NEB Class 11 Mathematics Curriculum

Maths (Mat. 401)
Syllabus

Full marks: 75 (Pass marks: 24)

Course Contents:

Unit 1: Algebra

1. Logic and Set: introduction of Logic, statements, logical connectives, truth tables, basic laws of logic, theorems based on set operations.  
2. Real numbers: field axioms, order axioms, interval, absolute value, geometric representation of real numbers. 
3. Function: Concept of cell cycle, types of cell division (amitosis, mitosis and meiosis) and significances
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 , Trigonometric, exponential, logarithmic function (simple cases only)
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.
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)
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 

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

Unit 3: Analytic geometry

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.
2. Circle: Condition of tangency of a line at a point to the circle, Tangent and normal to a circle.
3. Conic section: Standard equation of parabola, equations of tangent and normal to a parabola at a given point.

Unit 4: Vectors

1. Vectors: collinear and noncollinear vectors, coplanar and non-coplanar vectors, linear combination of vectors,
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 and Probability

1. Measure of Dispersion: introduction, standard deviation), variance, coefficient of variation, Skewness (Karl Pearson and Bowley)
2. Probability: independent cases, mathematical and empirical definition of probability, two basic laws of probability(without proof).

 Unit 6: Calculus

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.
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.
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

1. Linear programming Problems: linear programming problems(LPP), solution of LPP by simplex method (two variables)
2. Numerical computation: Characteristics of numerical computation, accuracy, rate of convergence, numerical stability, efficiency

 Unit 8: Mechanics Or Mathematics for Economics and Finance 

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.
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
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