Grade 12 Mathematics

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Grade XI–XII

Mat. 007 & 008

NEB Mathematics Grade XII

Grade XI & XII · Nepal CDC · 7 content areas · CDC Specification Grid 2078

01

Course Chapters

📄 Old Exam Questions

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03

MCQ Practice Test

04

Specification Grid — Grade XI & XII

16%

Knowledge

12 marks

24%

Understanding

18 marks

40%

Application

30 marks

20%

Higher Ability

15 marks

1

Algebra ▼

Hours

44

MCQ

2

SAQ

2

LAQ

1

20

marks

Question Types

MCQ × 2 = 2 marksSAQ × 2 = 10 marksLAQ × 1 = 8 marks

By Competency

Knowledge

MCQ:2 SAQ:2

Understanding

LAQ:1

Application

SAQ:2

Higher Ability

—

2

Trigonometry ▼

Hours

12

MCQ

3

SAQ

—

LAQ

—

6

marks

Question Types

MCQ × 3 = 3 marks

By Competency

Knowledge

—

Understanding

—

Application

MCQ:2

Higher Ability

MCQ:1

3

Analytic Geometry ▼

Hours

20

MCQ

—

SAQ

2

LAQ

1

9

marks

Question Types

SAQ × 2 = 10 marksLAQ × 1 = 8 marks

By Competency

Knowledge

—

Understanding

SAQ:1

Application

—

Higher Ability

SAQ:1 LAQ:1

4

Vectors ▼

Hours

12

MCQ

3

SAQ

—

LAQ

—

6

marks

Question Types

MCQ × 3 = 3 marks

By Competency

Knowledge

—

Understanding

MCQ:2

Application

—

Higher Ability

MCQ:1

5

Statistics & Probability ▼

Hours

12

MCQ

1

SAQ

1

LAQ

—

6

marks

Question Types

MCQ × 1 = 1 markSAQ × 1 = 5 marks

By Competency

Knowledge

—

Understanding

—

Application

MCQ:1 SAQ:1

Higher Ability

—

6

Calculus ▼

Hours

48

MCQ

4

SAQ

2

LAQ

1

22

marks

Question Types

MCQ × 4 = 4 marksSAQ × 2 = 10 marksLAQ × 1 = 8 marks

By Competency

Knowledge

—

Understanding

SAQ:1 LAQ:1

Application

MCQ:2 SAQ:2

Higher Ability

MCQ:1 LAQ:1

7

Computational Methods / Mechanics ▼

Hours

12

MCQ

1

SAQ

1

LAQ

—

6

marks

Question Types

MCQ × 1 = 1 markSAQ × 1 = 5 marks

By Competency

Knowledge

—

Understanding

SAQ:1

Application

MCQ:1

Higher Ability

—

FORMAT

Question Format Plan

MCQ

1 mark each
11 questions
K:2 · U:5 · A:2 · HA:2

11 marks

SAQ

5 marks each
8 questions
K:2 · U:1 · A:4 · HA:1

40 marks

LAQ

8 marks each
3 questions
K:0 · U:1 · A:1 · HA:1

24 marks

Grand Total — 22 Questions

K:4 · U:7 · A:7 · HA:4  |  160 working hours

75 marks

05

Curriculum & Course Info

Unit 1: Algebra (44)

1. Permutation and Combination
   1. Basic principle of counting
   2. Permutation of (a) set of objects all different (b) not all different (c) circular arrangement (d) repeated use
   3. Combination of things all different, Properties of combination
2. Binomial Theorem
   1. Binomial theorem for a positive integer, general term, Binomial coefficient
   2. Binomial theorem for any index (without proof), application to approximation
   3. Euler's number, Expansion of \( e^x, a^x, \log(1+x) \) (without proof)
3. Complex Numbers
   1. Polar form of complex numbers
   2. De Moivre's theorem and its application in finding roots
   3. Properties of cube roots of unity
   4. Euler's formula
4. Sequence and Series
   1. Sum of finite natural numbers, squares, cubes of first n natural numbers
   2. Principle of mathematical induction and use it to find sum
5. Matrix Based System of Linear Equations
   1. Solution by Cramer's rule up to three variables
   2. Solution by matrix method (row-equivalent and inverse) up to three variables

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Unit 2: Trigonometry (12)

1. Properties of a triangle — Sine law, Cosine law, Tangent law, Projection laws, Half angle laws
2. Solution of triangle (simple cases)

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Unit 3: Analytic Geometry (20)

1. Conic Section:Condition of tangency of a line at a point to the circle, Tangent and normal to a circle, Standard equation of parabola & Equations of tangent and normal to a parabola,Standard equations of Ellipse and Hyperbola

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Unit 4: Vectors (12)

1. Product of Vectors: Scalar product of two vectors, angle between two vectors, geometric interpretation of scalar product, properties of scalar product, application of scalar product in geometry and trigonometry, vector product of two vectors, geometrical interpretation of vector product, properties of vector product, application of vector product in geometry and trigonometry.

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Unit 5: Statistics and Probability (12)

1. Correlation, nature of correlation, correlation coefficient by Karl Pearson's method, interpretation of correlation coefficient, properties of correlation coefficient (without proof), rank correlation (only elementary concept), regression equation, regression line of y on x and x on y.
2. Probability — Dependent cases, conditional probability (without proof)

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Unit 6: Calculus (48)

1. Derivative: Rules for differentiating hyperbolic function and inverse hyperbolic function, L’Hospital's rule \(\frac{0}{0},\frac{\infty}{\infty}\), differentials, tangent and normal, derivative as rate of measure.
2. Anti-derivatives: Antiderivatives of standard integrals, integrals reducible to standard forms, integrals of rational function.
3. 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.

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Unit 7: Computational Methods (12)

1. System of linear equations — Gauss Elimination Method, Gauss Seidel Method
2. Linear Programming Problems (LPP) — Simplex method (two variables only)

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Unit 7: Mechanics (12)

1. Statics — Triangle law of forces and Lami's theorem
2. Dynamics — Newton's laws of motion and projectile

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Sample Project / Practical Works

Projects

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. Verify the sine law by taking particular triangle in four quadrants.
3. Verifications of
   1. Cosine law
   2. Projection law
4. Construction of ellipse by using a piece of pencil, rope and nails
5. Prepare a concrete material to show parabola by using thread and nail in wooden panel.
6. Construct an ellipse using a rectangle.
7. Express the area of triangle and parallelogram in terms of vector.
8. 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.
9. 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.
10. Find, how many peoples will be there after 5 years in your districts by using the concept of differentiation.
11. Verify that the integration is the reverse process of differentiation with examples and curves.
12. Identify different applications of Newton's law of motion and related cases in our daily life.
13. Investigate a daily life problem on projectile motion. Solve that problem and present in the classroom.
14. Write any one real life problem related to linear programming problem and solve that problem by using simplex method.

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Student Assessment

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 mathematics 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:

1. Inductive and deductive method
2. Problem solving method
3. Case study
4. Project work method
5. Question answer and discussion method
6. Discovery method/ use of ICT
7. Co-operative learning

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.

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:

Internal Evaluation (25 Marks)

Classroom Participation	Terminal Examinations	Project / Practical Work	Total
3	6	16	25

Classroom participation

Marks for classroom participation is 3 which is given on the basis of attendance and participation of students in classroom activities in each grade.

Marks from trimester examinations

At least two trimester examination should be conducted in each grade. Marks obtained by the students in trimester examinations will be converted into 6 full marks.

Project work/practical work

A mark for project work/practical work is 16. Criteria for marking practical works/project works

S. N.	Criteria	Marks
1.	Practical works/Project works	10
2.	Presentation and record keeping	6
		16

External / Final Examination (75 Marks)

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.

Secondary Education Examination
Specification Grid, 2078

Grade: 11 and 12Subject: Mathematics (Mat. 007 and 008)

SN	Content Area	Working hour	Competency level																						Area wise Marks	No. of Questions
			Knowledge (16%)				Understanding (24%)						Application (40%)						Higher Ability (20%)
			MCQ		SAQ		MCQ		SAQ		LAQ		MCQ		SAQ		LAQ		MCQ		SAQ		LAQ
			No. of Questions	Marks	No. of Questions	Marks	No. of Questions	Marks	No. of Questions	Marks	No. of Questions	Marks	No. of Questions	Marks	No. of Questions	Marks	No. of Questions	Marks	No. of Questions	Marks	No. of Questions	Marks	No. of Questions	Marks
1	Algebra	44	2	2	2	10	5	5	1	5	1	8	2	2	4	20	1	8	2	2	1	5	1	8	20	MCQ: 2 SAQ: 2 LAQ: 1
2	Trigonometry	12																							6	MCQ: 3
3	Analytic Geometry	20																							9	SAQ: 2 LAQ: 1
4	Vector	12																							6
5	Statistics & Probability	12																							6	MCQ: 1 SAQ: 1
6	Calculus	48																							22	MCQ: 4 SAQ: 2 LAQ: 1
7	Computational methods or Mechanics	12																							6	MCQ: 1 SAQ: 1
Total			12				18						30						15						75	MCQ: 11 SAQ: 8 LAQ: 3

Question format plan
S.N.	Types of Questions	Marks per question	Number of questions				Total number of questions	Total Marks
			Knowledge	Understanding	Application	Higher Ability
1.	Multiple Choice Question	1	2	5	2	2	11	11
2.	Short Answer Question	5	2	1	4	1	8	40
3.	Long Answer Question	8	0	1	1	1	3	24
Grand Total			4	7	7	4	22	75

Note:

• ▪Appropriate extra time will be provided for the handicapped students and the alternative questions to the figure-based questions should be prepared for blind students.
• ▪Questions should be prepared by giving the context and one question may have more than one sub-questions.
• ▪Application and higher ability questions can be made by relating the other content areas.
• ▪Questions should be made by addressing all the sub-areas of content.
• ▪At least one multiple choice question should be asked from each area (Trigonometry, Analytic geometry and Vector).

Marks Distribution by Competency

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Grade XI & XII · NEB Mathematics · Nepal CDC 2078 · Full Marks: 75 · 160 Working Hours