**Secondary Education Curriculum 2076**

**Subject - Mathematics (Optional)**

### Grade 11-XI Math Curriculum Subject Code-Mat.401 of year 2076 | Download in PDF.

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### 1. Introduction:

### Also Check:

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:

### 3. Grade-wise Learning Outcomes:

On completion of the course, the students will be able to:

**Learning Outcomes.**S.N. | Content domain/area | Grade 11 |
---|---|---|

1 | Algebra | 1.1 – 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. |

2 | Trigonometry | 2.1 – 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) |

3 | Analytic Geometry | 3.1 -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. |

4 | Vector | 4.1 – 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. |

5 | Statistics and Probability | 5.1 – 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. |

6 | Calculus | 6.1 – 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. |

7 | Computational Method | 7.1 – 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 |

8 | Mechanics | 8.1 – 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. |

8 | OR.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:

__Grade - 11-XI__S.N. | Content area | Contents | Working hours |
---|---|---|---|

1 | Algebra | 1.1 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 |

2 | Trigonometry | 2.1 Properties of a triangle (Sine law, Cosine law, tangent law, Projection laws, Half angle laws). 2.2 Solution of triangle(simple cases) | 8 |

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. 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 |

4 | Vectors | 4.1 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 |

5 | Statistics and Probability | 5.1 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 |

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, 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 |

7 | Computational method | 7.1 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 |

8 | MechanicsOr 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 |

Total | 126 |

### 5. Practical and project activities:

S.N. | Content area/domain | Working hours in grade 11 |
---|---|---|

1 | Algebra | 10 |

2 | Trigonometry | 2 |

3 | Analytic geometry | 4 |

4 | Vectors | 2 |

5 | Statistics and probability | 2 |

6 | Calculus | 10 |

7 | Computational methods | 2 |

8 | Mechanics Or Mathematics for Economics and Finance | 2 |

Total- | 34 |

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

- a. Make separate frequency distribution with class size 10.
- b. Which subject has more uniform/consistent result?
- c. Make the group report and present.

- 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.

### 6. Learning Facilitation Method and Process:

- 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:

### 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

- 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.

Classroom participation | Project work/Mathematical activity (at least 10 work/activities from the above mentioned project work/mathematical activities should be evaluated) | 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.

* Source:* https://www.dhanraj.com.np

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