UK Board Class 11 Mathematics Syllabus

1. समुच्चय
2. संबंध एवं फलन
3. त्रिकोणमितीय फलन
4. गणितीय आगमन का सिद्धांत
5. सम्मिश्र संख्याएँ और द्विघातीय समीकरण
6. रैखिक असामिकाएँ
7. क्रमचय और संचय
8. द्विपद प्रमेय
9. अनुक्रम तथा श्रेणी
10. सरल रेखाएँ
11. शंकु परिच्छेद
12. त्रिविमीय ज्यामिति का परिचय
13. सीमा और अवकलज
14. गणितीय विवेचन
15. सांख्यिकी
16. प्रायिकता

1. Sets
2. Relations and Functions
3. Trigonometric Functions
4. Principle of Mathematical Induction
5. Complex Numbers and Quadratic Equations
6. Linear Inequalities
7. Permutations and Combinations
8. Binomial Theorem
9. Sequences and Series
10. Straight Lines
11. Conic Sections
12. Introduction to Three Dimensional Geometry
13. Limits and Derivatives
14. Mathematical Reasoning
15. Statistics
16. Probability

Objectives For UK Board Class 11 Mathematics Syllabus

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.
• Feel the flow of reasons while proving a result or solving a problem.
• to apply the knowledge and skills acquired to solve problems and wherever possible, by more than one method.
• Develop positive attitude to think, analyze and articulate logically.
• Developing 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 environment, observance of small family norms, removal of social barriers, elimination of gender biases.
• to develop reverence and respect towards great Mathematicians for their contributions to the field of Mathematics.

COURSE STRUCTURE
UK Board Class 11 Mathematics Syllabus

One Paper Total Period–240 [35 Minutes Each] Three Hours Max Marks: 100

Unit-I: Sets and Functions

1. Sets (20) Periods
   Sets and their representations. Empty set. Finite and Infinite sets. Equal sets. Subsets. Subsets of a set of real numbers especially intervals (with notations). Power set. Universal set. Venn diagrams. Union and Intersection of sets. Difference of sets. Complement of a set. Properties of Complement.
2. Relations & Functions (20) Periods
   Ordered pairs. Cartesian product of sets. Number of elements in the Cartesian product of two finite sets. Cartesian product of the set of reals with itself (upto R x R x R). Definition of relation, pictorial diagrams, domain, co-domain and range of a relation. Function as a special type of relation. Pictorial representation of a function, domain, co-domain and range of a function. Real valued functions, domain and range of these functions, constant, identity, polynomial, rational, modulus, signum, exponential, logarithmic and greatest integer functions, with their graphs. Sum, difference, product and quotients of functions.
3. Trigonometric Functions (20) Periods
   Positive and negative angles. Measuring angles in radians and in degrees and conversion from one measure to another. Definition of trigonometric functions with the help of unit circle. Truth of the identity sin²x + cos²x = 1, for all x. Signs of trigonometric functions. Domain and range of trigonometric functions and their graphs. Expressing sin (x±y) and cos (x±y) in terms of sinx, siny, cosx & cosy and their simple applications. Deducing identities like the following:

Unit-II: Algebra

1. Principle of Mathematical Induction (10) Periods
   Process of the proof by induction, motivating the application of the method by looking at natural numbers as the least inductive subset of real numbers. The principle of mathematical induction and simple applications.
2. Complex Numbers and Quadratic Equations (15) Periods
   Need for complex numbers, especially −1‾‾‾√−1 , to be motivated by inability to solve some of the quardratic equations. Algebraic properties of complex numbers. Argand plane and polar representation of complex numbers. Statement of Fundamental Theorem of Algebra, solution of quadratic equations (with real coefficients) in the complex number system. Square root of a complex number.
3. Linear Inequalities (15) Periods
   Linear inequalities. Algebraic solutions of linear inequalities in one variable and their representation on the number line. Graphical solution of linear inequalities in two variables. Graphical method of finding a solution of system of linear inequalities in two variables.
4. Permutations and Combinations (10) Periods
   Fundamental principle of counting. Factorial n. (n!) Permutations and combinations, derivation of formulae for n_pr and n_cr and their connections, simple applications.
5. Binomial Theorem (10) Periods
   History, statement and proof of the binomial theorem for positive integral indices. Pascal’s triangle, General and middle term in binomial expansion, simple applications.
6. Sequence and Series (10) Periods
   Sequence and Series. Arithmetic Progression (A. P.). Arithmetic Mean (A.M.) Geometric Progression (G.P.), general term of a G.P., sum of n terms of a G.P., infinite G.P. and its sum, geometric mean (G.M.), relation between A.M. and G.M. Formulae for the following special sums

Unit-III: Coordinate Geometry

1. Straight Lines (10) Periods
   Brief recall of two dimensional geometry from earlier classes. Shifting of origin. Slope of a line and angle between two lines. Various forms of equations of a line: parallel to axis, point -slope form, slopeintercept form, two-point form, intercept form and normal form. General equation of a line. Equation of family of lines passing through the point of intersection of two lines. Distance of a point from a line.
2. Conic Sections (20) Periods
   Sections of a cone: circles, ellipse, parabola, hyperbola, a point, a straight line and a pair of intersecting lines as a degenerated case of a conic section. Standard equations and simple properties of parabola, ellipse and hyperbola. Standard equation of a circle.
3. Introduction to Three-dimensional Geometry (10) Periods
   Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance between two points and section formula.

Unit-IV: Calculus

1. Limits and Derivatives (30) Periods
   Derivative introduced as rate of change both as that of distance function and geometrically. Intuitive idea of limit. Limits of polynomials and rational functions trigonometric, exponential and logarithmic functions. Definition of derivative relate it to scope of tangent of the curve, derivative of sum, difference, product and quotient of functions. Derivatives of polynomial and trigonometric functions.

Unit-V: Mathematical Reasoning

1. Mathematical Reasoning (10) Periods
   Mathematically acceptable statements. Connecting words/ phrases – consolidating the understanding of “if and only if (necessary and sufficient) condition”, “implies”, “and/or”, “implied by”, “and”, “or”, “there exists” and their use through variety of examples related to real life and Mathema tics. Validating the statements involving the connecting words, difference among contradiction, converse and contrapositive.

Unit-VI: Statistics and Probability

1. Statistics (15) Periods
   Measures of Dispersion: Range, Mean deviation, variance and standard deviation of ungrouped/grouped data. Analysis of frequency distributions with equal means but different variances.
2. Probability (15) Periods
   Random experiments; outcomes, sample spaces (set representation). Events; occurrence of events, ‘not’, ‘and’ and ‘or’ events, exhaustive events, mutually exclusive events, Axiomatic (set theoretic) probability, connections with other theories of earlier classes. Probability of an event, probability of ‘not’, ‘and’ and ‘or’ events.

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 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.

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