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 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
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
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)
- Permutation and Combination
- Basic principle of counting
- Permutation of (a) set of objects all different (b) not all different (c) circular arrangement (d) repeated use
- Combination of things all different, Properties of combination
- Binomial Theorem
- Binomial theorem for a positive integer, general term, Binomial coefficient
- Binomial theorem for any index (without proof), application to approximation
- Euler's number, Expansion of \( e^x, a^x, \log(1+x) \) (without proof)
- Complex Numbers
- Polar form of complex numbers
- De Moivre's theorem and its application in finding roots
- Properties of cube roots of unity
- Euler's formula
- Sequence and Series
- Sum of finite natural numbers, squares, cubes of first n natural numbers
- Principle of mathematical induction and use it to find sum
- Matrix Based System of Linear Equations
- Solution by Cramer's rule up to three variables
- Solution by matrix method (row-equivalent and inverse) up to three variables
Unit 2: Trigonometry (12)
- Properties of a triangle — Sine law, Cosine law, Tangent law, Projection laws, Half angle laws
- Solution of triangle (simple cases)
Unit 3: Analytic Geometry (20)
- 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
Unit 4: Vectors (12)
- Product of Vectors — Scalar product, angle between two vectors, geometric interpretation, properties; Vector product, geometrical interpretation, properties, application in geometry & trigonometry.
Unit 5: Statistics and Probability (12)
- Correlation and Regression — Karl Pearson's method, rank correlation, regression equations
- Probability — Dependent cases, conditional probability
Unit 6: Computational Methods (12)
- System of linear equations — Gauss Elimination Method, Gauss Seidel Method
- Linear Programming Problems (LPP) — Simplex method (two variables only)
Unit 7: Mechanics (12)
- Statics — Triangle law of forces and Lami's theorem
- Dynamics — Newton's laws of motion and projectile
Sample Project / Practical Works
Projects
- Represent the binomial theorem of power 1, 2, and 3 by using concrete materials.
- Verify the sine law by taking particular triangle in four quadrants.
- Construct an ellipse using a piece of pencil, rope and nails.
- Express the area of triangle and parallelogram in terms of vector.
- Collect grades of 10 students in English and Mathematics; find correlation coefficient.
- Find projected population of your district after 5 years using differentiation.
- Identify applications of Newton's law of motion in daily life.
Student Assessment
Internal Evaluation (25 Marks)
| Classroom Participation | Terminal Examinations | Project / Practical Work | Total |
|---|---|---|---|
| 3 | 6 | 16 | 25 |
External / Final Examination (75 Marks)
Marks Distribution by Competency
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