NEB Class 11 Mathematics: Complete Syllabus & Notes

Class 11 Mathematics: The Ultimate Syllabus and Curriculum Guide

This guide provides a comprehensive overview of the Class 11 Mathematics curriculum, syllabus, and project works as per the Secondary Education Curriculum 2078.

A visual representation for Class 11 Mathematics concepts.

1. Course Description

Secondary Education Curriculum 2078 – Mathematics

Subject code: Mat. 401 (Grade 11)

Credit hrs: 5 | Working hrs: 160

Introduction

Mathematics is indispensable in many fields, including engineering, medicine, natural sciences, finance, and other social sciences. This course for Grade 11 and 12 is designed for students who wish to pursue further studies where a strong mathematical foundation is required. It includes content like Algebra, Trigonometry, Analytic Geometry, Vectors, Statistics and Probability, Calculus, and Computational Methods or Mechanics.

Level-wise Competencies

Upon completion, students will be able to:

  1. Use basic properties of elementary and inverse functions.
  2. Use principles of elementary logic, matrices, sequences, and combinatorics.
  3. Identify and derive equations for lines and conic sections.
  4. Solve problems related to real and complex numbers.
  5. Articulate the value of statistics and probability in everyday life.
  6. Apply derivatives to determine the nature and extrema of functions.
  7. Explain and use anti-derivatives in various situations.

2. Detailed Class 11 Mathematics Syllabus

1. Algebra

  • 1.1 Logic and Set: Statements, logical connectives, truth tables, theorems based on set operations.
  • 1.2 Real numbers: Geometric representation, interval, absolute value.
  • 1.3 Function: Domain and range, Inverse function, composite function, types of functions.
  • 1.4 Curve sketching: Odd/even functions, periodicity, symmetry, monotonicity, graphs of quadratic, cubic, rational ($\frac{1}{ax+b}$), trigonometric ($a\sin(bx), a\cos(bx)$), exponential ($e^x$), and logarithmic ($\ln x$) functions.
  • 1.5 Sequence and series: Arithmetic, geometric, harmonic sequences; AM, GM, HM and their relations; sum of infinite geometric series.
  • 1.6 Matrices and determinants: Transpose, Minors, cofactors, Adjoint, Inverse matrix, Properties of determinants.
  • 1.7 Quadratic equation: Nature of roots, relation between roots and coefficient, symmetric roots.
  • 1.8 Complex number: Algebra, geometric representation, modulus, conjugate, square root.

2. Trigonometry

  • 2.1 Inverse circular functions.
  • 2.2 Trigonometric equations and general values.

3. Analytic Geometry

  • 3.1 Straight Line: Length of perpendicular, Bisectors of angles.
  • 3.2 Pair of straight lines: General equation of second degree, angle between lines, Bisectors of angles.
  • 3.3 Coordinates in space: Distance between two points, direction cosines and ratios.

4. Vectors

  • 4.1 Vectors: Collinear, non-collinear, linearly dependent/independent, coplanar/non-coplanar vectors, linear combination.

5. Statistics and Probability

  • 5.1 Measure of Dispersion: Standard deviation, variance, coefficient of variation, Skewness.
  • 5.2 Probability: Independent cases, mathematical and empirical definition, two basic laws of probability.

6. Calculus

  • 6.1 Limits and continuity: Limits, indeterminate forms, continuity, types of discontinuity.
  • 6.2 Derivatives: Derivatives by definition, rules of differentiation, parametric and implicit functions, higher order derivatives, monotonicity, extreme values, concavity, points of inflection.
  • 6.3 Anti-derivatives: Integration by substitution and parts, the definite integral, area under a curve, area between two curves.

7. Computational Methods Or Mechanics

  • Computational Methods
    • 7.1 Numerical computation: Roots of equations (bisection and Newton-Raphson method).
    • 7.2 Numerical integration: Trapezoidal rule and Simpson’s rule.
  • Mechanics
    • 7.1 Statics: Resultant forces, parallelogram law, composition and resolution of forces.
    • 7.2 Dynamics: Motion in a straight line, uniform acceleration, motion under gravity, motion on an inclined plane.

3. Sample Project/Practical Works

  1. Find the area of a shaded region by continuously dividing a square.
  2. Demonstrate truth values of conjunction and disjunction using logic gate circuits.
  3. Prepare a model to illustrate values of sine and cosine functions.
  4. Draw the graph of $\cos^{-1}x$ using the graph of $\cos x$ and demonstrate mirror reflection.
  5. Derive the length of the perpendicular from a point to a line.
  6. Verify the equation of a line passing through the intersection of two lines.
  7. Verify the angle in a semi-circle is a right angle using vectors.
  8. Collect scores of students, create frequency distributions, and compare the consistency.
  9. Analyze outcomes of rolling two dice simultaneously 20 times.
  10. Research and present applications of derivatives in daily life.
  11. Find the area of a circular region around your school using integration.
  12. Find the roots of a polynomial equation using ICT tools.

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 11 Mathematics Micro-Syllabus

1. Algebra

  1. 1.1 Be acquainted with logical connectives and construct truth tables.
  2. 1.2 Prove set identities.
  3. 1.3 Define interval and absolute value of real numbers.
  4. 1.4 Find domain and range of a function.
  5. 1.5 Find inverse function and calculate composite function.
  6. 1.6 Define odd and even functions, periodicity, and monotonicity.
  7. 1.7 Sketch graphs of various functions.
  8. 1.8 Define and classify sequence and series.
  9. 1.9 Solve problems on arithmetic, geometric and harmonic sequences.
  10. 1.10 Establish relation among AM, GM and HM.
  11. 1.11 Find the sum of infinite geometric series.
  12. 1.12 Obtain transpose of matrix and verify its properties.
  13. 1.13 Calculate minors, cofactors, adjoint, determinant and inverse.
  14. 1.14 Solve problems using properties of determinants.
  15. 1.15 Define polynomial function and equation.
  16. 1.16 State and apply fundamental theorem of algebra.
  17. 1.17 Find roots of a quadratic equation and establish relations.
  18. 1.18 Form a quadratic equation with given roots.
  19. 1.19 Define a complex number and solve related problems.
  20. 1.20 Find conjugate and modulus of a complex number.
  21. 1.21 Find square root of a complex number.

2. Trigonometry

  1. 2.1 Define inverse trigonometric functions and establish relations.
  2. 2.2 Find the general solution of trigonometric equations.

3. Analytic Geometry

  1. 3.1 Find the length of perpendicular from a point to a line.
  2. 3.2 Find the equation of bisectors of the angles between two lines.
  3. 3.3 Write the condition for a general second-degree equation to represent a pair of lines.
  4. 3.4 Find the angle and bisectors between a pair of lines.
  5. 3.5 Find distance between points in space, direction cosines and ratios.

4. Vectors

  1. 4.1 Identify collinear and non-collinear vectors.
  2. 4.2 Identify coplanar and non-coplanar vectors.
  3. 4.3 Write linear combination of vectors.
  4. 4.4 Identify linearly dependent and independent vectors.

5. Statistics and Probability

  1. 5.1 Calculate standard deviation, variance and coefficient of variation.
  2. 5.2 Calculate coefficient of skewness by Karl Pearson method.
  3. 5.3 Define terms related to probability.
  4. 5.4 Find probability using the two basic laws.

6. Calculus

  1. 6.1 Define limits of a function.
  2. 6.2 Identify indeterminate forms.
  3. 6.3 Apply algebraic properties of limits.
  4. 6.4 Evaluate limits of various functions.
  5. 6.5 Define and test continuity of a function.
  6. 6.6 Define and classify discontinuity.
  7. 6.7 Interpret derivatives geometrically.
  8. 6.8 Find derivatives by the first principle.
  9. 6.9 Find derivatives using rules of differentiation.
  10. 6.10 Find derivatives of parametric and implicit functions.
  11. 6.11 Calculate higher order derivatives.
  12. 6.12 Check the monotonicity of a function.
  13. 6.13 Find extreme values of a function.
  14. 6.14 Find the concavity of a function.
  15. 6.15 Define integration as reverse of differentiation.
  16. 6.16 Evaluate integrals using basic formulas.
  17. 6.17 Integrate by substitution and by parts.
  18. 6.18 Evaluate the definite integral.
  19. 6.19 Find area between two curves.

7. Computational Methods Or Mechanics

Computational methods

  1. 7.1 Solve equations by bisection and Newton-Raphson method.
  2. 7.2 Integrate numerically by trapezoidal rule and Simpson’s rule.

Mechanics

  1. 7.1 Find resultant forces by parallelogram law.
  2. 7.2 Solve problems on composition and resolution of forces.
  3. 7.3 Obtain resultant of coplanar forces.
  4. 7.4 Solve problems on motion of a particle.

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