ISC Mathematics Class 11 Syllabus
The syllabus is divided into three sections: A, B and C. Section A is compulsory. You have a choice of attempting questions from either Section B or Section C. There is one paper of three hours duration of 80 marks.
1. Sets and Functions
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. Practical problems on union and intersection of two and three sets. Difference of sets. Complement of a set. Properties of Complement of Sets.
(ii) Relations & Functions
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.
Function as a type of mapping, types of functions (one to one, many to one, onto, into) 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 quotient of functions.
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.
Identities related to sin 2x, cos2x, tan 2x, sin3x, cos3x and tan3x. General solution of trigonometric equations of the type siny = sina, cosy = cosa and tany = tana. Properties of triangles (proof and simple applications of sine rule cosine rule and area of triangle).
(i) Principle of Mathematical Induction
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.
(ii) Complex Numbers
Introduction of complex numbers and their representation, Algebraic properties of complex numbers. Argand plane and polar representation of complex numbers. Square root of a complex number. Cube root of unity.
(iii) Quadratic Equations
Statement of Fundamental Theorem of Algebra, solution of quadratic equations (with real coefficients).
(iv) Permutations and Combinations
Fundamental principle of counting. Factorial n. (n!) Permutations and combinations, derivation of formulae for nPr and nCr and their connections, simple application.
(v) Binomial Theorem
History, statement and proof of the binomial theorem for positive integral indices. Pascal's triangle, General and middle term in binomial expansion, simple applications.
(vi) Sequence and Series
Sequence and Series. Arithmetic Progression (A. P.). Arithmetic Mean (A.M.) Geometric Progression (G.P.), general term of a G.P., sum of first 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.
3. Coordinate Geometry
(i) Straight Lines
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, slope intercept 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.
Equations of a circle in:
- Standard form.
- Diameter form.
- General form.
- Parametric form.
Given the equation of a circle, to find the centre and the radius.
Finding the equation of a circle.
- Given three non collinear points.
- Given other sufficient data for example centre is (h, k) and it lies on a line and two points on the circle are given, etc.
- Condition for tangency
- Equation of a tangent to a circle
(i) Limits and Derivatives
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.
5. Statistics and Probability
Measures of dispersion: range, mean deviation, variance and standard deviation of ungrouped/grouped data. Analysis of frequency distributions with equal means but different variances.
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 studied in earlier classes. Probability of an event, probability of 'not', 'and' and 'or' events.
6. Conic Section
Sections of a cone, 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.
7. Introduction to three-dimensional Geometry
Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance between two points and section formula.
- As an extension of 2-D
- Distance formula.
- Section and midpoint form
8. Mathematical Reasoning
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 the Mathematics and real life.
Validating the statements involving the connecting words, Difference between contradiction, converse and contrapositive.
- Combined mean and standard deviation.
- The Median, Quartiles, Deciles, Percentiles and Mode of grouped and ungrouped data
10. Correlation Analysis
- Definition and meaning of covariance.
- Coefficient of Correlation by Karl Pearson.
- Rank correlation by Spearman's (Correction included).
11. Index Numbers and Moving Averages
(i) Index Numbers
- Price index or price relative.
- Simple aggregate method.
- Weighted aggregate method.
- Simple average of price relatives.
- Weighted average of price relatives (cost of living index, consumer price index).
(ii) Moving Averages
- Meaning and purpose of the moving averages.
- Calculation of moving averages with the given periodicity and plotting them on a graph.
- If the period is even, then the centered moving average is to be found out and plotted.