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
   1. Condition of tangency of a line at a point to the circle
   2. Tangent and normal to a circle
   3. Standard equation of parabola & Equations of tangent and normal to a parabola
   4. Standard equations of Ellipse and Hyperbola

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Unit 4: Vectors (12)

1. Product of Vectors — Scalar product, angle between two vectors, geometric interpretation, properties; Vector product, geometrical interpretation, properties, application in geometry & trigonometry.

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Unit 5: Statistics and Probability (12)

1. Correlation and Regression — Karl Pearson's method, rank correlation, regression equations
2. Probability — Dependent cases, conditional probability

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Unit 6: 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 by using concrete materials.
2. Verify the sine law by taking particular triangle in four quadrants.
3. Construct an ellipse using a piece of pencil, rope and nails.
4. Express the area of triangle and parallelogram in terms of vector.
5. Collect grades of 10 students in English and Mathematics; find correlation coefficient.
6. Find projected population of your district after 5 years using differentiation.
7. Identify applications of Newton's law of motion in daily life.

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