Quantitative Aptitude for the CA Common Proficiency Test

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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