Class 11 Basic Mathematics

Secondary Education Curriculum
2078
Basic Mathematics

Working hrs: 160

1. Introduction

Mathematics is an indispensable in many fields. It is essential in the field of engineering, medicine, natural sciences, finance and other social sciences. The branch of mathematics concerned with application of mathematical knowledge to other fields and inspires new mathematical discoveries. The new discoveries in mathematics led to the development of entirely new mathematical disciplines. School mathematics is necessary as the backbone for higher study in different disciplines. Mathematics curriculum at secondary level is the extension of mathematics curriculum offered in lower grades (1 to 10) and is the foundation course for higher study.

This course of Mathematics is designed for grade 11 and 12 students who wish to choose as an alternative of Social Study and Life Skill education subject as per the curriculum structure prescribed by the National Curriculum Framework, 2076. This course will be delivered using both the conceptual and theoretical inputs through demonstration and presentation, discussion, and group works as well as practical and project works in the real world context. This course includes different contents like; Algebra, Trigonometry, Analytic Geometry, Vectors, Statistics and Probability, Calculus and Computational Methods or Mechanics.

2. Level-wise Competencies

 On completion of this course, students will have the following competencies:

1. use basic properties of elementary functions and their inverse including linear, quadratic, reciprocal, polynomial, rational, absolute value, exponential, logarithm, sine, cosine and tangent functions.
2. use principles of elementary logic to find the validity of statement and also acquire knowledge of matrix, sequence and series, and combinatory.
3. identify and derive equations for lines, circles, parabolas, ellipses, and hyperbolas.
4. solve the problems related to real and complex numbers.
5.  articulate personal values of statistics and probability in everyday life.
6. use vectors and mechanics in day to day life.
7. apply derivatives to determine the nature of the function and determine the maxima and minima of a function in daily life context.
8. explain anti-derivatives as an inverse process of derivative and use them in various situations.
9. apply numerical methods to solve algebraic equation and calculate definite integrals and use simplex method to solve linear programming problems (LPP).
10. use relative motion, Newton’s laws of motion in solving related problems.

Scope and Sequence of Contents

1. Algebra (33+11hrs)

1. Logic and Set: Statements, logical connectives, truth tables, theorems based on set operations.
2. Real numbers: Geometric representation of real numbers, interval, absolute value.
3. Function: Domain and range of a function, Inverse function, composite function, introduction of types of functions; algebraic (linear, quadratic & cubic), Transcendental (trigonometric, exponential, logarithmic)
4. Curve sketching: Odd and even functions, periodicity of a function, symmetry (about origin, x-and y-axis), monotonicity of a function, sketching the graphs of Quadratic, Cubic and some rational functions (1/×), Trigonometric (Sinx, Cosx), exponential (ex), logarithmic function (Inx)
5. Sequence and series: Arithmetic, geometric, harmonic sequences and series and their properties A.M, G.M, H.M and their relations, sum of infinite geometric series
6. Matrices and determinants: Transpose of a matrix and its properties, Minors and cofactors, Adjoint, Inverse matrix, Determinant, Properties of determinants (without proof)
7. Quadratic equation: Nature and roots of a quadratic equation, Relation between roots and coefficient. Formation of a quadratic equation, Symmetric roots, one or both roots common.
8. Complex number: Imaginary unit, algebra of complex numbers, geometric representation, absolute (Modulus) value and conjugate of a complex numbers and their properties, square root of a complex number

2. Trigonometry (9+3hrs)

1. Inverse circular functions.
2. Trigonometric equations and general values

3. Analytic Geometry (15+5hrs)

1. Straight Line: Length of perpendicular from a given point to a given line, Bisectors of the angles between two straight lines.
2. Pair of straight lines: General equation of second degree in x and y, condition for representing a pair of lines, Homogenous second-degree equation in x and y, angle between pair of lines, Bisectors of the angles between pair of lines
3. Coordinates in space: Points in space, distance between two points, direction cosines and ratios of a line

4. Vectors (9+3hrs)

1. Vectors: Collinear and non collinear vectors, coplanar and non-coplanar vectors, linear combination of vectors, linearly dependent and independent

5. Statistics & Probability (9+3hrs)

1. Measure of Dispersion: Standard deviation, variance, coefficient of variation, Skewness, Karl Pearson’s coefficient of skewness
2. Probability: Independent cases, mathematical and empirical definition of probability, two basic laws of probability (without proof).

6. Calculus (36+12hrs)

1. Limits and continuity: Limits of a function, indeterminate forms. algebraic properties of limits (without proof), Basic theorems on limits of algebraic, trigonometric, exponential and logarithmic functions, continuity of a function, types of discontinuity, graphs of discontinuous function.
2. Derivatives: Derivative of a function, derivatives of Stgebraic, trigonometric, inverse of trigonometric, exponential and logarithmic functions by definition (simple forms), rules of differentiation. derivatives of parametric and implicit functions, higher order derivatives, geometric interpretation of derivative, monotonicity of a function, interval of monotonicity,
3. Extreme values of a function, concavity, points of inflection.
4. Anti-derivatives: Integration using basic integrals, integration by substitution and by parts methods, the definite integral, the definite integral as an area under the given curve, area between two curves.

7. Computational Methods(9+3hrs)

1. Numerical computation: Roots of algebraic and transcendental equation (bisection and Newton Raphson method)
2. Numerical integration: Trapezoidal rule and Simpson’s rule

OR

7. Mechanics (9+3hrs)

1. Statics: Forces and resultant forces, parallelogram law of forces, composition and resolution of forces, Resultant of coplanar forces acting on a point.
2. Dynamics: Motion of particle in a straight line,
3. Motion with uniform acceleration, motion under the gravity, motion down a smooth inclined plane.