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# NEB Class 11 Mathematics Syllabus 2080

NEB Class 11 Mathematics Syllabus 2080; Complete Updated Syllabus of NEB Class 11 Mathematics for NEB Exam 2081.

## Grade 11 Mathematics Syllabus

Complete Syllabus of NEB Class 11 Mathematics for NEB Exam 2080.

Subject Mathematics 11 Mat. 401 5 160

### 1. Introduction

Mathematics is an indispensable in many fields. It is essential in the field of engineering, medicine, natural sciences, finance and other social sciences. The branch of mathematics concerned with application of mathematical knowledge to other fields and inspires new mathematical discoveries. The new discoveries in mathematics led to the development of entirely new mathematical disciplines. School mathematics is necessary as the backbone for higher study in different disciplines. Mathematics curriculum at secondary level is the extension of mathematics curriculum offered in lower grades (1 to 10).

This course of Mathematics is designed for grade 11 and 12 students as an optional subject as per the curriculum structure prescribed by the National Curriculum Framework, 2075. This course will be delivered using both the conceptual and theoretical inputs through demonstration and presentation, discussion, and group works as well as practical and project works in the real world context. Calculation strategies and problem solving skills will be an integral part of the delivery.

This course includes different contents like; Algebra, Trigonometry, Analytic Geometry, Vectors, Statistics and Probability, Calculus, Computational Methods and Mechanics or Mathematics for Economics and Finance.

Student’s content knowledge in different sectors of mathematics with higher understanding is possible only with appropriate pedagogical skills of their teachers. So, classroom teaching must be based on student-centered approaches like project work, problem solving etc.

Also Check: Class 11 Model Question (All Subject)

### Class 11 Mathematics Subject List

 SN Content area/domain LH Class 11 1 Algebra 10 2 Trigonometry 2 3 Analytic geometry 4 4 Vectors 2 5 Statistics & Probability 2 6 Calculus 10 7 Computational methods 2 8 Mechanics or Mathematics for Economics and Finance 2 Total 34

## Class 11 Mathematics: NEB Syllabus

Scope and Sequence of Contents

Unit Topics
Unit 1: Algebra

• 1.1 Logic and Set: Statements, logical connectives, truth tables, theorems based on set operations.
• 1.2 Real numbers: Geometric representation of real numbers, interval,absolute value.
• 1.3 Function: Domain and range of a function, Inverse function, composite function, introduction of functions; algebraic (linear,quadratic & cubic), Transcendental (trigonometric, exponential, logarithmic)
• 1.4 Curve sketching: Odd and even functions, periodicity of a function,symmetry (about origin, X-and Y-axis),monotonicity of a function, sketching the graphs of Quadratic, Cubic and rational functions of the form 1 / (ax + b) where a ≠ 0,Trigonometric (asin bx and acos bx),exponential (ex),logarithmic function (lnx)
• 1.5 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
• 1.6 Matrices and determinants: Transpose of a matrix and its properties, Minors and cofactors, Adjoint, Inverse matrix, Determinant, Properties of determinants (without proof)
• 1.7 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.
• 1.8 Complex number: Imaginary unit, algebra of complex numbers, geometric representation, absolute (Modulus) value and conjugate of a complex numbers and their properties, square root of a complex number.

Unit 2: Trigonometry

• 2.1 Inverse circular functions
• 2.2 Trigonometric equations and general values

Unit 3: Analytic Geometry

• 3.1 Straight Line: Length of perpendicular from a given point to a given line, Bisectors of the angles between two straight lines.
• 3.2 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
• 3.3 Coordinates in space: Points in space, distance between two points, direction cosines and ratios of a line

Unit 4: Vectors
• 4.1 Vectors: Collinear and non collinear vectors, coplanar and non-coplanar vectors, linear combination of vectors, Linearly dependent and independent
Unit 5: Statistics and Probability

• 5.1 Measure of Dispersion: Standard deviation, variance, coefficient of variation, Skewness, Karl Pearson's coefficient of skewness.
• 5.2 Probability: Independent cases, mathematical and empirical definition of probability, two basic laws of probability (without proof).

Unit 6: Calculus

• 6.1 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.
• 6.2 Derivatives: Derivative of a function, derivatives of algebraic, trigonometric, inverse of 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 values of a function, concavity, points of inflection.
• 6.3 Anti-derivatives: 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 or Mechanics

• 7.1 Numerical computation: Roots of algebraic and transcendental equation (bisection and Newton-Raphson method)
• 7.2 Numerical integration: Trapezoidal rule and Simpson's rule

Or Mechanics

• 7.1 Statics: Forces and resultant forces, parallelogram law of forces, composition and resolution of forces, Resultant of coplanar forces acting on a point.
• 7.2 Dynamics: Motion of particle in a straight line, Motion with uniform acceleration, motion under the gravity, motion down a smooth inclined plane.

Total LH: 160 Hours

### 5. Practical and Project Activities

The students are required to do different practical activities in different content areas and the teachers should plan in the same way. Total of 34 working hours is allocated for practical and project activities in each of the grades 11 and 12.

The following table shows estimated working hours for practical activities in different content areas of grade 11 and 12

 SN Content area/domain LH in each of the grades 11 and 12 1 Algebra 10 2 Trigonometry 2 3 Analytic geometry 4 4 Vectors 2 5 Statistics & Probability 2 6 Calculus 10 7 Computational methods 2 8 Mechanics or Mathematics for Economics and Finance 2 Total 34

Here are some sample (examples) of practical and project activities.

Sample project works/mathematical activities for grade 12

1. Represent the binomial theorem of power 1, 2, and 3 separately by using concrete materials and generalize it with n dimension relating with Pascal’s triangle.

2. Take four sets R, Q, Z, N and the binary operations +, ‒, ×. Test which binary operation forms group or not with R, Q, Z, N.

3. Prepare a model to explore the principal value of the function sin–1x using a unit circle and present in the classroom.

4. Draw the graph of sin‒1x, using the graph of sin x and demonstrate the concept of mirror reflection (about the line y = x).

5. Fix a point on the middle of the ceiling of your classroom. Find the distance between that point and four corners of the floor. 6. Construct an ellipse using a rectangle.

7. Express the area of triangle and parallelogram in terms of vector.

8. Verify geometrically that: ?⃗ × (?⃗ + ?) = ?⃗ × ?⃗ + ?⃗ × ?⃗ ?

9. Collect the grades obtained by 10 students of grade 11 in their final examination of English and Mathematics. Find the correlation coefficient between the grades of two subjects and analyze the result.

10. Find two regression equations by taking two set of data from your textbook. Find the point where the two regression equations intersect. Analyze the result and prepare a report.

11. Find, how many peoples will be there after 5 years in your districts by using the concept of differentiation.

12. Verify that the integration is the reverse process of differentiation with examples and curves.

13. Correlate the trapezoidal rule and Simpson rule of numerical integration with suitable example.

14. Identify different applications of Newton’s law of motion and related cases in our daily life.

15. Construct and present Cobweb model and lagged Keynesian macroeconomic model.

### 6. Learning Facilitation Method and Process

Teacher has to emphasis on the active learning process and on the creative solution of the exercise included in the textbook rather than teacher centered method while teaching mathematics. Students need to be encouraged to use the skills and knowledge related to maths in their house, neighborhood, school and daily activities. Teacher has to analyze and diagnose the weakness of the students and create appropriate learning environment to solve mathematical problems in the process of teaching learning. The emphasis should be given to use diverse methods and techniques for learning facilitation. However, the focus should be given to those method and techniques that promote students’ active participation in the learning process. The following are some of the teaching methods that can be used to develop mathematical competencies of the students:

• Inductive and deductive method
• Problem solving method
• Case study
• Project work method
• Question answer and discussion method
• Discovery method/ use of ICT
• Co-operative learning

### 7. Student Assessment

Evaluation is an integral part of learning process. Both formative and summative evaluation system will be used to evaluate the learning of the students. Students should be evaluated to assess the learning achievements of the students. There are two basic purposes of evaluating students in Mathematics: first, to provide regular feedback to the students and bringing improvement in student learning-the formative purpose; and second, to identify student’s learning levels for decision making.

#### a. Internal Examination/Assessment

i. Project Work:

Each Student should do one project work from each of eight content areas and has to give a 15 minute presentation for each project work in classroom. These seven project works will be documented in a file and will be submitted at the time of external examination. Out of eight projects, any one should be presented at the time of external examination by each student.

ii. Mathematical activity:

Mathematical activities mean various activities in which students willingly and purposefully work on Mathematics. Mathematical activities can include various activities like (i) Hands-on activities (ii) Experimental activities (iii) physical activities. Each student should do one activity from each of eight content area (altogether seven activities). These activities will be documented in a file and will be submitted at the time of external examination. Out of eight activities, any one should be presented at the time of external examination by each student.

iii. Demonstration of competency in classroom activity:

During teaching learning process in classroom, students demonstrate 10 competencies through activities. The evaluation of students’ performance should be recorded by subject teacher on the following basis.

· Through mathematical activities and presentation of project works.

· Identifying basic and fundamental knowledge and skills.

· Fostering students’ ability to think and express with good perspectives and logically on matters of everyday life.

· Finding pleasure in mathematical activities and appreciate the value of mathematical approaches.

· Fostering and attitude to willingly make use of mathematics in their lives as well as in their learning.

iv. Marks from trimester examinations:

Marks from each trimester examination will be converted into full marks 3 and calculated total marks of two trimester in each grade.

The weightage for internal assessment are as follows:

Classroom participation Project work / Mathematical activity Demonstration of competency in classroom activity Marks from terminal exams Total
3 10 6 6 25

#### b. External Examination/Evaluation

External evaluation of the students will be based on the written examination at the end of each grade. It carries 75 percent of the total weightage. The types and number questions will be as per the test specification chart developed by the Curriculum Development Centre.

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