Department of Pre-University Education, KarnatakaPUC Karnataka Commerce Class 12

# Basic Mathematics Class 12 PUC Karnataka Commerce Department of Pre-University Education, Karnataka Topics and Syllabus

## Units and Topics

#Unit/TopicMarks
100 Algebra -
200 Commercial Arithmetic -
300 Trigonometry -
400 Analytical Geometry -
500 Calculus -
Total -

## Syllabus

100 Algebra
101 Matrices and Determinants
• Introduction
• Matrices
• Types of Matrices
• Algebra of Matrices
• Determinants
• Expansion or evaluation of a determinant
• Properties of Determinants
• Solution of Linear Equations – (Cramer’s Rule / det method)
• Minors and Cofactor and Adjoint of a square matrix
• Singular and non-singular Matrices
• Inverse of a Matrix
• Solution of system of Linear Equations by Matrix method
• Application Problems to Commerce
102 Permutations and Combinations
• Introduction
• The Factorial
• Fundamental Principle of Counting
• Permutation vs. Combination
• Permutations
• Types of Permutations
• Circular Permutations
• Combinations
103 Probability
• Introduction
• Definitions and some important terms
• Three systematic approach
• Classical or Mathematical approach
• Conditional Probability
• Multiplication theorem
104 Binomial Theorem
• Introduction
• Binomial Theorem
• General Term in the Binomial Expansion
• Middle Term in the Binomial Expansion
• Term independent of ‘x’ in the Binomial Expansion
• Co-efficient of a particular power of x in the Binomial Expansion
• Application Problems
105 Partial Fractions
• Introduction
• Rational Fractions
• Proper and Improper Fractions
• Reduction of Improper Fraction to the sum of a polynomial and a proper rational fraction
• Partial Fractions
106 Mathematical Logic
• Introduction
• Proportion and Truth Values
• Logical Connectives
• Logical Equivalences
• Converse, Inverse and Contra positive of a conditional
200 Commercial Arithmetic
201 Ratio and Proportions
• Introduction
• Ratio
• Porporation
• Properties of Proportions
• Time and Work, Time and Distance and Mixtures
202 Bill Discounting
• Bill of Exchange
• Discount Date
• Discount Period
• Discount Rate
• True Present Value
• Discount (i) True Discount (ii) Banker’s Discount
• Banker’s Gain
• Discounted Value of the Bill
203 Stocks and Shares
• Introduction
• Definition of a Stock
• Nominal Interest (or Dividend)
• Yield
• Brokerage
204 Learning Curve
• Introduction
• Learning Curve
• Learning Curve Ratio
• Learning Effect
• Learning Curve Equation
205 Linear Programming Problems (Lpp)
• Introduction
• Definition of Linear Programming
• Formulation of Linear Programming
• Graphical Solutions for Linear Programming Problems
206 Sales Tax and Value Added Tax

Introduction
Sales Tax (ST)

300 Trigonometry
301 Heights and Distances

Introduction
Angle of Elevation and Angle of Depression

302 Compound Angles, Multiple Angles, Submultiple Angles and Transformation Formulae
• Introduction
• Trigonometrically Ratios of Compound Angles
• Multiple Angles
• Sub multiple Angles
• Transformation Formulae
400 Analytical Geometry
401 Circles
• Introduction
• Definition and Equation of a circle in different forms.
• General Equation of a Circle
• Length of the Chord of the Circle
• Points of Intersection of a line and a circle (chords and tangents)
402 Parabola
• Introduction to Conic Section - Parabola
• Definition of Parabola and other forms of Parabola
• Four Standard forms of Parabola and their Graphs
500 Calculus
501 Limit and Continuity of a Function
• Introduction
• Variables and Constants
• Definition of a Function
• Types of Functions
• Limit of a Function
• Algebra of Limits
• Evaluation of Limits
• Evaluation of Standard Limits
• Statement of some Standard Limits
• Limit at Infinity and Infinite Limits
• Left Hand and Right Hand Limits
• Continuity of a Function
502 Differential Calculus
• Introduction
• Increment
• Derivative of a Function
• Derivative at a point
• Differentiability
• Relation between Continuity and Differentiability
• Differentiation by the method of first principles
• Algebra of Derivatives of Functions
• Composite Functions
• Differentiation of Implicit Functions
• Derivatives of Infinite Series
• Logarithmic Differentiation
• Differentiation of Parametric functions
• Second order Derivatives
503 Application of Derivatives
• Introduction
• Derivative as a Rate Measure
• ncreasing and Decreasing functions
• Maxima and Minima
• Total cost, Average cost and Marginal Cost
• Total Revenue, Average Revenue and Marginal Revenue
504 Indefinite Integrals
• Introduction
• Primitive and Antiderivative
• Indefinite Integral
• Standard Integrals
• Properties of Indefinite Integrals
• Integration by Substitution
• Integration by Partial Fractions
• Integration by Parts
505 Definite Integral and Its Applications to Areas
• Fundamental theorem of Integral Calculus
• Application of Definite Integrals to area bonded by curves and lines with axes
• Area between curves
• Application of Definite Integrals to cost and revenue functions