Indianbooklet.com COMMON PROFICIENCY TEST m o c . t QUANTITATIVE e l k APTITUDE o o b n a i d n I Indianbooklet.com Indianbooklet.com PREFACE D m eveloping Quantitative Aptitude is important for the students of Chartered Accountancy Course as professional work in future will demand analytical and quantitative skills. Through this section of CPT, it is intended to develop analytical ability of the students using basic mathematical and statistical techniques. By this, students will be equipped with the knowledge to absorb various concepts of other subjects of the o chartered accountancy course like accounting, auditing and assurance, financial management, cost accounting, management accounting, etc. c The first part of the study material (Chapters 1 - 9) covers basic mathematical techniques like ratio, proportion, indices, logarithms, equations and inequalities, simple and compound interests, permutations . and combinations, sequence and series, sets, relations and basics of differential integral calculus. The t second part of the study material (Chapters 10 – 16) covers basic principles of statistical techniques and measurement thereof. e The entire study material has been written in a simple and easy to understand language. A number of l illustrations have been incorporated in each chapter to explain various concepts and related computational k techniques dealt within each chapter. A reasonably good question bank has been included in the study material which will help the students to prepare for the CPT examination. o This study material has been prepared by a team of experts comprising of Dr. Bishwapati Chaudhuri, Prof. Swapan Banerjee, Dean of Commerce St. Xavier College, Kolkata, Dr. Sampa Bose, Dr. Shaligram Shukla, o CA. Anjan Bhattacharyya, Shri Indrajit Das, Dr. S.K.Chatterjee, Former Additional Director (SG) and Shri A.K. Aggarwal, Former Additional Director of ICAI. The entire work was co-ordinated by Shri S. Bardhan, Assistant Director, EIRC of the bICAI. n a i d n I Indianbooklet.com Indianbooklet.com SYLLABUS Quantitative Aptitude (50 Marks) Objective : m To test the grasp of elementary concepts in Mathematics and Statistics and application of the same as useful quantitative tools. Contents o 1. Ratio and proportion, Indices, Logarithms c 2. Equations Linear – simultaneous linear equations up to three variables, quadratic and cubic equations in one . variable, equations of a straight line, intersection of straight lines, graphical solution to linear equa- tions. t 3. Inequalities e Graphs of inequalities in two variables – common region. 4. Simple and Compound Interest including annuity – Appllications 5. Basic concepts of Permutations and Combinations k 6. Sequence and Series – Arithmetic and geometric progressions o 7. Sets, Functions and Relations 8. Limits and Continuity – Intuitive Approach o 9. Basic concepts of Differential and Integral Calculus (excluding trigonometric functions) 10. Statistical description of data b (a) Textual, Tabular & Diagrammatic representation of data. (b) Frequency Distribution. n (c) Graphical representation of frequency distribution – Histogram, Frequency Polygon, Ogive 11. Measures of Central Tendency and Dispersion a Arithmetic Mean, Median – Partition Values, Mode, Geometric Mean and Harmonic, Mean, Standard deviation, Quartile deviation 12. Correlation andi Regression d 13. Probability and Expected Value by Mathematical Expectation 14. Theoretical Distributions n Binomial, Poisson and Normal. 15. Sampling Theory I Basic Principles of sampling theory , Comparison between sample survey and complete enumeration, Errors in sample survey, Some important terms associated with sampling, Types of sampling, Theory of estimation, Determination of sample size. 16. Index Numbers Indianbooklet.com Indianbooklet.com CONTENTS MATHEMATICS m Chapter 1 - Ratio and Proportion, Indices, Logarithms 1.1 Ratio 1.2 o 1.2 Proportion 1.7 1.3 Indices 1.14 c 1.4 Logarithm 1.22 Additional Question Bank 1.34 . Chapter 2 - Equations t e 2.1 Introduction 2.2 2.2 Simple Equation 2.2 l 2.3 Simultaneous Linear Equations in two unknowns 2.6 k 2.4 Method of Solution 2.6 2.5 Method of Solving Simultaneous Lineaor Equation with three variables 2.8 2.6 Problems Leading to Simultaneous Equations 2.13 o 2.7 Quadratic Equation 2.15 2.8 How to Construct a Quadratic Equation 2.16 b 2.9 Nature of the Roots 2.16 2.10 Problems on Quadratic Equation 2.23 n 2.11 Solution of Cubic Equation 2.26 2.12 Application oaf Equations in Co-ordinate Geometry 2.28 2.13 Equation of a Straight Line 2.29 i 2.14 Graphical Solution to Linear Equations 2.35 d Additional Question Bank 2.39 n Chapter 3 - Inequalities I3.1 Inequalities 3.2 3.2 Linear Inequalities in one variable and the Solution space 3.2 Additional Question Bank 3.19 Indianbooklet.com Indianbooklet.com CONTENTS Chapter 4 - Simple and Compound Interest Including Annuity - Applications m 4.1 Introduction 4.2 4.2 Why is Interest Paid? 4.2 4.3 Definition of Interest and some other Related Terms 4.3 o 4.4 Simple Interest and Compound Interest 4.3 4.5 Effective Rate of Interest c 4.17 4.6 Annuity 4.21 . 4.7 Future Value 4.23 t 4.8 Present Value 4.27 e 4.9 Sinking Fund 4.33 4.10 Applications 4.34 l k Additional Question Bank 4.39 o Chapter 5 - Basic Concepts of Permutations and Combinations 5.1 Introduction o 5.2 5.2 The Factorial 5.3 5.3 Permutations b 5.3 5.4 Results 5.5 5.5 Circular Permutations 5.9 n 5.6 Permutation with Restrictions 5.10 5.7 Combinations 5.15 a 5.8 Standard Results 5.22 Additional Question Bank 5.31 i d Chapter 6 - Sequence and Series - Arithmetic and Geometric Progressions n 6.1 Sequence 6.2 6.2 Series 6.3 I 6.3 Arithmetic Progression (A.P.) 6.3 6.4 Geometric Progression (G.P.) 6.9 6.5 Geometric Mean 6.11 Additional Question Bank 6.21 Indianbooklet.com Indianbooklet.com CONTENTS Chapter 7 - Sets, Functions and Relations m 7.1 Sets 7.2 7.2 Venn Diagrams 7.5 7.3 Product Sets 7.9 o 7.4 Relations and Functions 7.10 7.5 Domain & Range of a Function 7.10 c 7.6 Various Types of Function 7.10 Additional Question Bank 7.22 . t Chapter 8 - Limits and Continuity - Intuitive Approach e 8.1 Introduction 8.2 8.2 Types of Functions l 8.3 8.3 Concept of Limit k 8.5 8.4 Useful Rules of Theorems on Limits 8.7 o 8.5 Some Important Limits 8.8 8.6 Continuity 8.16 o Additional Question Bank 8.24 Chapter 9 - Basic Concbepts of Differential and Integral Calculus (A) Differential Calculus n 9.A.1 Introduction 9.2 9.A.2 Derivative or Differential Coefficient 9.2 a 9.A.3 Some Standard Results (Formulas) 9.5 9.A.4 Derivative of a Function of Function 9.8 i 9.A.5 Implicit Functions 9.8 d 9.A.6 Parametric Equation 9.9 9.A.7 Logarithmic Differentiation 9.9 n 9.A.8 Some More Examples 9.10 9.A.9 Basic Idea about Higher Order Differentiation 9.12 I 9.A.10 Geometric Interpretation of the Derivative 9.13 (B) Integral Calculus 9.B.1 Integration 9.18 9.B.2 Basic Formulas 9.19 Indianbooklet.com Indianbooklet.com CONTENTS 9.B.3 Method of Substitution (change of variable) 9.21 9.B.4 Integration By Parts m9.23 9.B.5 Method of Partial Fraction 9.24 9.B.6 Definite Integration 9.27 9.B.7 Important Properties o 9.28 Additional Question Bank 9.37 c STATISTICS Chapter 10 - Statistical Description of D.ata t 10.1 Introduction of Statistics 10.2 e 10.2 Collection of Data 10.4 10.3 Presentation of Data 10.6 l 10.4 Frequency Distribution 10.14 k 10.5 Graphical representation of Frequency Distribution 10.19 Additional Question Bank 10.37 o Chapter 11 - Measures of Central Tendency and Dispersion o 11.1 Definition of Central Tendency 11.2 11.2 Criteria for an ideal measure of Central Tendency 11.2 b 11.3 Arithmetic Mean 11.3 11.4 Median – Partition Values 11.8 n 11.5 Mode 11.14 11.6 Geometric Mean and Harmonic Mean 11.15 a 11.7 Exercise 11.23 11.8 Definition ofi Dispersion 11.30 11.9 Range d 11.31 11.10 Mean Deviation 11.32 11.11 Stanndard Deviation 11.38 11.12 Quartile Deviation 11.47 11.13IExercise 11.54 Additional Question Bank 11.61 Indianbooklet.com Indianbooklet.com CONTENTS Chapter 12 - Correlation and Regression m 12.1 Introduction 12.2 12.2 Bivariate Data 12.2 12.3 Correlation Analysis 12.5 o 12.4 Measures of Correlation 12.6 12.5 Regression Analysis 12.25 c 12.6 Properties of Regression Lines 12.34 12.7 Review of Correlation and Regression Analysis . 12.37 Additional Question Bank t 12.51 e Chapter 13 - Probability and Expected Value by Mathematical Expectation 13.1 Introduction l 13.2 k 13.2 Random Experiment 13.2 13.3 Classical Definition of Probability 13.3 o 13.4 Statistical Definition of Probability 13.8 13.5 Operations on Events: Set Theoretic Approach to Probability 13.10 o 13.6 Axiomatic or Modern Definition of Probability 13.13 13.7 Addition Theorems 13.14 b 13.8 Conditional Probability and Compound Theorem of Probability 13.17 13.9 Random Variable-Its Probability Distribution 13.26 n 13.10 Expected Value of a Random Variable 13.28 Additional Question Bank 13.49 a Chapter 14 - Theoretical Distributions i 14.1 Introductidon 14.2 14.2 Binomial Distribution 14.3 14.3 Poisnson Distribution 14.10 14.4 Normal Distribution or Gaussian Distribution 14.19 14.5 IChi-square Distribution, t-Distribution and F-Distribution 14.33 Additional Question Bank 14.49 Indianbooklet.com Indianbooklet.com CONTENTS Chapter 15 - Sampling Theory m 15.1 Introduction 15.2 15.2 Basic Principles of Sample Survey 15.3 15.3 Comparison between Sample Survey and Complete Enumeration o 15.4 15.4 Errors in Sample Survey 15.4 15.5 Some important terms associated with Sampling c 15.5 15.6 Types of Sampling 15.11 . 15.7 Theory of Estimation 15.14 t 15.8 Determination of sample size for a Specific Precision 15.23 e Additional Question Bank 15.31 l Chapter 16 - Index Numbers k 16.1 Introduction 16.2 o 16.2 Issues Involved 16.3 16.3 Construction of Index Number 16.3 o 16.4 Usefulness of Index Numbers 16.10 16.5 Deflating Time Series using Index Numbers 16.10 b 16.6 Shifting and Splicing of Index Numbers 16.11 16.7 Test of Adequacy 16.12 n Additional Question Bank 16.20 a Appendices i d n I Indianbooklet.com Indianbooklet.com M A m T o H c . E t e M l k A o o T b I n C a i S d n I Indianbooklet.com