Class 12 Mathematics Curriculum
12 science NEB Curriculum Mathematics
NEB New Curriculum
Updated on: Jan 20,
2024
Compulsory Mathematics (Mat. 402)
Syllabus
Full marks: 75 (Pass marks: 24)
Course Contents:
Unit 1: Algebra
- Permutation and combination
- 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
- Binomial Theorem
- Binomial theorem for a
positive integral index, general term. Binomial coefficient, Binomial
theorem for any index (without proof), application to approximation.
Euler's number. Expansion of 𝑒x, 𝑎x
and log(1+x) (without proof)
- Elementary Group Theory
- Binary operation,
Binary operation on sets of integers and their properties, Definition of
a group, Finite and infinite groups. Uniqueness of identity, Uniqueness
of inverse, Cancelation law, Abelian group.
- 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.
- Quadratic equation
- Nature and roots of a
quadratic equation, Relation between roots and coefficient. Formation of
a quadratic equation, Symmetric roots, one or both roots common.
- Mathematical induction
- Sum of finite natural
numbers, sum of squares of first n-natural numbers, Sum of cubes of first
n- natural numbers, Intuition and induction, principle of mathematical
induction.
- Matrix based system of linear equation
- Consistency of system
of linear equations, Solution of a system of linear equations by Cramer's
rule. Matrix method (row- equivalent and Inverse) up to three variables.
Unit 2: Trigonometry
- Inverse circular functions.
- Trigonometric equations and general values
Unit 3: Analytic geometry
- Conic section
- Standard equations of
Ellipse and hyperbola.
- Coordinates in space
- direction cosines and
ratios of a line general equation of a plane, equation of a plane in
intercept and normal form, plane through 3 given points, plane through
the intersection of two given planes, parallel and perpendicular planes,
angle between two planes, distance of a point from a plane.
Unit 4: Vectors
- Product of Vectors
- vector product of two
vectors, geometrical interpretation of vector product, properties of
vector product, application of vector product in plane trigonometry.
- Scalar triple Product
- introduction of scalar
triple product
Unit 5: Statistics and Probability
- 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 by Spearman, regression
equation, regression line of y on x and x on y.
- Probability
- Dependent cases,
conditional probability (without proof), binomial distribution, mean and
standard deviation of binomial distribution (without proof).
Unit 6: Calculus
- Derivatives
- derivative of inverse
trigonometric, exponential and logarithmic function by definition,
relationship between continuity and differentiability, rules for
differentiating hyperbolic function and inverse hyperbolic function,
L’Hospital's rule (0/0, ∞/∞), differentials, tangent and normal,
geometrical interpretation and application of Rolle’s theorem and mean
value theorem.
- Anti-derivatives
- antiderivatives,
standard integrals, integrals reducible to standard forms, integrals of
rational function.
- 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.
Unit 7: Computational method
- Computing Roots
- Approximation &
error in computation of roots in nonlinear equation, Algebraic and
transcendental equations & their solution by bisection and Newton-
Raphson Methods
- System of linear equations
- Gauss elimination
method, Gauss- Seidal method, Ill conditioned systems.
- Numerical integration
- Trapezoidal and
Simpson's rules, estimation of errors.
Unit 8: Mathematics for economics and finance:
- Statics
- Resultant of like and
unlike parallel forces.
- Dynamics
- Newton's laws of
motion and projectile.
- Mathematics for economics and finance
- Consumer and Producer
Surplus, Quadratic functions in Economics, Input-Output analysis,
Dynamics of market price, Difference equations, The Cobweb model, Lagged
Keynesian macroeconomic model.
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