Quantitative Aptitude for the CA Common Proficiency Test

Cover
Contents
Foreword
Preface
Acknowledgements
About the Author
Part A: Business Mathematics
	Chapter 1: Ratio and Proportion
		Introduction
			Inverse Ratio
			Types of Ratio
				Compound Ratio
				Duplicate Ratio
				Sub Duplicate Ratio
				Triplicate Ratio
				Sub Triplicate Ratio
			Proportion
				Continued Proportion
				Mean Proportional
			Properties of Proportion
		Solved Examples
			Key Points to Remember
		Practice Exercises
		Answers
	Chapter 2: Indices
		Introduction
			Fundamental Laws of Indices
			Meaning of a0
			Meaning of a–n where n is a Positive Integer
			Meaning of ap/q where p and qare Positive Integers
		Solved Examples
			Key Points to Remember
		Practice Exercise
		Answers
	Chapter 3: Logarithms
		Introduction
			Laws of Logarithm
			Logarithms and Antilogarithms
				Common Logarithms
				Characteristic and Mantissa
		Solved Examples
			Key Points to Remember
		Practice Exercise
		Answers
	Chapter 4: Equations
		Linear Equations
			Formation of Linear Equation in One Variable
			Simultaneous Equations in Two or Three Variables
			Simultaneous Equations in Three Variables
		Quadratic Equation
		Cubic Equation
		Co-ordinate Geometry
		Solved Examples
			Key points to Remember
		Practice Exercise
		Answers
	Chapter 5: Inequalities
		Graph of Linear Inequalities
			Linear Inequalities in Two Variables
		Solved Examples
			Key Points to Remember
		Practice Exercise
		Answers
	Chapter 6: Interest and Annuity
		Interest and Annuity
			Simple Interest
				Formula for Calculating Simple Interest
			Compound Interest
				Formula for Calculating Compound Interest
			Annuities
				Leasehold Estate
				Free-hold Estate
				Amortization
				Formula for Future Value of Annuity Regular
				Formula for the Amount of Annuity Due
				Present Value of an Annuity Regular
				Present Value of Deferred Annuity
				Present Value of a Perpetuity
		Solved Examples
			Key points to remember
		Practice Exercise
		Answers
	Chapter 7: Permutations and Continuations
		Permutations and Combinations
			Permutations
			Combinations
		Solved Examples
			Key Points to Remember
		Practice Exercise
		Answers
	Chapter 8: Sequences and Series
		Arithmetic and Geometric Progression
			Arithmetic Progression
				Sum to N Terms
				Properties of an AP
			Arithmetic Mean (AM)
			Arithmetic Means
			Geometric Progression
				Formula for the Sum to N Terms
				Sum to Infinity
			Geometric Mean (GM)
				n Geometric Means Between A and B
		Solved Examples
			Key Points to Remember
		Practice Exercise
		Answers
	Chapter 9: Sets, Relations and Functions
		Sets
			Finite and Infinite Sets
			Description of Sets
				The Tabulation Method
				Set-builder Method
			Singleton Set
			Null Set
			Subset
				Notation
			Equality of Sets
			Number of Subsets of a Set
			Disjoint Sets
			Universal Set
			Set Operations
				Union of Sets
				Intersection of Sets
				Difference of Sets
				Complement of a Set
			Venn Diagram
			Law of Sets
			Number of Elements in a Set
			Cartesian Product
		Relations and Functions
			Identity Relation
			Inverse Relation
			Reflexive Relation
			Symmetric Relation
			Transitive Relation
			Definition
		Function
			Definition
		Types of Functions
			Representation of a Function
		Solved Examples
			Key Points to Remember
		Practice Exercise
		Answers
	Chapter 10: Limits and Continuity
		Introduction
			Limits
			Limit of a Function
				Properties of Limits
			Standard Limit Theorems
			Continuity
				Properties of Continuous Functions
		Solved Examples
			Key Points to Remember
		Practice Exercise
		Answers
	Chapter 11: Differentiation and Integration
		Differentiation
			Logarithmic Differentiation
			Parametric Differentiation
			Differentiation of Implicit Functions
		Integral Calculus
			Arbitrary Constants
			Two General Rules
			Integration by Substitution
			Integration by Partial Fractions
			Integration by Parts
			Definite Integrals
			Properties of Definite Integrals
			Applications of Integration
		Solved Examples
			Key Point to Remember
		Differentiation
		Integration
		Practice Exercise
		Answers
Part B: Statistics
	Chapter 1: Statistical Description of Data
		Introduction
			Statistical Methods
			Limitations of Statistics
			Misuses
		Collection of Data
			The purpose of Inquiry
			Scope of Inquiry
			Sources of Information
			Sources of Secondary Data
			Collection of Primary Data
				Direct Personal Investigation
				Indirect Oral Investigation
				Information Through Correspondents
				Questionnaire by Mail
				Techniques to be Followed by Field Investigators
				Precautions for Preparing Questionnaire
				Statistical Unit
				Standard of Accuracy
				Sample Questionnaire
		Classification and Tabulation
			Qualitative Classification
			Quantitative Classification
			Geographical Classification
			Chronological Classification
			Tabulation
			Frequency Distribution
		Diagrammatic Representation
			Bar Diagrams
			Simple Bar Diagram
			Multiple Bar Diagram
			Component Bar Diagram
			Percentage Bar Diagram
			Pie Diagram
			Pictogram
			Graphical Representation
			Frequency Polygon
			Frequency Curve
			Cumulative Frequency Curve (Ogive)
			Ogive
		Solved Examples
		Practice Exercise
		Answers
	Chapter 2: Measures of Central Tendency
		Arithmetic Mean (AM)
		Weighted Arithmetic Mean
			Formulae for Calculating Arithmeticmean in a Frequency Distribution
			Properties of Arithmetic Mean
		Combined Mean
		Geometric Mean
		Harmonic Mean
		Combined Harmonic Mean
		Merits and Demerits of Arithmetic Mean as an Average
			Merits
			Demerits
		Geometric Mean
			Merits
			Demerits
		Harmonic Mean
			Merits
			Demerits
		Median
			Merits
			Demerits
		Quartiles and Deciles
			Formulae
		Mode
		Merits and Demerits
			Merits
			Demerits
		Mean, Median and Mode
		Solved Examples
			Key Points to Remember
		Practice Exercise
		Answers
	Chapter 3: Measures of Dispersion
		Meaning of Dispersion
			Different Measures of Dispersion
			Range
				Merits and Demerits
			Quartile Deviation
				Merits and Demerits
			Mean Deviation
			Definition
			Relative Measure
				Merits and Demerits
			Standard Deviation
				Formula for Calculating SD
				Merits and Demerits
			Relative Measure
				Formulae
			Combined Mean and SD
			Quartile Deviation
			Mean Deviation
			Standard Deviation
		Solved Examples
			Key Points to Remember
				Formulae
		Practice Exercise
		Answers
	Chapter 4: Correlation and Regression
		Positive Correlation
		Negative Correlation
		No Correlation
		Simple Correlation
		Scatter Diagram
		Numerical Value of the Correlation Coefficient
		Rank Correlation
		Properties of Correlation Coefficient
			Limitations
		Concurrent Deviation
			Methods of Calculating Correlation Coefficient
				Merits
				Demerits
		Probable Error
		Regression
			Explained Variation
		Solved Examples
			Key Points to Remember
				Correlation and Regression
				Regression Lines
		Practice Exercise
		Answers
	Chapter 5: Probability and Expected Value
		Introduction
			Classical Definition
			Addition Theorem
				Odds in Favour and Odds Against an Event
			Axiomatic Approach
			Axioms of Probability
			Addition Theorem
			Conditional Probability
			Multiplication Theorem
			Independent Events
		Permutation
		Combination
			Random Variable and Expected Value
			Probability Mass Function
			Probability Density Function
			Distribution Function
			Expected Value
				Properties
				Variance of a Random Variable
				Properties
		Solved Examples
			Key Points to Remember
				Probability
					Classical Definition
					Statistical Definition
					Modern Definition
					Mutually Exclusive Events
					Mutually Exclusive and Exhaustive Events
					Independent Events
					Conditional Probability
					Odds in Favour of an Event
					Odds Against an Event
					Addition Theorem
					Multiplication Theorem
					Mathematical Expectation (Expected Values)
					Properties of Expected Value
					Standard Deviation
		Practice Exercise
		Answers
	Chapter 6: Theoretical Distributions
		Binomial Distribution
			Definition
			Theorem
			Mode of the Binomial Distribution
			Binomial Frequency Distribution
		Poisson Distribution
			Additive Property of Poisson Random Variables
			Poisson Frequency Distribution
		Normal Distribution
			Characteristic of Normal Distribution
			Standard Normal Probability Distribution
			Additive Property
		Solved Examples
			Key Points to Remember
			Binomial Distributions
			Poisson Distribution
			Normal Distributions
		Practice Exercise
		Answers
	Chapter 7: Sampling Theory
		Preliminary Concepton Sampling
			Types of Samples
				Deliberate, Purpositive or Judgement Sampling
				Quota Sampling
				Cluster Sampling
		Probability Sampling
			Random Sampling
			Stratified Sampling
			Systematic Sampling (Serial Selection)
			Multi-stage Dampling
		Sampling and Non-Sampling Errors
			Large Samples
				Population
				Sample
				Parameter and Statistic
				Sampling Distribution
				Sampling Distribution of Mean
				Characteristics of a Sampling Distribution
				Interpretation of Standard Error of the Mean
				Central Limit Theorem
				Finite Population
				Test of Hypothesis
			Sampling Distribution of Proportion
				Confidence Interval
				Confidence Limits for the Population Mean
				Confidence Interval for Population Proportion
				Determination of Sample Size
				Hypothesis Testing Procedure–one Tailtest and Two Tail Test
			Significance Level
				One Tail Test
				Two Tail Test
				Procedure for Test of Hypothesis
		Solved Examples
			Key Points to Remember
				Sampling Theory
		Practice Exercise
		Answers
	Chapter 8: Index Number
		Introduction
			Methods of Constructionof Index-Numbers
			Unweighted Aggregate Price Index
			Weighted Aggregate Index Number
			Fisher’s Price Index Number
			Bowley’s Price Index Number
				Average of Relative Price Indices
				Unweighted Arithmetic Meanprice Relative Index
				Weighted AM Relative Index
			Quantity Index Number
			Tests for Index Numbers
				Time Reversal Test
				Factor Reversal Test
				Circular Test
			Chain Base Method
			Advantages of Chain Base Index Number
			Cost of Living Index Number
			Uses of Index Numbers
			General Problems in the Construction of Index Numbers
				Purpose of Index Number
				Selection of Items
				Choice of the Base
				Determination of Weights
				Selection of Average
			List of Formulae
				Price Index
				Quantity Index
				Base Shifting
			Splicing of Index Numbers
		Solved Examples
			Key Points to Remember
		Practice Exercise
		Answers
Model Question Papers
	Model Question Paper I
		Answers
	Model Question Paper II
		Answers
	Model Question Paper III
		Answers
	Model Question Paper IV
		Answers
	Model Question Paper V
		Answers
	Model Question Paper VI
		Answers
	Model Question Paper VII
		Answers
Appendix