CBSE Class 12 Board Examination (Mathematics) Mock Test

CBSE Class 12 Mathematics Board Examination Mock Test

Overview of the CBSE Class 12 Mathematics Exam

The Central Board of Secondary Education (CBSE) Class 12 Board Examination in Mathematics is a crucial assessment for students pursuing higher education, particularly in science, engineering, and commerce streams. This examination evaluates a student's understanding of advanced mathematical concepts, problem-solving abilities, and application skills. A strong performance in this exam is vital for academic and career progression.

The Class 12 Mathematics syllabus is designed to provide a solid foundation in various branches of mathematics, including algebra, calculus, vector algebra, three-dimensional geometry, and probability. The exam structure typically includes a mix of objective and subjective questions, ranging from very short answer types to long answer types, requiring detailed solutions. Our mock tests are meticulously crafted to mirror the actual CBSE board exam pattern, helping students familiarize themselves with the question types, marking scheme, and time management.

Detailed Syllabus for CBSE Class 12 Mathematics

The CBSE Class 12 Mathematics syllabus is divided into several units, each covering specific topics. Here's a comprehensive breakdown:

1. Relations and Functions: Types of relations (reflexive, symmetric, transitive and equivalence relations), One-to-one and onto functions. Inverse Trigonometric Functions: Definition, domain, range, principal value branch, properties of inverse trigonometric functions.
2. Algebra: Matrices: Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew symmetric matrices. Operation on matrices: Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication and scalar multiplication. Non-commutativity of multiplication of matrices and existence of multiplicative inverse. Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists.
3. Determinants: Determinant of a square matrix (up to 3 x 3 matrices), properties of determinants, minors, cofactors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix.
4. Calculus:
   • Continuity and Differentiability: Continuity and Differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit functions. Concept of exponential and logarithmic functions. Derivatives of logarithmic and exponential functions. Logarithmic differentiation. Second order derivatives. Rolle’s and Lagrange’s Mean Value Theorems (without proof) and their geometric interpretation.
   • Applications of Derivatives: Applications of derivatives: rate of change of bodies, increasing/decreasing functions, tangents and normals, maxima and minima (first derivative test and second derivative test) simple problems.
   • Integrals: Integration as inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions and by parts, Evaluation of simple integrals of the following types and problems based on them. Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.
   • Applications of Integrals: Applications in finding the area under simple curves, especially lines, circles/parabolas/ellipses (in standard form only), area between any of the two above said curves (the region should be clearly identifiable).
   • Differential Equations: Definition, order and degree, general and particular solutions of a differential equation. Formation of differential equation whose general solution is given. Solution of differential equations by method of separation of variables, solutions of homogeneous differential equations of first order and first degree. Solutions of linear differential equation of the type: dy/dx + Py = Q, where P and Q are functions of x or constants. dx/dy + Px = Q, where P and Q are functions of y or constants.
5. Vectors and Three Dimensional Geometry:
   • Vector Algebra: Vectors and scalars, magnitude and direction of a vector. Direction cosines and direction ratios of a vector. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Scalar (dot) product of vectors, projection of a vector on a line. Vector (cross) product of vectors. Scalar triple product.
   • Three Dimensional Geometry: Direction cosines and direction ratios of a line joining two points. Cartesian equation and vector equation of a line, skew lines, shortest distance between two lines. Angle between two lines. Cartesian and vector equation of a plane. Angles between (i) two lines, (ii) two planes, (iii) a line and a plane. Distance of a point from a plane.
6. Linear Programming: Introduction, terminology associated with Linear Programming problems (LPP), graphical method of solution for problems in two variables, feasible and infeasible regions, feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).
7. Probability: Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution, mean and variance of random variable. Bernoulli trials and Binomial distribution.

Test Rules

1. The exam duration is 3 hours (180 minutes).
2. The maximum marks are 80.
3. All questions are compulsory; however, internal choice is provided in some questions.
4. The question paper is divided into five sections: A, B, C, D, and E.
5. Section A consists of multiple-choice questions (MCQs) and assertion-reason-based questions.
6. Section B consists of very short answer type questions.
7. Section C consists of short answer type questions.
8. Section D consists of long answer type questions.
9. Section E consists of case study based questions.
10. Use of calculators is strictly prohibited.
11. Students must show all necessary steps and workings clearly.

Scoring and Passing Marks

The CBSE Class 12 Mathematics exam is typically out of 80 marks for the theory paper. The remaining 20 marks are usually for internal assessment/practical work. To pass the subject, a student needs to score a minimum of 33% marks in the aggregate (theory + practicals/internal assessment combined) and often also in the theory paper separately. Each question carries specific marks, usually indicated against it. There is no negative marking for incorrect answers.

Preparation Tips

1. Understand the Syllabus Thoroughly: Go through each topic in the syllabus and ensure you understand the concepts well. Refer to the NCERT textbook as it is the primary resource for the CBSE board exams.
2. Practice Regularly: Mathematics is all about practice. Solve a wide variety of problems from each chapter. Don't just read solutions; try to solve them yourself.
3. Master Formulas and Theorems: Create a formula sheet for quick revision. Understand the derivation and application of key theorems.
4. Solve Previous Year Papers: Practicing past year's question papers will give you an idea of the exam pattern, important topics, and common question types. This also helps in time management.
5. Attempt Mock Tests: Regularly taking full-length mock tests helps simulate exam conditions, identify weak areas, and improve speed and accuracy. Pay attention to case-study questions and their structure.
6. Time Management: During practice and the actual exam, allocate time judiciously to each section and question. Don't spend too much time on a single difficult question.
7. Clear Doubts Promptly: Don't let doubts accumulate. Get them clarified by your teachers or peers immediately.
8. Revision: Consistently revise all topics, especially before the exam. Focus on key concepts and problem-solving techniques.
9. Presentation: In the actual exam, present your solutions clearly and systematically. Show all steps, as marks are often awarded for methodology.

By following these tips and utilizing our comprehensive mock tests, you can significantly enhance your preparation and confidently face the CBSE Class 12 Mathematics Board Examination.