Learning Outcomes
Permutation and combination
- Solve the problems related to basic principle of counting.
- Solve the problems related to permutation and combinations.
Binomial Theorem:
- State and prove binomial theorems for positive integral index.
- State binomial theorem for any integer.
- Find the general term and binomial coefficient.
- Use binomial theorem in application to approximation.
- Define Euler's number.
- Expand \(e^x, a^x, \log(1+x) \) using binomial theorem.
Complex numbers
- Express complex number in polar form.
- State and prove De Moivre's theorem.
- 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.
Sequence and series:
- Find the sum of finite natural numbers, sum of squares of first n-natural
numbers, sum of cubes of first n-natural numbers.
- Find the sum of finite natural numbers, calculate sum of squares of first n-natural numbers, sum of cubes of first n-natural numbers by using mathematical induction.
Matrix based system of linear equation
- Solve system of linear equations by Cramer's rule and matrix methods (row-equivalent and inverse) up to
three variables
Trigonometry
- Solve the problems using properties of a triangle (sine law, cosine law, tangent law, projection laws, half angle laws)
- Solve the triangle (simple cases)
Analytic geometry
- 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.
Vectors
- Find scalar product of two vectors, angle between two vectors and interpret scalar
product geometrically.
- Solve the problems using properties of scalar product
- Apply properties of scalar product of vectors in trigonometry and geometry.
- Define vector product of two vectors, and interpret vector product geometrically.
- Solve the problems using roperties of vector product.
- Apply vector product in geometry and trigonometry
Statistics and Probability
- Calculate correlation coefficient by Karl Pearson's method.
- Calculate rank correlation coefficient by Spearman method.
- 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.
Calculus
- Differentiate the hyperbolic function and inverse hyperbolic function
- Evaluate the limits by L'hospital's rule (for \( \frac{0}{0}, \frac{\infty}{\infty}\))
- Find the tangent and normal by using derivatives.
- Find the derivative as rate of measure
- Find the anti-derivatives of standard integrals, integrals reducible to standard forms .
- Solve the differential equation of first order and first degree by separable variables, homogenous, linear and exact differential equation
Computational methods
- Solve the system of linear equations by Gauss Elimination method, Gauss Seidel Method (up to 3
variables)
- Solve the linear programming problems (LPP) by simplex method
Mechanics
- Solve the forces/vectors related problems using triangle laws of forces and Lami’s theorem
- Solve the problems related to Newton's laws of motion and projectile.
Sample project works/practical works for grade 12
- 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.
- Verify the sine law by taking particular triangle in four quadrants.
- Verifications of a) Cosine law b) Projection law
- Construction of ellipse by using a piece of pencil, rope and nails
- Prepare a concrete material to show parabola by using thread and nail in wooden panel.
- Construct an ellipse using a rectangle.
- Express the area of triangle and parallelogram in terms of vector.
- 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.
- 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.
- Find how many peoples will be there after 5 years in your districts by using the concept of differentiation.
- Verify that the integration is the reverse process of differentiation with examples and curves.
- Identify different applications of Newton's law of motion and related cases in our daily life.
- Investigate a daily life problem on projectile motion. Solve that problem and present in the classroom.
- Write any one real life problem related to linear programming problem and solve that problem by using simplex method.
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 evaluation
Internal assessment includes classroom participation, terminal examinations, and project
work/practical work (computer works and lab work) and presentation. The scores of evaluation
will be used for providing feedback and to improve their learning. Individual and group works are
assigned as projects.
The basis of internal assessment is as follows:
| Classroom
participation | Marks from terminal
examinations | project work/practical work | Total |
| 3 | 6 | 16 | 25 |
(i) Classroom participation
The mark for classroom participation is 3 which is given on the basis of attendance and
participation of students in activities in each grade.
(ii) Marks from trimester examinations
Marks from each trimester examination will be converted into full marks 3 and calculated total
marks of two trimesters in each grade.
(iii) Project work/practical work
Each Student should do at least one project work/practical work from each of seven content areas
and also be required to give a 15 minutes presentation for each project work and practical work in
classroom. These seven project works/practical works will be documented in a file and will be
submitted at the time of practical evaluation. Out of seven projects/practical works from each area
any one project work/practical work should be presented at the time of practical evaluation by
student.
b. Final/External Examination
Final/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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