Note Mandir

Subject

Mathematics

Structured Mathematics resources featuring concept-based notes, important formulas, solved examples, and practice problems designed to improve analytical thinking and ensure strong exam performance.

Mathematics

NEW SYLLABUS (NEB)

Teaching Hours: 120
Full Marks: 100(75T + 25P)
Credit hrs: 5
Pass Marks: 27T + 8P
1. Algebra
33 + 11 Hrs

1.1 Permutation and combination: Basic principle of counting, Permutation of (a) set of objects all different (b) set of objects not all different (c) circular arrangement (d) repeated use of the same objects, Combination of things all different, Properties of combination.

1.2 Binomial Theorem: Binomial theorem for a positive integer, general term, Binomial coefficient, Binomial theorem for any index (without proof), application to approximation, Euler’s number, Expansion of er, at and log(1+x) (without proof)

1.3 Complex numbers: Polar form of complex numbers, De Moivre’s theorem and its application in finding the roots of a complex number, properties of cube roots of unity. Euler’s formula.

1.4 Sequence and series: Sum of finite natural numbers, sum of squares of first n-natural numbers, Sum of cubes of first n-natural numbers, principle of mathematical Induction.

1.5 Matrix based system of linear equation: Solution of a system of linear equations by Cramer’s rule and matrix method (row-equivalent and inverse) up to three variables.

2. Trigonometry
9 + 3 Hrs

2.1: Properties of a triangle (Sine law, Cosine law, tangent law, Projection laws, Half angle laws)

2.2: Solution of triangle (simple cases)

3. Analytic Geometry
15 + 5 Hrs
3.1 Conic Section: Condition of tangency of a line at a point to the circle, Tangent and normal to a circle, Standard equation of parabola, equations of tangent and normal to a parabola at a given point, Standard equations of Ellipse and hyperbola.
4. Vectors
9 + 3 Hrs
4.1: Product of Vectors; Scalar product of two vectors, angle between two vectors, geometric interpretation of scalar product, properties of scalar product, application of scalar product in geometry and trigonometry, vector product of two vectors, geometrical interpretation of vector product, properties of vector product, application of vector product in geometry and trigonometry.
5. Statistics & Probability,
9 + 3 Hrs
5.1: Correlation and Regression: Correlation, nature of correlation, correlation coefficient by Karl Pearson’s method, interpretation of correlation coefficient, properties of correlation coefficient (without proof), rank correlation (only elementary concept), regression equation, regression line of y on x and x on y.
5.2 Probability: Dependent cases, conditional probability (without proof).
6. Calculas
36 + 12 Hrs

6.1 Derivatives: Rules for differentiating hyperbolic function and inverse hyperbolic function, L’Hospital’s rule (0/0, ∞/∞), differentials, tangent and normal, derivative as rate of measure

6.2 Anit-derivatives: Anti- derivatives of standard integrals, integrals reducible to standard forms, integrals of rational function.

6.3 Differential equations: Differential equation and its order, degree, differential equations of first order and first degree, differential equations with separable variables, homogenous, linear and exact differential equations.

7. Computational Methods
9 + 3 Hrs

7.1: System of linear equations: Gauss Elimination Method, Gauss Seidel Method

7.2: Linear programming problems (LPP): Simplex method (two variables only)

Or, Mechanics

7.1 Statics: Triangle law of forces and Lami’s theorem.

7.2 Dynamics: Newton’s laws of motion and projectile.