Mathematics Mock Tests

WB SLST 2025 Mathematics Syllabus (Class XI-XII)

This syllabus covers fundamental and advanced topics in mathematics designed to prepare students for the WB SLST 2025 examination. Emphasis is placed on both theoretical understanding and practical problem-solving skills.

1. Algebra (Classical & Modern)

• Equations: Study of polynomial roots including methods to find roots, Cardanos solution for cubic equations, and application of Descartes Rule of Signs to determine the number of positive and negative roots.
• Theorems: Understanding and application of the Rational Root Theorem and Lagranges Theorem for solving polynomial equations.
• Modern Algebra: Introduction to algebraic structures such as groups, rings, and fields, including their properties and characteristics.

2. Matrix Theory

• Matrix operations including addition, multiplication, and scalar multiplication.
• Computation of adjoint and inverse of matrices, and important determinant identities.
• Study of real quadratic forms and their classification.

3. Calculus & Real Functions

• Concepts of limits, continuity, and differentiability of real functions.
• Evaluation of standard limits such assin x / x ,log(1x) / x , and(ex - 1) / x .
• Important theorems including Darbouxs Theorem, Rolles Theorem, and the Mean Value Theorem with proofs and applications.

4. Integration & Series

• Techniques of definite and indefinite integration including substitution and integration by parts.
• Evaluation of special integrals such as1/(x a)n and integrals involving trigonometric forms.
• Study of improper integrals and criteria for convergence.

5. Differential Equations

• Formulation and solution of first and second-order differential equations.
• Methods including variable separable, homogeneous equations, linear differential equations, and use of the differential operator (D-operator) method.

6. Analytical Geometry (2D & 3D)

• Study of conic sections: parabola, ellipse, and hyperbola with their standard equations and properties.
• Equations and properties of lines, planes, spheres, and angle bisectors in two and three dimensions.
• 3D geometry topics including direction cosines, skew lines, and sphere intersections.

7. Mechanics & Linear Programming

• Fundamentals of particle motion including velocity and acceleration.
• Concepts of constraints and the work-energy principle in mechanics.
• Linear Programming Problems (LPP): formulation of objective functions, identification of feasible regions, and determination of solution sets using graphical and analytical methods.

8. Probability & Statistics

• Probability distributions including Binomial, Poisson, Normal, and Multinomial distributions with their properties and applications.
• Statistical methods such as correlation and regression analysis, and parameter estimation techniques.

9. Numerical Analysis

• Root-finding methods: Bisection Method, Regula Falsi, and Newton-Raphson Method with convergence criteria.
• Interpolation techniques and numerical integration methods including Trapezoidal Rule and Simpsons Rule.

Important Notes: Focus on understanding theorem proofs and their applications. Practice problem-solving regularly to master integration techniques and differential equations. For Linear Programming, graphical methods are essential for visualizing feasible regions.

WB SLST 2025 Mathematics Syllabus (Class IX-X)

This syllabus is designed to prepare students for the WB SLST 2025 examination, covering key mathematical concepts from Algebra to Probability & Statistics. Emphasis is placed on both theoretical understanding and practical problem-solving skills.

I. Algebra

Classical Algebra:

• Complex Numbers: Definition, operations, polar form, De Moivre's theorem
• Polynomials: Degree, factorization, remainder theorem
• Roots of Equations: Nature and relation of roots, solving quadratic and higher degree equations
• Determinants and Matrices: Properties, evaluation, applications in solving linear equations
• Linear Equations: Systems of linear equations and their solutions using matrices and determinants

Modern Algebra:

• Sets and Mappings: Types of sets, functions, one-to-one and onto mappings
• Groups, Rings, and Fields: Basic definitions and examples
• Vector Spaces: Definition, subspaces, basis, dimension
• Quadratic Forms and Eigenvalues: Introduction and applications
• Cayley-Hamilton Theorem: Statement and simple applications

II. Geometry

2D Geometry:

• Transformation of Axes: Translation and rotation of coordinate axes
• Conics: Parabola, ellipse, hyperbola standard equations and properties
• Pair of Lines: Conditions for pair of straight lines, angle between lines
• Tangents and Polars: Definitions and properties related to conics

3D Geometry:

• Lines and Planes: Equations, intersections, and angles between them
• Distances and Angles: Between points, lines, and planes
• Skew Lines: Definition and shortest distance between skew lines

III. Differential Calculus

• Sequences and Limits: Understanding convergence and limit concepts
• Continuity: Definition and properties of continuous functions
• Differentiation: Rules, techniques, and higher order derivatives
• Maxima and Minima: Finding local maxima and minima of functions
• Partial Derivatives: Functions of several variables and their partial derivatives
• Applications: Tangents, normals, and envelopes of curves

IV. Integral Calculus

• Integration Methods: Indefinite integrals, substitution, integration by parts
• Definite Integrals: Properties and evaluation
• Reduction Formulae: Techniques for solving complex integrals
• Double Integrals: Computation and applications
• Applications: Calculating area, volume, and surface area of solids

V. Differential Equations

• First and Second Order ODEs: Basic concepts and solutions
• Homogeneous Equations: Methods of solving
• Bernoulli Equations: Form and solution techniques
• Clairauts Equations: General and singular solutions
• Eulers Equations: Solution methods for linear differential equations with variable coefficients

VI. Vector Algebra

• Vectors: Definition, types, and properties
• Scalar and Vector Products: Computation and geometric interpretations
• Applications: Use of vectors in geometry and physics problems

VII. Analytical Dynamics

• Motion: Types of motion, displacement, velocity, acceleration
• Newtons Laws of Motion: Statements and applications
• Energy: Kinetic and potential energy concepts
• Simple Harmonic Motion (SHM): Characteristics and equations
• Projectiles: Trajectory and range calculations
• Central Force Motion: Basic principles and examples

VIII. Linear Programming

• Formulation: Setting up linear programming problems
• Graphical Method: Solution of two-variable problems
• Simplex Method: Algorithm and applications
• Duality: Concept and relation to primal problems
• Transportation and Assignment Problems: Formulation and solution techniques

IX. Numerical Methods

• Interpolation: Methods and applications
• Numerical Integration: Trapezoidal and Simpsons rules
• Equation Solving: Bisection method and Newton-Raphson method

X. Probability & Statistics

• Central Tendency: Mean, median, mode
• Dispersion: Range, variance, standard deviation
• Probability Concepts: Basic probability, conditional probability
• Bayes Theorem: Statement and applications

Important Notes: Regular practice of problem-solving is essential. Focus on understanding theorems and their applications. Use graphical methods where applicable to enhance conceptual clarity. Time management during exams is crucial.