UK Board Class 12 Mathematics Syllabus

The Syllabus in the subject of Mathematics has undergone changes from time to time in
accordance with growth of the subject and emerging needs of the society. Senior Secondary
the stage is a launching stage from where the students go either for higher academic education in Mathematics or for professional courses like Engineering, Physical and Bioscience, Commerce or Computer Applications.

The present revised syllabus has been designed in accordance with National Curriculum Framework 2005 and as per guidelines are given in Focus Group on Teaching of Mathematics 2005 which is to meet the emerging needs of all categories of students. Motivating the topics from real life situations and other subject areas, greater emphasis has been laid on the application of various concepts.

Objectives

The broad objectives of teaching Mathematics at senior school stage intend to help the students To:

• Acquire knowledge and critical understanding, particularly by way of motivation and visualization, of basic concepts, terms, principles, symbols, and mastery of underlying processes and skills.
• to feel the flow of reasons while proving a result or solving a problem.
• Apply the knowledge and skills acquired to solve problems and wherever possible, by more than one method.
• Develop a positive attitude to think, analyze and articulate logically.
• Develop an interest in the subject by participating in related competitions.
• Acquaint students with different aspects of Mathematics used in daily life.
• Develop an interest in students to study Mathematics as a discipline.
• Developing awareness of the need for national integration, protection of the environment, observance of small family norms, removal of social barriers, elimination of gender biases.
• Develop reverence and respect towards great Mathematicians for their contributions to the field of Mathematics.

UK Board Class 12 Mathematics Syllabus

One Paper Time: 3 hrs.
Max Marks. 100

Unit-I: Relations and Functions

1. Relations and Functions 15 Periods
   Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions, composite functions, an inverse of a function. Binary operations.
2. Inverse Trigonometric Functions 15 Periods
   Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions.

Unit-II: Algebra

1. Matrices 25 Periods
   The concept, notation, order, equality, types of matrices, zero and identity matrix, the 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 non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2).The concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).
2. Determinants 25 Periods
   The 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 the inverse of a matrix.

Unit-III: Calculus

1. Continuity and Differentiability 20 Periods
   Continuity and differentiability, the derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit functions. The concept of exponential and logarithmic functions.
   Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of functions expressed in parametric forms. Second order derivatives. Rolle’s and Lagrange’s Mean Value Theorems (without proof) and their geometric interpretation.
2. Applications of Derivatives 10 Periods
   Applications of derivatives: the rate of change of bodies, increasing/decreasing functions, tangents and normals, use of derivatives in approximation, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations).
3. Integrals 20 Periods
   Integration as inverse process of differentiation. Integration ofavariety of functions by substitution, by partial fractions and by parts, Evaluation of simple integrals of the following types and problems based on them.
   ∫dxx2±a2,∫dxx2±a2√,∫dxa2−x2√,∫dxax2+bx+c,∫dxax2+bx+c√∫dxx2±a2,∫dxx2±a2,∫dxa2−x2,∫dxax2+bx+c,∫dxax2+bx+c
   ∫px+qax2+bx+cdx,∫px+qax2+bx+c√dx,∫a2±x2‾‾‾‾‾‾‾√dx,∫x2−a2‾‾‾‾‾‾‾√dx∫px+qax2+bx+cdx,∫px+qax2+bx+cdx,∫a2±x2dx,∫x2−a2dx
   ∫ax2+bx+c‾‾‾‾‾‾‾‾‾‾‾‾√dx,∫(px+q)ax2+bx+c‾‾‾‾‾‾‾‾‾‾‾‾√dx∫ax2+bx+cdx,∫(px+q)ax2+bx+cdx
   Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.

Unit-IV: Vectors and Three-Dimensional Geometry

1. Vectors 15 Periods
   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, the addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Definition, Geometrical Interpretation, properties, and application of scalar (dot) product of vectors, vector (cross) product of vectors, a scalar triple product of vectors.
2. Three – dimensional Geometry 15 Periods
   Direction cosines and direction ratios of a line joining two points.Cartesian equation and vector equation of a line, coplanar and skew lines, the shortest distance between two lines. Cartesian and vector equation of a plane. The angle between (i) two lines, (ii) two planes, (iii) a line and a plane. The distance of a point from a plane.

Unit-V: Linear Programming

1. Linear Programming 20 Periods
   Introduction, related terminology such as constraints, objective function, optimization, different types of linear programming (L.P.) problems, mathematical formulation of L.P. problems, graphical method of solution for problems in two variables, feasible and infeasible regions (bounded or unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).

Unit-VI: Probability

1. Probability 30 Periods
   Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, Random variable, and its probability distribution, mean and variance of the random variable. Repeated independent (Bernoulli) trials and Binomial distribution.

Prescribed Books For UK Board Class 12 Mathematics Syllabus

1. Maths Textbook for Class XI, NCERT Publications
2. Mathematics Part I – Textbook for Class XII, NCERT Publication
3. Maths Part II – Textbook for Class XII, NCERT Publication
4. Mathematics Exemplar Problem for Class XI, Published by NCERT
5. Mathematics Exemplar Problem for Class XII, Published by

QUESTION WISE BREAK UP

1. No chapter wise weightage. Care to be taken to cover all the chapters.
2. Suitable internal variations may be made for generating various templates keeping the overall weightage to the different form of questions and typology of questions same.

Choice(s):
There will be no overall choice in the question paper.
However, 30% internal choices will be given in 4 marks and 6 marks questions.