SRMJEEE 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 SRMJEEE, not a summary of it.

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
     • 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. 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. 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. 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. 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

Mathematics flashcards for SRMJEEE

21 of 50 cards from the Mathematics deck — real questions with worked 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 $a \neq 0$.

21. 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 $ax^2 + bx + c = 0$.

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