NEB Class 12 Mathematics: Complete Syllabus & Notes

Class 12 Mathematics: The Ultimate Syllabus and Curriculum Guide

This guide provides a comprehensive overview of the Class 12 Mathematics curriculum, syllabus, and project works as per the Secondary Education Curriculum 2078.

A visual representation for Class 12 Mathematics concepts.

1. Course Description

Secondary Education Curriculum 2078 – Mathematics

Subject code: Mat. 402 (Grade 12)

Credit hrs: 5 | Working hrs: 160

Introduction

Mathematics is an indispensable tool in many fields. The Class 12 Mathematics curriculum is an extension of the foundation built in previous grades and is essential for higher studies in engineering, medicine, natural sciences, finance, and other disciplines. This course is designed to provide both conceptual and theoretical inputs through various teaching methods, including practical and project works. For more official details, you can visit the NEB official website.

Level-wise Competencies

On completion of the Grade 11-12 course, students will be able to:

  1. Use basic properties of elementary functions and their inverses.
  2. Use principles of combinatorics, binomial theorem, and complex numbers.
  3. Identify and derive equations for conic sections.
  4. Apply vector products in geometry and trigonometry.
  5. Articulate the value of correlation, regression, and probability.
  6. Apply derivatives and anti-derivatives to solve real-world problems.
  7. Apply numerical methods and the simplex method to solve problems.
  8. Use Newton’s laws of motion in solving related problems.

2. Detailed Class 12 Mathematics Syllabus

1. Algebra

  • 1.1 Permutation and combination: Basic principle of counting, Permutations, Combinations.
  • 1.2 Binomial Theorem: Theorem for a positive integer, general term, binomial coefficient, theorem for any index, application to approximation, Euler’s number, Expansion of $e^x, a^x$ and $\log(1+x)$.
  • 1.3 Complex numbers: Polar form, De Moivre’s theorem and its application, properties of cube roots of unity, Euler’s formula.
  • 1.4 Sequence and series: Sum of finite natural numbers, sum of squares, sum of cubes, principle of mathematical induction.
  • 1.5 Matrix based system of linear equation: Solution by Cramer’s rule and matrix method (row-equivalent and inverse) up to three variables.

2. Trigonometry

  • 2.1 Properties of a triangle: Sine law, Cosine law, tangent law, Projection laws, Half angle laws.
  • 2.2 Solution of triangle: Simple cases.

3. Analytic Geometry

  • 3.1 Conic section: Condition of tangency to a 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.

4. Vectors

  • 4.1 Product of Vectors: Scalar product, vector product, their geometric interpretations, properties, and applications.

5. Statistics and Probability

  • 5.1 Correlation and Regression: Correlation coefficient by Karl Pearson’s method, rank correlation, regression equations.
  • 5.2 Probability: Dependent cases, conditional probability.

6. Calculus

  • 6.1 Derivatives: Derivatives of hyperbolic and inverse hyperbolic functions, L’Hospital’s rule ($\frac{0}{0}, \frac{\infty}{\infty}$), differentials, tangent and normal, derivative as rate of measure.
  • 6.2 Anti-derivatives: Anti-derivatives of standard integrals, integrals reducible to standard forms, integrals of rational function.
  • 6.3 Differential equations: Order, degree, equations of first order and first degree (separable, homogenous, linear, exact).

7. Computational Methods Or Mechanics

  • Computational Methods
    • 7.1 System of linear equations: Solved by Gauss Elimination and Gauss-Seidel Method.
    • 7.2 Linear programming: Solved by simplex method.
  • Mechanics
    • 7.1 Resultant forces: Parallelogram law, triangle law, Lami’s theorem.
    • 7.2 Newton’s laws of motion and projectile.
    • 7.3 Resultant of coplanar forces.
    • 7.4 Motion of particle in a straight line.

3. Sample Project/Practical Works

  1. Represent the binomial theorem using concrete materials and relate it to Pascal’s triangle.
  2. Verify the sine law by taking a particular triangle in four quadrants.
  3. Construct an ellipse using a piece of pencil, rope, and nails.
  4. Prepare a concrete material to show a parabola using thread and nails.
  5. Express the area of a triangle and parallelogram in terms of vectors.
  6. Collect grades of students in two subjects, find the correlation coefficient, and analyze the result.
  7. Find two regression equations from a data set and analyze their intersection point.
  8. Estimate the population of your district after 5 years using the concept of differentiation.
  9. Verify that integration is the reverse process of differentiation with examples.
  10. Identify applications of Newton’s laws of motion in daily life.
  11. Investigate and solve a daily life problem involving projectile motion.
  12. Formulate and solve a real-life problem using the simplex method.

4. Chapter-wise Notes

Unit Chapter Name Notes
Algebra
1Algebra
Trigonometry
2Trigonometry
Analytic Geometry
3Analytic Geometry
Vectors
4Vectors
Statistics & Probability
5Statistics and Probability
Calculus
6Calculus
Computational Methods Or Mechanics
7Computational Methods Or Mechanics

5. Class 12 Mathematics Micro-Syllabus

1. Algebra

  1. 1.1 Solve problems related to the basic principle of counting.
  2. 1.2 Solve problems related to permutation and combinations.
  3. 1.3 State and prove the binomial theorem for a positive integral index.
  4. 1.4 State the binomial theorem for any integer.
  5. 1.5 Find the general term and binomial coefficient.
  6. 1.6 Use the binomial theorem in applications to approximation.
  7. 1.7 Define Euler’s number.
  8. 1.8 Expand $e^x, a^x$ and $\log(1+x)$ using the binomial theorem.
  9. 1.9 Express a complex number in polar form.
  10. 1.10 State and prove De Moivre’s theorem.
  11. 1.11 Find the roots of a complex number by De Moivre’s theorem.
  12. 1.12 Solve problems using properties of the cube roots of unity.
  13. 1.13 Apply Euler’s formula.
  14. 1.14 Find the sum of finite natural numbers, sum of squares, and sum of cubes.
  15. 1.15 Use mathematical induction to find sums.
  16. 1.16 Solve a system of linear equations by Cramer’s rule and matrix methods.

2. Trigonometry

  1. 2.1 Solve problems using properties of a triangle (sine law, cosine law, etc.).
  2. 2.2 Solve triangles (simple cases).

3. Analytic Geometry

  1. 3.1 Solve problems related to the condition of tangency of a line to a circle.
  2. 3.2 Find the equations of tangent and normal to a circle.
  3. 3.3 Find the standard equation of a parabola.
  4. 3.4 Find the equations of tangent and normal to a parabola.
  5. 3.5 Obtain standard equations of an ellipse and hyperbola.

4. Vectors

  1. 4.1 Find the scalar product of two vectors, angle between them, and interpret geometrically.
  2. 4.2 Solve problems using properties of the scalar product.
  3. 4.3 Apply the scalar product in trigonometry and geometry.
  4. 4.4 Define vector product of two vectors and interpret geometrically.
  5. 4.5 Solve problems using properties of the vector product.
  6. 4.6 Apply the vector product in geometry and trigonometry.

5. Statistics and Probability

  1. 5.1 Calculate the correlation coefficient by Karl Pearson’s method.
  2. 5.2 Calculate the rank correlation coefficient by Spearman’s method.
  3. 5.3 Interpret the correlation coefficient.
  4. 5.4 Obtain the regression line of y on x and x on y.
  5. 5.5 Solve simple problems of probability using combinations.
  6. 5.6 Solve problems related to conditional probability.

6. Calculus

  1. 6.1 Differentiate the hyperbolic function and inverse hyperbolic function.
  2. 6.2 Evaluate limits by L’Hospital’s rule (for $\frac{0}{0}, \frac{\infty}{\infty}$).
  3. 6.3 Find the tangent and normal by using derivatives.
  4. 6.4 Find the derivative as a rate of measure.
  5. 6.5 Find the anti-derivatives of standard and reducible integrals.
  6. 6.6 Solve differential equations of the first order and first degree.

7. Computational Methods Or Mechanics

Computational methods

  1. 7.1 Solve the system of linear equations by Gauss Elimination and Gauss-Seidel method.
  2. 7.2 Solve linear programming problems (LPP) by the simplex method.

Mechanics

  1. 7.1 Solve forces/vectors related problems using triangle laws of forces and Lami’s theorem.
  2. 7.2 Solve problems related to Newton’s laws of motion and projectile.
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