2 + b^2}$ and $\theta = \arg(z)$ with $\tan\theta = \frac{b}{a}$.

  14. In the Argand plane, what do the horizontal and vertical axes represent?

    The horizontal (x) axis represents the real part of $z$ and the vertical (y) axis represents the imaginary part. The point $(a,b)$ represents $z = a + bi$.

  15. State De Moivre's theorem for a positive integer $n$.

    $(\cos\theta + i\sin\theta)^n = \cos(n\theta) + i\sin(n\theta)$ for all integers $n$.

  16. Give the formula for the $n$ distinct $n$-th roots of unity.

    The $n$-th roots of unity are $z_k = \cos\frac{2\pi k}{n} + i\sin\frac{2\pi k}{n} = e^{2\pi i k/n}$ for $k = 0, 1, \dots, n-1$.

  17. What is the sum of all $n$-th roots of unity?

    The sum of all $n$-th roots of unity is $0$ (for $n \geq 2$). Their product is $(-1)^{n+1}$.

  18. If $\omega$ is a non-real cube root of unity, state the two defining relations.

    $1 + \omega + \omega^2 = 0$ and $\omega^3 = 1$.

  19. Give the moduli and argument rules for the product of two complex numbers.

    For $z_1, z_2$: $|z_1 z_2| = |z_1||z_2|$ and $\arg(z_1 z_2) = \arg(z_1) + \arg(z_2)$.

  20. State the quadratic formula for the roots of $ax^2 + bx + c = 0$.

    $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, where $a \neq 0$.

Show the other 30 Mathematics flashcards

  1. Define the discriminant of a quadratic equation and what it determines.

    The discriminant is $\Delta = b^2 - 4ac$. It determines the nature of the roots of $ax^2 + bx + c = 0$.

  2. Classify the nature of the roots of $ax^2+bx+c=0$ (real coefficients) by the sign of the discriminant.

    If $\Delta > 0$: two distinct real roots. If $\Delta = 0$: two equal (repeated) real roots. If $\Delta < 0$: two distinct complex conjugate roots.

  3. For $ax^2 + bx + c = 0$ with roots $\alpha$ and $\beta$, state the sum and product of roots.

    Sum: $\alpha + \beta = -\frac{b}{a}$. Product: $\alpha\beta = \frac{c}{a}$.

  4. How do you form a quadratic equation given its roots $\alpha$ and $\beta$?

    $x^2 - (\alpha + \beta)x + \alpha\beta = 0$, i.e. $x^2 - (\text{sum})x + (\text{product}) = 0$.

  5. For a cubic $ax^3 + bx^2 + cx + d = 0$ with roots $\alpha, \beta, \gamma$, state the three Vieta relations.

    $\alpha+\beta+\gamma = -\frac{b}{a}$, $\quad \alpha\beta+\beta\gamma+\gamma\alpha = \frac{c}{a}$, $\quad \alpha\beta\gamma = -\frac{d}{a}$.

  6. When is the product of two matrices $AB$ defined, and what is the order of the result?

    $AB$ is defined when the number of columns of $A$ equals the number of rows of $B$. If $A$ is $m \times n$ and $B$ is $n \times p$, then $AB$ is $m \times p$.

  7. State the formula for the inverse of a square matrix $A$ in terms of its adjoint.

    $A^{-1} = \frac{1}{\det(A)} \,\text{adj}(A)$, valid when $\det(A) \neq 0$ (i.e. $A$ is non-singular).

  8. For a $2 \times 2$ matrix $A = \begin{pmatrix} a & b \\ c & d \end{pmatrix}$, give its inverse.

    $A^{-1} = \frac{1}{ad - bc} \begin{pmatrix} d & -b \\ -c & a \end{pmatrix}$, provided $ad - bc \neq 0$.

  9. What is the determinant of a $2 \times 2$ matrix $\begin{pmatrix} a & b \\ c & d \end{pmatrix}$?

    $\det = ad - bc$.

  10. State the multiplicative property of determinants for square matrices $A$ and $B$.

    $\det(AB) = \det(A)\,\det(B)$. Also $\det(A^T) = \det(A)$ and $\det(kA) = k^n \det(A)$ for an $n \times n$ matrix.

  11. What happens to a determinant when two rows (or columns) are interchanged?

    The determinant changes sign (is multiplied by $-1$). If two rows or columns are identical, the determinant is $0$.

  12. State Cramer's rule for solving the system $a_1x + b_1y = c_1$, $a_2x + b_2y = c_2$.

    $x = \frac{D_x}{D}$, $y = \frac{D_y}{D}$, where $D = \begin{vmatrix} a_1 & b_1 \\ a_2 & b_2 \end{vmatrix}$, and $D_x, D_y$ replace the respective coefficient column with the constants. Requires $D \neq 0$.

  13. Using the matrix method, how is the system $AX = B$ solved when $A$ is invertible?

    $X = A^{-1}B$, valid when $\det(A) \neq 0$. The solution is then unique.

  14. For a system $AX = B$, classify solutions by $\det(A)$ (Cramer's rule perspective).

    If $\det(A) \neq 0$: unique solution (consistent). If $\det(A) = 0$ and $(\text{adj}\,A)B = 0$: infinitely many or none. If $\det(A)=0$ and $(\text{adj}\,A)B \neq 0$: no solution (inconsistent).

  15. State the formula for the $n$-th term of an arithmetic progression (AP).

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

  16. State the formula for the sum of the first $n$ terms of an AP.

    $S_n = \frac{n}{2}\big[2a + (n-1)d\big] = \frac{n}{2}(a + l)$, where $l$ is the last term.

  17. State the formula for the $n$-th term and sum of a geometric progression (GP).

    $n$-th term: $a_n = ar^{n-1}$. Sum: $S_n = \frac{a(r^n - 1)}{r - 1}$ for $r \neq 1$.

  18. What is the sum to infinity of a GP, and when does it exist?

    $S_\infty = \frac{a}{1 - r}$, valid only when $|r| < 1$.

  19. Define a harmonic progression (HP) and how its $n$-th term is found.

    An HP is a sequence whose reciprocals form an AP. Its $n$-th term is $\frac{1}{a + (n-1)d}$, where $a, d$ are the first term and common difference of the corresponding AP of reciprocals.

  20. State the relationship (inequality) between the arithmetic mean (AM), geometric mean (GM) and harmonic mean (HM) of positive numbers.

    $\text{AM} \geq \text{GM} \geq \text{HM}$, with equality when all numbers are equal. Also $\text{GM}^2 = \text{AM} \times \text{HM}$ for two numbers.

  21. State the general binomial theorem for $(a+b)^n$ where $n$ is a positive integer.

    $(a+b)^n = \sum_{r=0}^{n} \binom{n}{r} a^{n-r} b^{r}$, where $\binom{n}{r} = \frac{n!}{r!(n-r)!}$.

  22. Write the general (general $(r+1)$-th) term in the expansion of $(a+b)^n$.

    $T_{r+1} = \binom{n}{r} a^{n-r} b^{r}$.

  23. How many terms are in the expansion of $(a+b)^n$ and what is the sum of all binomial coefficients?

    There are $n+1$ terms. The sum of all binomial coefficients is $\sum_{r=0}^{n}\binom{n}{r} = 2^n$.

  24. How do you find the middle term(s) in the expansion of $(a+b)^n$?

    If $n$ is even, there is one middle term: $T_{\frac{n}{2}+1}$. If $n$ is odd, there are two middle terms: $T_{\frac{n+1}{2}}$ and $T_{\frac{n+3}{2}}$.

  25. State the formula for the number of permutations of $n$ distinct objects taken $r$ at a time.

    $^nP_r = \frac{n!}{(n-r)!}$.

  26. State the formula for the number of combinations of $n$ distinct objects taken $r$ at a time.

    $^nC_r = \frac{n!}{r!\,(n-r)!}$, and $^nP_r = r! \cdot {}^nC_r$.

  27. State the symmetry and Pascal's rule properties of combinations.

    Symmetry: $^nC_r = {}^nC_{n-r}$. Pascal's rule: $^nC_r + {}^nC_{r-1} = {}^{n+1}C_r$.

  28. State the classical (theoretical) definition of the probability of an event $E$.

    $P(E) = \frac{\text{number of favourable outcomes}}{\text{total number of equally likely outcomes}} = \frac{n(E)}{n(S)}$, with $0 \leq P(E) \leq 1$.

  29. State the addition theorem of probability for two events $A$ and $B$.

    $P(A \cup B) = P(A) + P(B) - P(A \cap B)$. For mutually exclusive events, $P(A \cup B) = P(A) + P(B)$.

  30. State the conditional probability and multiplication theorem for two events.

    $P(A \mid B) = \frac{P(A \cap B)}{P(B)}$ (for $P(B) > 0$). Multiplication: $P(A \cap B) = P(B)\,P(A \mid B)$. For independent events, $P(A \cap B) = P(A)P(B)$.

SRMJEEE Mathematics FAQ

What is in the SRMJEEE Mathematics syllabus?

SRMJEEE Mathematics is split into 5 chapters: Algebra, Trigonometry, Coordinate Geometry, Calculus and Vectors and Statistics. Together they contain 22 topics and 47 sub-topics.

How many chapters are in SRMJEEE Mathematics?

5 chapters, containing 22 topics and 47 sub-topics. The largest chapter is Algebra, with 6 topics.

Are there flashcards for SRMJEEE Mathematics?

Yes — a 50-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.