Secondary Education Curriculum      2076

Maths

 

Grades: 11 and 12                  

Subject code: Mat. 401 ( Grade 11 ),

Mat. 402 (Grade 12)

Credit hrs: 5                                                     

Working hrs: 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.

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.

3.    Grade-wise Learning Outcomes

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

 

S.

N.

Content Domain/area

Learning Outcomes

Grade 11

Grade 12

1.

Algebra

1.1 acquaint with logical connectives and use them.

         solve the problems related to permutation and combinations.

         state and prove binomial theorems for positive integral index.

         state binomial theorem for any index (without proof).

         find the general term and binomial coefficient.

         use binomial theorem in application to approximation.

         define Euler's number.

            Expand ex, ax and log(1+x) using binomial theorem.

         define binary operation and apply binary operation on sets of integers.

            state properties of binary operations.

         define group, finite group, infinite group and abelian group.

         prove the uniqueness of identity, uniqueness of inverse, cancelation law.

             state and prove De Moivre's theorem.

 

 

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: a , 𝑥2−𝑎2 ,   a   ,𝑎𝑥2 + bx +

𝑥        𝑥−𝑎    𝑥+𝑎

c, a𝑥3), trigonometric,

exponential, logarithmic functions.

               define sequence and series.

         classify sequences and series (arithmetic, geometric, harmonic).

         solve the problems related to arithmetic, geometric and harmonic sequences and series.

               establish relation among A.M,

G. M and H.M.

         find the sum of infinite geometric series.

         obtain transpose of matrix and verify its properties.

         calculate minors, cofactors, adjoint, determinant and inverse of a square matrix.

         solve the problems using properties of determinants.

               define a complex number.

         solve the problems related to algebra of complex numbers.

         represent complex number geometrically.

         find conjugate and absolute value (modulus) of a complex numbers and verify their properties.

         find square root of a complex number.

         express complex number in polar form.

            find the roots of a complex number by De Moivre's theorem.

            solve the problems using properties of cube roots of unity.

         apply Euler's formula.

            define polynomial function and polynomial equation.

            state and apply fundamental theorem of algebra (without proof).

            find roots of a quadratic equation.

            establish the relation between roots and coefficient of quadratic equation.

            form a quadratic equation with given roots.

            sum of finite natural numbers, sum of squares of first n-natural numbers, sum of cubes of first n-natural numbers, intuition and induction, principle of mathematical induction.

            using principle of mathematical induction, find the sum of finite natural numbers, sum of squares of first n-natural numbers, sum of cubes of first n-natural numbers.

            solve system of linear equations by Cramer's rule and matrix method (row- equivalent and inverse) up to three variables.

2.

Trigonometr y

2.1 solve the problems using properties of a triangle (sine law, cosine law, tangent law, projection laws, half angle laws).

2.1 define inverse circular functions.

establish the relations on inverse circular functions.


 

 

2.2 solve the triangle(simple cases)

2.2 find the general solution of trigonometric equations

3.

Analytic geometry

            find the length of perpendicular from a given point to a given line.

            find the equation of bisectors of the angles between two straight lines.

            write the condition of general equation of second degree in x and y to represent a pair of straight lines.

            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.

            solve the problems related to condition of tangency of a line at a point to the circle.

            find the equations of tangent and normal to a circle at given point.

            find the standard equation of parabola.

            find the equations of tangent and normal to a parabola at given point.

            obtain standard equation of ellipse and hyperbola.

            find direction ratios and direction cosines of a line.

            find the general equation of a plane.

            find equation of a plane in intercept and normal form.

            find the equation of plane through three given points.

            find the equation of geometric plane through the intersection of two given planes.

            find angle between two geometric planes.

            write the conditions of parallel and perpendicular planes.

            find the distance of a point from a plane.

4.

Vectors

            identify collinear and non- collinear vectors; coplanar and non-coplanar vectors.

            write linear combination of vectors.

            find scalar product of two vectors.

find angle between two vectors.

            interpret scalar product of vectors geometrically.

            apply properties of scalar product of vectors in trigonometry and geometry.

         define vector product of two vectors, interpretation vector product geometrically.

         solve the problems using properties of vector product.

         apply vector product in plane trigonometry and geometry.

5.

Statistics and

5.1 calculate the measures of

5.1 calculate correlation coefficient

 

Probability

dispersion (standard deviation).

by Karl Pearson's method.

 

5.2 calculate variance, coefficient of variation and coefficient of skewness.

5.2 calculate rank correlation coefficient by Spearman method.

 

               define random experiment, sample space, event, equally likely cases, mutually exclusive events, exhaustive cases, favorable cases, independent and dependent events.

               find the probability using two basic laws of probability.

            interpret correlation coefficient.

            obtain regression line of y on x and x on y.

            solve the simple problems of probability using combinations.

            solve the problems related to conditional probability.

 

 

5.7 use binomial distribution and calculate mean and standard deviation of binomial distribution.

6.

Calculus

6.1 define limits of a function.

            find the derivatives of inverse trigonometric, exponential and logarithmic functions by definition.

            establish the relationship between continuity and differentiability.

            differentiate the hyperbolic function and inverse hyperbolic function

            evaluate the limits by L'hospital's rule (for 0/0, ∞/∞).

            find the tangent and normal by using derivatives.

            interpret geometrically and verify Rolle's theorem and Mean Value theorem.

            find the anti-derivatives of standard integrals, integrals reducible to standard forms and rational function (using partial fractions also).

            solve the differential equation of first order and first degree

by separable variables, homogenous, linear and exact

 

 

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).

 

 

         find the derivatives of parametric and implicit functions.

         calculate higher order derivatives.

         check the monotonicity of a function using derivative.

         find extreme values of a function.

         find the concavity of function by using derivative.

         define integration as reverse of differentiation.

         evaluate the integral using basic integrals.

         integrate by substitution and by integration by parts method.

         evaluate the definite integral.

         find area between two curves.

differential equation.

7.

Computation al methods

         tell the basic idea of characteristics of numerical computing, accuracy, rate of convergence, numerical stability, efficiency).

         approximate error in computing roots of non-linear equation.

         solve algebraic polynomial and transcendental equations by bisection method

         solve algebraic polynomial and transcendental equations by Newton-Raphson methods.

         solve the linear programming problems (LPP) by simplex method of two variables.

         integrate numerically by trapezoidal and Simpson's rules and estimate the errors.

8.

Mechanics

         find resultant forces by parallelogram of forces.

         solve the problems related to composition and resolution of forces.

         obtain resultant of coplanar forces/vectors acting on a point.

         solve the forces/vectors related problems using Lami’s theorem.

         solve the problems of motion of particle in a straight line, motion with uniform acceleration,

            find the resultant of like and unlike parallel forces/vectors.

            solve the problems related to Newton's laws of motion and projectile.

 

 

 

 

Or

motion under the gravity, motion in a smooth inclined plane.

 

 

Or

Or

8.1 interpret results in the context of original real- world problems.

         use quadratic functions in economics,

         understand input- output analysis and dynamics of market price.

            find difference equations.

         work with Cobweb model and lagged Keynesian macroeconomic model.

         explain mathematically equilibrium and break-even.

         construct mathematical models involving consumer and producer surplus.

         use quadratic functions in economics.

            do input- output analysis.

            analyze dynamics of market.

         construct difference equations, 8.11understand cobweb model,

lagged Keynesian macroeconomics model.

 

Mathematics for Economics and Finance

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 area

Grade 11

Grade 12

Contents

Working hrs

 

Working hrs

1

Alge bra

1.1 Logic and Set: introduction of Logic, statements, logical connectives, truth tables, basic laws of logic, theorems based on set operations.

 

 

 

 

32

1.1 Permutation and combination: Basic principle of counting, Permutation of (a) set of objects all different (b) set of objects not all different (c) circular arrangement (d) repeated use of the same objects. Combination of

 

 

 

 

32

 

 

1.2 Real numbers: field axioms, order

 

 

 

 

axioms, interval, absolute value, geometric representation of real numbers.

         Function: Review, domain & range of a function, Inverse function, composite function, functions of special type, algebraic (linear, quadratic & cubic), Trigonometric, exponential, logarithmic)

         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

(𝑎 , 𝑥2−𝑎2 ,   𝑎   ,a𝑥2 + 𝑏𝑥 +

𝑥        𝑥−𝑎    𝑥+𝑎

𝑐, 𝑎𝑥3), Trigonometric,

exponential, logarithmic function (simple cases only)

         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.

         Matrices and determinants: Transpose of a matrix and its properties,

 

things all different, Properties of combination

         Binomial Theorem: Binomial theorem for a positive integral index, general term. Binomial coefficient, Binomial theorem for any index (without proof), application to approximation. Euler's number. Expansion of 𝑒𝑥, 𝑎𝑥 and log(1+x) (without proof)

         Elementary Group Theory: Binary operation, Binary operation on sets of integers and their properties, Definition of a group, Finite and infinite groups. Uniqueness of identity, Uniqueness of inverse, Cancelation law, Abelian group.

         Complex numbers: De Moivre's theorem and its application in finding the roots of a complex number, properties of cube roots of unity. Euler's formula.

         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.

         Mathematical induction: Sum of finite natural numbers, sum of squares of first n-natural numbers, Sum of cubes of first n- natural numbers, Intuition and induction, principle of mathematical induction.

         Matrix based system of linear equation: Consistency of system of

linear equations, Solution of

 


 

 

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.

 

a system of linear equations by Cramer's rule. Matrix method (row- equivalent and Inverse) up to three variables.

 

2

Trigono metry

           Properties of a triangle (Sine law, Cosine law, tangent law, Projection laws, Half angle laws).

          Solution of triangle(simple cases)

 

 

 

8

            Inverse circular functions.

         Trigonometric equations and general values

 

 

 

8

3

Analytic Geometr y

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

 

 

 

 

 

 

 

14

         Conic section: Standard equations of Ellipse and hyperbola.

         Coordinates in space: direction cosines and ratios of a line general equation of a plane, equation of a plane in intercept and normal form, plane through 3 given points, plane through the intersection of two given planes, parallel and perpendicular planes, angle between two planes, distance of a point from a plane.

 

 

 

 

 

 

 

14

 

 

lines.

         Circle: Condition of tangency of a line at a point to the circle, Tangent and normal to a circle.

         Conic section: Standard equation of parabola, equations of tangent and normal to a parabola at a given point.

 

 

 

4

Vectors

              Vectors: collinear and non collinear vectors, coplanar and non- coplanar vectors, linear combination of vectors,

          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

         Product of Vectors: vector product of two vectors, geometrical interpretation of vector product, properties of vector product, application of vector product in plane trigonometry.

         Scalar triple Product: introduction of scalar triple product

 

 

 

 

 

 

 

8

5

Statistics & Probabili ty

          Measure of

Dispersion: introduction, standard deviation), variance, coefficient of variation, Skewness (Karl Pearson and Bowley)

          Probability: independent cases, mathematical and empirical definition of probability, two basic laws of probability(without proof).

 

 

 

 

 

 

 

 

10

         Correlation and Regression: correlation, nature of correlation, correlation coefficient by Karl Pearson's method, interpretation of correlation coefficient, properties of correlation coefficient (without proof), rank correlation by Spearman, regression equation, regression line of y on x and x on y.

         Probability: Dependent cases, conditional probability (without proof), binomial distribution, mean and

standard deviation of

 

 

 

 

 

 

 

 

10

 

 

 

 

binomial distribution (without proof).

 

6

Calculus

           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.

          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.

          Anti-derivatives:

anti-derivative. integration using basic integrals, integration

by substitution and by

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

32

         Derivatives: derivative of inverse trigonometric, exponential and logarithmic function by definition, relationship between continuity and differentiability, rules for differentiating hyperbolic function and inverse hyperbolic function, L’Hospital's rule (0/0, ∞/∞), differentials, tangent and normal, geometrical interpretation and application of Rolle’s theorem and mean value theorem.

         Anti-derivatives: anti- derivatives, standard integrals, integrals reducible to standard forms, integrals of rational function.

         Differential equations: differential equation and its order, degree, differential equations of first order and first degree, differential equations with separable variables, homogenous, linear and exact differential equations.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

32

 

 

parts methods, the definite integral, the definite integral as an area under the given curve, area between two curves.

 

 

 

7

Computa tional Methods

              Linear programming Problems: linear programming problems(LPP), solution of LPP by simplex method (two variables)

          Numerical computation Characteristics of numerical computation, accuracy, rate of convergence, numerical stability, efficiency

 

 

 

 

 

 

 

10

            Computing Roots:

Approximation & error in computation of roots in non- linear equation, Algebraic and transcendental equations & their solution by bisection and Newton- Raphson Methods

          System of linear equations:

Gauss elimination method, Gauss- Seidal method, Ill conditioned systems.

         Numerical integration Trapezoidal and Simpson's rules, estimation of errors.

 

 

 

 

 

 

 

10

8

Mechani cs

Or

 

 

 

 

 

 

 

 

 

 

 

 

Mathem atics for Economi cs and Finance

         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.

         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

         Mathematics for economics and finance:

 

 

 

 

 

 

 

 

 

 

 

12

         Statics: Resultant of like and unlike parallel forces.

         Dynamics: Newton's laws of motion and projectile.

         Mathematics for economics and finance: Consumer and Producer Surplus, Quadratic functions in Economics, Input-Output analysis, Dynamics of market price, Difference equations, The Cobweb model, Lagged Keynesian macroeconomic model.

 

 

 

 

 

 

 

 

 

 

 

12

 

 

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

 

 

 

Total

 

126

 

126

 

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

 

 

S. No.

 

Content area/domain

Working hrs 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 11

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

p

angles which are multiples of 2 and p.

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.

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: 𝑐⃗ × (𝑎⃗ + 𝑏̅ ) =  𝑐⃗ × 𝑎⃗ + 𝑐⃗ × 𝑏̅

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 (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.