High School · Grade XI
MathematicsSubject Code: ME1107 The Grade XI Mathematics syllabus is organised into thirteen compulsory units . Each unit carries separate marks and together they form a 3-hour examination of 100 marks .
Every unit emphasises: conceptual understanding, procedural fluency, problem solving, reasoning and mathematical communication across algebra, geometry, trigonometry, calculus foundation and probability.
Total Marks: 100 Time: 3 Hours All 13 units are compulsory.
Instructions: Separate marks are assigned to each unit. The detailed break-up is given in the table below, followed by unit-wise learning outcomes and key areas of study.
Sets and their representations - roster and set-builder form. Empty (null) set, singleton set. Finite and infinite sets. Equal and equivalent sets. Subsets, proper subsets; power set. Universal set and complement of a set. Intervals as subsets of ℝ (open, closed, semi-open). Venn diagrams. Union, intersection, disjoint sets and difference of sets. Laws of operations on sets - union, intersection, distributive laws. De Morgan’s laws and properties of complements. Practical problems on union and intersection; counting elements of sets. Ordered pairs and equality of ordered pairs. Cartesian product of sets; number of elements; simple products like ℝ × ℝ. Definition of a relation as a subset of a Cartesian product. Arrow diagrams and pictorial representation of relations. Domain, co-domain and range of a relation. Function as a special type of relation; when a relation is a function. Real-life functional relationships in problem situations. Pictorial and graphical representation of functions. Domain, co-domain and range of a function; even and odd functions. Algebra of functions (sum, difference, product). Real valued functions and their graphs: constant, identity, linear, quadratic, polynomial, rational, modulus, signum, greatest integer. Positive and negative angles. Measuring angles in degrees and radians; conversion between them. Defining trigonometric functions using the unit circle. Signs of trigonometric functions in different quadrants. Values of trigonometric functions at standard angles (0, π/6, π/4, π/3, π/2, etc.). Reciprocal and co-function relationships. Domain and range of trigonometric functions. Trigonometric functions as periodic functions - amplitude, argument, period and graphs. Trigonometric functions of sum and difference of two angles. Identities involving sin 2x, cos 2x, tan 2x, sin 3x, cos 3x, tan 3x. General solution of simple trigonometric equations (sin x = sin a, cos x = cos a, tan x = tan a). Sine and cosine rules and simple applications including area of triangle/parallelogram. Need for complex numbers motivated by unsolved quadratic equations. Imaginary unit ‘i’ and basic concept of imaginary quantities. Standard form of a complex number z = a + ib; real and imaginary parts. Purely real and purely imaginary complex numbers; equality of complex numbers. Addition and subtraction of complex numbers and their properties. Conjugate and modulus of a complex number; basic properties. Multiplication and division of complex numbers; multiplicative inverse. Polar (trigonometric) form of a complex number - modulus and argument. Geometrical representation of complex numbers in the Argand plane. Fundamental theorem of algebra - statement and understanding. Square roots of a complex number. Solving quadratic equations in the complex number system. Cube roots of unity and their properties. De Moivre’s theorem - statement and applications. Concept of linear inequalities. Algebraic solutions of linear inequalities in one variable. Representation of solutions of linear inequalities in one variable on the number line. Simultaneous linear inequalities in one variable and their solution set. Algebraic solutions of linear inequalities in two variables. Graphical solution of linear inequalities in two variables. Systems of linear inequalities in two variables and their graphical solution. Inequalities involving modulus functions. Idea of wavy curve method for higher degree polynomial inequalities expressed as products (x + a)(x + b)… Fundamental principles of counting - addition and multiplication. Factorial n (n!): meaning, notation and computation. Representing products of consecutive numbers using factorial notation. Permutations - basic concept and simple applications. Combinations - basic concept and simple applications. Derivation of basic properties of combinations. Types of permutations: linear, circular, restricted permutations. Permutations with conditions (particular element always included / never included). Permutations of objects not all distinct; permutations with repetition. Pascal’s triangle and patterns of binomial coefficients. History, statement and proof of binomial theorem for positive integral indices. Expanding expressions using the binomial theorem. General term in binomial expansion. Middle term(s) in a binomial expansion for even and odd number of terms. Term from the end (pth term from the end). Simple applications of binomial theorem to algebraic problems. Arithmetic Progressions (A.P.) and Geometric Progressions (G.P.). Recognising and proving whether a sequence is A.P. or G.P. nth term of an A.P. and of a G.P. Finding specific terms of A.P. and G.P. Generating sequences from given recursive relations. Arithmetic mean (A.M.) - definition, finding A.M. and inserting n A.M.s. Geometric mean (G.M.) - definition, finding G.M. and inserting n G.M.s. Sum to n terms of an A.P. Sum to n terms of a G.P. Sum of an infinite G.P. (|r| < 1). Relation between A.M. and G.M. Revision of two-dimensional geometry: distance between two points, area of triangle, section formula, midpoint, centroid, in-centre. Shifting of origin and effect on equation of a curve/line. Slope of a line - from angle of inclination and from coordinates of two points. Condition for parallel and perpendicular lines using slopes. Angle between two lines. Various forms of equation of a line: lines parallel to axes, point-slope form, slope-intercept form, two-point form, intercept form, normal form. Using different forms of the line to find missing parameters. General equation of a line and reduction to standard forms. Family of lines passing through intersection of two lines (l₁ + k l₂ = 0). Distance of a point from a line. Distance between two parallel lines. Introduction to sections of a cone - circle, parabola, ellipse, hyperbola. Circle: standard form, centre (h, k), radius r; circle with centre at origin; circle from endpoints of diameter. General form of the equation of a circle. Parabola: standard forms (right/left/upward/downward); axis, vertex, focus, directrix, latus rectum. General form of parabola and reduction to standard form; finding key elements and equation under given conditions. Ellipse: standard forms (horizontal and vertical); centre, vertices, axes, foci, directrices, eccentricity, latus rectum. General form of ellipse and reduction to standard form; finding key elements and equation. Hyperbola: standard form and conjugate hyperbola; centre, vertices, foci, axes, directrices, eccentricity, latus rectum. General form of hyperbola and reduction to standard form; finding key elements and equation. Simple applications involving parabola, ellipse and hyperbola. Coordinate axes and coordinate planes in three dimensions. Coordinates of a point in space. Distance between two points in 3D. Section formula in three dimensions. Direction cosines and direction ratios of a line. Angle between two lines in space (basic ideas). Limit of a function - intuitive idea. Basic (fundamental) results on limits and their applications. Standard limits (simple algebraic and trigonometric forms). Trigonometric limits (e.g. sin x / x types, etc.). Infinite limits and one-sided limits (left-hand and right-hand). Concept of continuity of a real-valued function at a point and on an interval. Random experiment, outcomes and sample space (set representation). Events as subsets of sample space; ‘or’, ‘and’, and ‘not’ events. Impossible, sure, simple, compound, mutually exclusive and exhaustive events. Independent events, equally likely events and complementary events (idea). Axiomatic (set-theoretic) approach to probability. Probability of an event and its complement. Odds in favour of and odds against an event. 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