This course NEB Mathematics Syllabus deals with the fundamentals of advanced mathematical concepts. It also tries to consolidate the concepts and skills learned in Mathematics Syllabus courses at the school level. It is desirable at the end of each unit sufficient related problems be solved.
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Grade XI NEB Syllabus – Mathematics Syllabus
Mathematics
Grade: XI
Full Marks: 100
Teaching hours: 150
I. Introduction of NEB Mathematics Syllabus
This course deals with the fundamentals of advanced mathematical concepts. It also tries to consolidate the concepts and skills learned in Mathematics Syllabus courses at the school level. It is desirable at the end of each unit sufficient related problems be solved.
II. Specific Objectives of NEB Mathematics Syllabus
On completion of this Mathematics Syllabus is students will be able to:
1. use principles of elementary logic to find the validity of the statement,
2. state field and order axioms of the real number system;
3. define functions and illustrate them graphically;
4. sketch and curves;
5. use trigonometrical relations to find general values, understand inverse circular functions and their properties and to find property & solution of the triangle;
6. state properties of A.S, G.S., and H.S.Understand infinite series and use method of mathematical induction to establish the result.
7. define transpose, adjoint and the inverse of a matrix, state properties of determinants;
8. use matrix and determinant to solve a system of linear equations;
9. explain the idea of a complex number, verify their properties, prove De-moivre’s theorem and use it;
10. define polynomial equations, establish fundamental theorem of algebra and quadratic equation, and find the relation between roots and coefficients of a quadratic polynomials;
11. define straight lines, pair of lines in terms of coordinates and establish their properties;
12. define circle in terms of coordinates and establish their properties;
13. define limit of a function, establish properties of limits;
14. define continuity of a function using the concept of limit;
15. define a derivative of a function and give its geometrical interpretation as the rate of change;
16. use derivative to determine the nature of the function and determine the maxima and minima of a function and apply differentiation to find tangent& normal, increasing& decreasing function;
17. define antiderivative as an inverse process of derivative and use various methods of integration; and
18. define integration as the area of the sum, and apply definite integral to find the area between the curves.
III. Course Contents of NEB Mathematics Syllabus
Unit 1. Sets, Real Number System and Logic 10 hrs
Sets:
Sets and set operations, theorems based on set operations.
Real Number System:
Real numbers, field axioms, order axioms, interval, absolute value, a geometrical representation of the real numbers.
Logic:
Introduction, statements, Logical Connectives, Truth tables, Basic laws of logic
Unit 2: Relations, Functions, and Graphs 12 hrs
Relations:
Ordered pair, Cartesian product, geometrical representation of the Cartesian product, Relation, Domain and range of a relation, Inverse of a relation.
Functions:
Definitions, Domain, and range of a function, functions defined as mappings, inverse function, composite function, functions of special type (Identity, constant, absolute value, greatest integer), Algebraic (linear, quadratic and cubic), Trigonometric, exponential logarithmic functions and their graphs.
Unit 3: Curve Sketching 10 hrs
Odd and even functions, periodicity of a function, symmetry (about x-axis, y-axis, and origin) of elementary functions, monotonicity of a function, Sketching graphs of polynomial functions,,, x2, x3), Trigonometric, exponential, logarithmic functions (simple cases only)
Unit 4: Trigonometry 10 hrs
Inverse circular functions, Trigonometric equations and general values, properties of a triangle(sine law, Cosine law, tangent law, projection laws, half-angle law)s, the area of a triangle. Solution of a triangle (simple cases)
Unit 5: Sequence and Series, and Mathematical Induction 12 hrs Sequence and series:
Sequence and series, type of sequences and series (Arithmetic, Geometric, Harmonic), Properties of Arithmetic, Geometric, and Harmonic sequences, A.M, G.M., and H.M, Relation among A.M., G.M. and H.M. sum of infinite geometric series.
Mathematical Induction:
Sum of finite natural numbers, the sum of squares of first n-natural numbers, the sum of cubes of first natural numbers. Intuition and introduction, the principle of mathematical induction.
Unit 6: Matrices and Determinants 8 hrs
Matrices and operation on matrices (review), Transpose of matrix and its properties, Minors and Cofactors, Adjoint, Inverse matrix. The determinant of a square matrix, properties of determinants(without proof) up to 3×3.
Unit 7: System of Linear equations 8 hrs
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 8: Complex Number 12 hrs
Definition of a complex number, Imaginary unit, Algebra of complex numbers, Geometric representation of a complex number, Conjugate and absolute value (Modulus) of complex numbers and their properties, Square root of a complex number, Polar form of a complex number, product and Quotient of complex numbers. De Moivre’s theorem and its application in finding the roots of a complex number, properties of cube roots of unity.
Unit 9: Polynomial Equations 8 hrs
Polynomial function and polynomial equations, Fundamental the theorem of algebra (without proof), Quadratic equation Nature and roots of a quadratic equation, Relation between roots and coefficients, Formation of quadratic equation, Symmetric roots, one or both roots common.
Unit 10 Co-ordinate Geometry 12 hrs
Straight-line:
Review of various forms of the equation of straight lines, Angle between two straight lines, condition for parallelism and perpendicularity, length of the perpendicular from a given point to a given line, Bisectors of the angles between two straight lines.
Pair of lines:
General equation of second degree in x and y, condition for representing a pair of lines, Homogeneous second-degree equation in x and y, The angle between pair of lines, Bisectors of the angles between pair of lines.
Unit 11: Circle 10 hrs
Equation of a circle in various forms(Centre at origin, center at any point, general equation of a circle, a circle with a given diameter), Condition of Tangency of a line at a point to the circle, Tangent and normal to a circle.
Unit 12: Limits and Continuity 10 hrs
Limits of function, Indeterminate forms, Algebraic properties of limits(without proof), Theorem on limits of algebraic, Trigonometric, Exponential and logarithmic functions
sin 1 log 1
lim , lim sin , lim , lim
→ → → →
Continuity of a function, Types of discontinuity, Graph of discontinuous function.
Unit 13: The Derivatives 8 hrs
A 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.
Unit 14: Applications of derivatives 12 hrs
Geometric interpretation of the derivative, Monotonicity of a function, The interval of monotonicity, Extrema of a function, Concavity, points of inflection, derivatives as rate measure.
Unit 15: Antiderivatives and its applications 10 hrs
Antiderivative, Integration using basic integrals, Integration by substitution and by parts method, the definite integral, The definite integral as an area under the given curve, Area between two curves.
IV. Evaluation Scheme of NEB Mathematics
No. of questions
|
Marks
|
Total
|
Remarks
|
15
|
2
|
30
|
covering all units
|
10
|
4
|
40
|
with for OR questions from the same
|
5
|
6
|
30
|
with two OR questions from the same
|
The questions of 6 marks will be asked from the units with 12 more credit hours.
V. Reference books of NEB Mathematics
1. Bajracharya, Parkash Muni, Fundamentals of Mathematics-XI, Buddha Publication, Ktm
2. Adhikary, D.B., Elements of Mathematics-Xi, Ekata Books and Distributors, Ktm
3. G.C. Phan Bahadur et.al., Mathematics-XI, Asmita Books Publication, Ktm
4. Awasthi, Ramesh Prasad, Mathematics XI, Unice Educational Publication, Ktm
5. Mahato, Hem Chandra Et.al., Mathematics-XI, G-7 Publication Pvt.Ltd.Ktm
6. Mishra, Sailendra Kumar et.al., Conceptual Mathematics-XI, Divya Deuuralis Publication, ktm
7. Bajracharya, D.R. and et.al, Basic Mathematics-Xi, Sukunda Pustak Bhawan, Ktm
8. Sharma, Basat Raj et.al, Essentials of Mathematics-XI, I.M Publication Pvt. Ltd., Ktm
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