Class 12 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 (31hrs)

1. Permutation and combination: Basic principle of counting, Permutation of (a) set of objects all different (b) set of objects not all different(c) circular arrangement (d) repeated use of the same objects, Combination of things all different, Properties of combination
2. Binomial Theorem: Binomial theorem for a positive integral index, general term, Binomial coefficient, Binomial theorem for any index (without proof), application to approximation, Euler’s number, Expansion of e*, a° and log(1+x) (without proof)
3. Elementary Group Theory: Binary operation, Binary operation on sets of integers and their properties, Definition of a group, finite and infinite groups. Uniqueness of identity, Uniqueness of inverse, Cancelation law, Abelian group.
4. Complex numbers: De Moivre’s theorem and its application in finding the roots of a complex number, properties of cube roots of unity. Euler’s formula.
5. 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.
6. Sequence and series: Sum of finite natural numbers, sum of squares of first n-natural numbers, Sum of cubes of first n- natural numbers, principle of mathematical induction.
7. Matrix based system of linear equation: Solution of a system of linear equations by Cramer’s rule and matrix method (row- equivalent and inverse) up to three variables.

2. Trigonometry (8hrs)

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

3. Analytic Geometry (13hrs)

1. Conic section: Standard equations of Ellipse and hyperbola.
2. Coordinates in space: direction cosines and ratios of a line, general equation of a plane, equation of a plane in intercept and normal form, plane through 3 given points, plane through the intersection of two given planes, parallel and perpendicular planes, angle between two planes, distance of a point from a plane.

4. Vectors(7hrs)

1. Product of Vectors: vector product of two vectors, geometrical interpretation of vector product, properties of vector product, application of vector product in geometry and trigonometry.

5. Statistics & Probability (9hrs)

1. Correlation and Regression: Correlation, nature of correlation, correlation coefficient by Karl Pearson’s method, interpretation of correlation coefficient, properties of correlation coefficient (without proof), rank correlation by Spearman, regression equation, regression line of y on x and x on y.
2. Probability: Dependent cases, conditional probability (without proof), binomial distribution, mean and standard deviation of binomial distribution (without proof)

6. Calculus (31hrs)

1. Derivatives: derivative of inverse trigonometric, exponential and logarithmic function by definition, relationship between continuity and differentiability, rules for differentiating hyperbolic function and inverse hyperbolic function, L’Hospital’s rule (0/0, ∞/∞), differentials, tangent and normal, geometrical interpretation and application of Rolle’s theorem and mean value theorem.
2. Anti-derivatives: anti-derivatives of standard integrals, integrals reducible to standard forms, integrals of rational function.
3. Differential equations: differential equation and its order, degree, differential equations of first order and first degree, differential equations with separable variables, homogenous, linear and exact differential equations.

7. Computational (10hrs)

1. Linear programming problems (LP): simplex method (maximization problems only)
2. System of linear equations: Gauss Elimination method

8. Methods Mechanics (11hrs)
Or
Mathematics for Economics and Finance (11hrs)

1. Statics: Resultant of like and unlike parallel forces.
2. Dynamics: Newton’s laws of motion and projectile.
3. Mathematics for economics and finance: Consumer and Producer Surplus, Quadratic functions in Economics, Input-Output analysis, Dynamics of market price, Difference equations, The Cobweb model, Lagged Keynesian macroeconomic model.