# Mathematics - XI Syllabus

## Unit 1: Algebra – 32 Working Hours

1.1 Logic and Set:

introduction of Logic, statements, logical connectives, truth tables, basic laws of logic, theorems based on set operations.

1.2 Real numbers:

field axioms, order axioms, interval, absolute value, geometric representation of real numbers.

1.3 Function:

Review, domain & range of a function, Inverse function, composite function, functions of special type, algebraic (linear, quadratic & cubic), Trigonometric, exponential, logarithmic)

1.4 Curve sketching:

odd and even functions, periodicity of a function, symmetry (about origin, x-and y-axis), monotonicity of a function, sketching graphs of polynomials and some rational functions
($\frac{a}{x}, \frac{x^2-a^2}{x-a}, \frac{a}{x+a}, ax^2+bx+c, ax^3$), Trigonometric, exponential, logarithmic function (simple cases only)

1.5 Sequence and series:

arithmetic, geometric, harmonic sequences and series and their properties A.M, G.M, H.M and their relations, sum of infinite geometric series.

1.6 Matrices and determinants:

Transpose of a matrix and its properties,  Minors and cofactors, Adjoint, Inverse matrix, Determinant of a square matrix, Properties of determinants (without proof)

1.7 Complex number:

definition imaginary unit, algebra of complex numbers, geometric representation, absolute value (Modulus) and conjugate of a complex numbers and their properties, square root of a complex number, polar form of complex numbers.

## Unit 2: Trigonometry – 8 Working Hours

2.1 Properties of a triangle (Sine law, Cosine law, tangent law, Projection laws, Half angle laws).
2.2 Solution of triangle(simple cases)

## Unit 3: Analytic Geometry – 14 Working Hours

3.1 Straight Line:

length of perpendicular from a given point to a given line. Bisectors of the angles between two straight lines.
Pair of straight lines: General equation of second degree in x and y, condition for representing a pair of lines. Homogenous second-degree equation in x and y. angle between pair of lines. Bisectors of the angles between pair of  lines.

3.2 Circle:

Condition of tangency of a line at a point to the circle, Tangent and normal to a circle.

3.3 Conic section:

Standard equation of parabola, equations of tangent and normal to a parabola at a given point.

## Unit 4: Vectors – 8 Working Hours

4.1 Vectors:

collinear and non collinear vectors, coplanar and noncoplanar vectors, linear combination of vectors,

4.2 Product of vectors:
scalar product of two vectors, angle between two vectors, geometric interpretation of scalar product, properties of scalar product, condition of perpendicularity.

## Unit 5: Statistics & Probability – 10 Working Hours

5.1 Measure of Dispersion:
introduction, standard deviation), variance, coefficient of variation, Skewness (Karl Pearson and Bowley)

5.2 Probability:
independent cases, mathematical and empirical definition of probability, two basic laws of probability(without proof).

## Unit 6: Calculus – 32 Teaching Hours

6.1 Limits and continuity:

limits of a function, indeterminate forms. algebraic properties of limits (without proof), Basic theorems on limits of algebraic, trigonometric, exponential and logarithmic functions, continuity of a function, types of discontinuity, graphs of discontinuous function.
6.2 Derivatives:
derivative of a function, derivatives of algebraic, trigonometric, exponential and logarithmic functions by definition (simple forms), rules of differentiation. derivatives of parametric and implicit functions, higher order derivatives, geometric interpretation of derivative, monotonicity of a function, interval of monotonicity, extreme of a function, concavity, points of inflection, derivative as rate of measure.
6.3 Anti-derivatives:
anti-derivative. integration using basic integrals, integration by substitution and by parts methods, the definite integral, the definite integral as an area under the given curve, area between two curves.

## Unit 7: Computational Methods – 10 Working Hours

7.1 Linear programming Problems:

linear programming problems(LPP), solution of LPP by simplex method (two variables)

7.2 Numerical computation
Characteristics of numerical computation, accuracy, rate of convergence, numerical stability, efficiency

## 8. Mechanics Or Mathematics for Economics and Finance – 12 Working Hours

8.1 Statics:

Forces and resultant forces, parallelogram law of forces, composition and resolution of forces, Resultant of coplanar forces acting on a point, Triangle law of forces and Lami’s theorem.

8.2 Dynamics:

Motion of particle in a straight line, Motion with uniform acceleration, motion under the gravity, motion down a smooth inclined plane. The concepts and theorem restated and formulated as application of calculus
8.3 Mathematics for economics and finance:

Mathematical Models and Functions, Demand and supply, Cost, Revenue, and profit functions, Elasticity of demand, supply and income , Budget and Cost Constraints, Equilibrium and break even.