OVERVIEW:
The National Examination Board (NEB) of Nepal has included the study of Derivatives in the Class 12 syllabus of Mathematics. Derivatives are a fundamental concept in Calculus and play a crucial role in various fields such as Physics, Economics, and Engineering.
The syllabus for Class 12 Mathematics consists of the following topics in the Derivatives module:
Limits and Continuity: Definition of limit, standard limits, evaluation of limits using algebraic methods, continuity of a function at a point, intermediate value theorem.
Differentiation: Derivative of a function, differentiation rules (power rule, product rule, quotient rule, chain rule), derivative of trigonometric functions, implicit differentiation, logarithmic differentiation.
Applications of Derivatives: Rate of change and tangents, maxima and minima, optimization problems, curve sketching, mean value theorem, L'Hôpital's rule.
Integration: Antiderivatives, indefinite integrals, definite integrals, integration by substitution, integration by partial fraction, integration by parts.
Applications of Integrals: Area under the curve, definite integral as the limit of a sum, finding area using definite integrals, finding length of a curve.
Differential Equations: First order differential equations, solution of differential equations using separable variables, linear differential equations, homogeneous differential equations.
The syllabus covers the fundamentals of derivatives and integrals and their applications in various fields of Mathematics, Physics, and Economics. The topics are designed to provide a comprehensive understanding of the concept and develop the problem-solving skills of students.
The NEB conducts the final examination for Class 12 Mathematics, where the students are expected to demonstrate their knowledge and understanding of the topics covered in the syllabus. The examination tests the ability of the students to apply the concepts in real-life situations and solve practical problems.
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