Secondary Education Curriculum 2076
Subject - Mathematics (Optional)
Subject Code - Mat. 401
Credit Hour - 5
Working hour - 160
kusa.com.np presents you the Grade 11-XI Math (Optional) subject curriculum with Subject Code-Mat. 401 NEB 2076-2020. Check and download in PDF file of Mathematics (Optional) curriculum class 11-XI 2076-2020. 2076 New Curriculum of Grade 11-XI Math (Optional) Subject with subject code-Mat.401 and download it in PDF file. Enjoy!

### 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).

### Also Check:

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.

### 2. Level-wise Competencies:

On completion of this course, students will have the following competencies:
1. apply numerical methods to solve algebraic equation and calculate definite integrals and use simplex method to solve linear programming problems (LPP).
2. use principles of elementary logic to find the validity of statement.
3. make connections and present the relationships between abstract algebraic structures with familiar number systems such as the integers and real numbers.
4. use basic properties of elementary functions and their inverse including linear, quadratic, reciprocal, polynomial, rational, absolute value, exponential, logarithm, sine, cosine and tangent functions.
5. identify and derive equations or graphs for lines, circles, parabolas, ellipses, and hyperbolas,
6. use relative motion, Newton’s laws of motion in solving related problems.
7. articulate personal values of statistics and probability in everyday life.
8. apply derivatives to determine the nature of the function and determine the maxima and minima of a function and normal increasing and decreasing function into context of daily life.
9. explain anti-derivatives as an inverse process of derivative and use them in various situations.
10. use vectors and mechanics in day to day life.
11. develop proficiency in application of mathematics in economics and finance.

On completion of the course, the students will be able to:
Learning Outcomes.
1Algebra1.1 – acquaint with logical connectives and use them.
1.2 – construct truth tables.
1.3 – prove set identities.
1.4 – state field axioms, order axioms of real numbers.
1.5 – define interval and absolute value of real numbers.
1.6 – interpret real numbers geometrically.
1.7 – define ordered pair, Cartesian product, domain and range of relation, inverse of relation and solve the related problems.
1.8 – define domain and range of a function, inverse function composite function.
1.9 – find domain and range of a function.
1.10 – find inverse function of given invertible function.
1.11 – calculate composite function of given functions.
1.12 – define odd and even functions, periodicity of a function, monotonicity of a function.
1.13 – sketch graphs of polynomial functions(𝑒𝑔: 􀭟􀯫 , 􀯫􀰮􀬿􀯔􀰮 ,􀯫􀬿􀯔􀭟􀯫􀬾􀯔,𝑎𝑥􀬶 + bx + c, a𝑥􀬷), trigonometric,exponential, logarithmic functions.
1.14 – define sequence and series.
1.15 – classify sequences and series (arithmetic, geometric, harmonic).
1.16 – solve the problems related to arithmetic, geometric and harmonic sequences and series.
1.17 – establish relation among A.M, G. M and H.M.
1.18 – find the sum of infinite geometric series.
1.19 – obtain transpose of matrix and verify its properties.
1.20 – calculate minors, cofactors, adjoint, determinant and inverse of a square matrix.
1.21 – solve the problems using properties of determinants.
1.22 – define a complex number.
1.23 – solve the problems related to algebra of complex numbers.
1.24 – represent complex number geometrically.
1.25 – find conjugate and absolute value (modulus) of a complex numbers and verify their properties.
1.26 – find square root of a complex number.
1.27 – express complex number in polar form.
2Trigonometry2.1 – solve the problems using properties of a triangle (sine law,
cosine law, tangent law, projection laws, half angle laws).
2.2 – solve the triangle(simple cases)
3Analytic Geometry3.1 -find the length of perpendicular from a given point to a given line.
3.2 – find the equation of bisectors of the angles between two straight lines.
3.3 – write the condition of general equation of second degree in x and y to represent a pair of straight lines.
3.4 – find angle between pair of lines and bisectors of the angles
between pair of lines given by homogenous second degree equation in x and y.
3.5 – solve the problems related to condition of tangency of a line at a point to the circle.
3.6 – find the equations of tangent and normal to a circle at given point.
3.7 – find the standard equation of parabola.
3.8 – find the equations of tangent and normal to a parabola at given point.
4Vector4.1 – identify collinear and noncollinear vectors; coplanar and non-coplanar vectors.
4.2 – write linear combination of vectors.
4.3 – find scalar product of two vectors.
4.4 – find angle between two vectors.
4.5 – interpret scalar product of vectors geometrically.
4.6 – apply properties of scalar product of vectors in trigonometry and geometry.
5Statistics and Probability5.1 – calculate the measures of dispersion (standard deviation).
5.2 – calculate variance, coefficient of variation and coefficient of skewness.
5.3 – define random experiment, sample space, event, equally likely cases, mutually exclusive events, exhaustive cases, favorable cases, independent and dependent events.
5.4 – find the probability using two basic laws of probability.
6Calculus6.1 – define limits of a function.
6.2 – identify indeterminate forms.
6.3 – apply algebraic properties of limits.
6.4 – evaluate limits by using theorems on limits of algebraic, trigonometric, exponential and logarithmic functions.
6.5 – define and test continuity of a function.
6.6 – define and classify discontinuity.
6.7 – interpret derivatives geometrically.
6.8 – find the derivatives, derivative of a function by first principle (algebraic, trigonometric exponential and logarithmic functions).
6.9 – find the derivatives by using rules of differentiation (sum, difference, constant multiple, chain rule, product rule, quotient rule, power and general power rules).
6.10 – find the derivatives of parametric and implicit functions.
6.11 – calculate higher order derivatives.
6.12 – check the monotonicity of a function using derivative.
6.13 – find extreme values of a function.
6.14 – find the concavity of function by using derivative.
6.15 – define integration as reverse of differentiation.
6.16 – evaluate the integral using basic integrals.
6.17 – integrate by substitution and by integration by parts method.
6.18 – evaluate the definite integral.
6.19 – find area between two curves.
7Computational Method7.1 – tell the basic idea of characteristics of numerical computing, accuracy, rate of convergence, numerical stability, efficiency).
7.2 – approximate error in computing roots of non-linear equation.
7.3 – solve algebraic polynomial and transcendental equations by bisection method
8Mechanics8.1 – find resultant forces by parallelogram of forces.
8.2 – solve the problems related to composition and resolution of forces.
8.3 – obtain resultant of coplanar forces/vectors acting on a point.
8.4 – solve the forces/vectors related problems using Lami’s theorem.
8.5 – solve the problems of motion of particle in a straight line, motion with uniform acceleration, motion under the gravity, motion in a smooth inclined plane.
8OR.
Mathematics for Economics and Finance
8.1 – interpret results in the context of original real- world problems.
8.2 – test how well it describes the original real- world problem and how well it describes past and/or with what accuracy it predicts future behavior.
8.3 – Model using demand and supply function.
8.4 – Find cost, revenue, and profit functions.
8.5 – Compute elasticity of demands.
8.6 – Construct mathematical models involving supply and income, budget and cost constraint.
8.7 – Test the equilibrium and break even condition.

### 4. Scope and Sequence of Contents:

S.N.Content areaContentsWorking hours
1Algebra1.1 Logic and Set: introduction of Logic, statements, logical connectives, truth tables, basic laws of logic, theorems based on set operations.
1.2 Real numbers: field axioms, order axioms, interval, absolute value, geometric representation of real numbers.
1.3 Function: Review, domain & range of a function, Inverse function, composite function, functions of special type, algebraic (linear, quadratic & cubic), 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 graphs of polynomials and some rational functions (􀯔􀯫 , 􀯫􀰮􀬿􀯔􀰮 ,􀯫􀬿􀯔􀯔 􀯫􀬾􀯔,a𝑥􀬶 + 𝑏𝑥 +𝑐, 𝑎𝑥􀬷), Trigonometric, exponential, logarithmicfunction (simple cases only)
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 of a square matrix, Properties of determinants (without proof)
1.7 Complex number: definition imaginary unit, algebra of complex numbers, geometric representation, absolute value (Modulus) and conjugate of a complex numbers and their properties, square root of a complex number, polar form of complex numbers.
32
2Trigonometry2.1 Properties of a triangle (Sine law, Cosine law, tangent law, Projection laws, Half angle laws).
2.2 Solution of triangle(simple cases)
8
3Analytic geometry3.1 Straight Line: length of perpendicular from a given point to a given line. Bisectors of the angles between two straight lines. 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.
3.2 Circle: Condition of tangency of a line at a point to the circle, Tangent and normal to a circle.
3.3 Conic section: Standard equation of parabola, equations of tangent and normal to a parabola at a given point.
14
4Vectors4.1 Vectors: collinear and non collinear vectors, coplanar and noncoplanar vectors, linear combination of vectors,
4.2 Product of vectors: scalar product of two vectors, angle between two vectors, geometric interpretation of scalar product, properties of scalar product, condition of perpendicularity.
8
5Statistics and Probability5.1 Measure of Dispersion: introduction, standard deviation), variance, coefficient of variation, Skewness (Karl Pearson and Bowley)
5.2 Probability: independent cases, mathematical and empirical definition of probability, two basic laws of probability(without proof).
10
6Calculus6.1 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, 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 of a function, concavity, points of inflection, derivative as rate of measure.
6.3 Anti-derivatives: anti-derivative. 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.
32
7Computational method7.1 Linear programming Problems: linear programming problems(LPP), solution of LPP by simplex method (two variables)
7.2 Numerical computation Characteristics of numerical computation, accuracy, rate of convergence, numerical stability, efficiency
10
8Mechanics
Or
Mathematics for Economics and Finance
8.1 Statics: Forces and resultant forces, parallelogram law of forces, composition and resolution of forces, Resultant of coplanar forces acting on a point, Triangle law of forces and Lami’s theorem.
8.2 Dynamics: Motion of particle in a straight line, Motion with uniform acceleration, motion under the gravity, motion down a smooth inclined plane. The concepts and theorem restated and formulated as application of calculus
8.3 Mathematics for economics and finance: Mathematical Models and Functions, Demand and supply, Cost, Revenue, and profit functions, Elasticity of demand, supply and income , Budget and Cost Constraints, Equilibrium and break even
12

Total126

### 5. Practical and project activities:

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

### Sample project works/mathematical activities for grade 11/button.

1. Take a square of arbitrary measure assuming its area is one square unit. Divide it in to four equal parts and shade one of them. Again take one not shaded part of that square and shade one fourth of it. Repeat the same process continuously and find the area of the shaded region.
2. Write two simple statements related to mathematics and write four compound statements by using them.
3. Prepare a model to illustrate the values of sine function and cosine function for different angles which are multiples of 2 and .
4. Verify the sine law by taking particular triangle in four quadrants.
5. Prepare a concrete material to show parabola by using thread and nail in wooden panel.
6. Verify that the equation of a line passing through the point of intersection of two lines a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 is of the form (a1x + b1y + c1) + K(a2x + b2y + c2) = 0.
7. Prepare a model and verify that angle in a semi-circle is a right angle by using vector method.
8. Geometrically interpret the scalar product of two vectors.
9. Collect the scores of grade 10 students in mathematics and English from your school.
• a. Make separate frequency distribution with class size 10.
• b. Which subject has more uniform/consistent result?
• c. Make the group report and present.
10. Roll two dices simultaneously 20 times and list all outcomes. Write the events that the sum of numbers on the top of both dice is a) even b) odd in all above list. Examine either they are mutually exclusive or not. Also find the probabilities of both events.
11. Collect the data of age of more than 100 peoples of your community.
• a. Make continuous frequency distributions of class size 20, 15, 12, 10, 8 and 5.
• b. Construct histograms and the frequency polygons and frequency curves in each cases.
• c. Estimate the area between the frequency curve and frequency polygon in each
• cases.
• d. Find the trend and generalize the result.
• e. Present the result in class.
12. A metallic bar of length 96 inch was used to make a rectangular frame. Find the dimension of the rectangular metallic frame with maximum area.
13. Find the roots of any polynomial by using ICT and present in the classroom.
14. Search a daily life problem on projectile motion. Solve that problem and present in the classroom.
15. Construct mathematical models involving supply and income, budget and cost constraint of a production company.

### 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 participationProject work/Mathematical activity (at least 10 work/activities from the above mentioned project work/mathematical activities should be evaluated)Demonstration of competency in classroom activityMarks from terminal examsTotal
3106625

### 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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