# Syllabus of AFC2 Quantitative Methods

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## Syllabus GRID

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## Course Outline

The course outline gives an overview of Syllabus of AFC Quantitative Methods for Winter 2021. The detailed Syllabus of AFC Business Communication for Winter 2021 attempt is given below.

## Mathematics:

### Basic Mathematics:

• Exponential and logarithmic functions
• Equation of straight line
• Application of straight line in business and economics
• Simultaneous equation- linear and quadratic
• Coordinate system
• System of linear inequalities and their graphical presentation
• Factorisation of equations including factorisation by completion of squares
• Arithmetic progression
• Geometric progression

### Financial mathematics:

• Simple interest
• Compound interest
• Present value
• Future value
• Annuities
• Internal rate of return
• Interpolation and perpetuities

### Linear Programming:

• Graphical solution to linear programming problems involving redundant constraints, bounded and unbounded feasible regions, no feasible solution and alternative optimum solution

### Calculus:

• Rules for differentiation- Sum, difference, product and quotient rules of differentiation
• Marginal function, calculation of revenue, cost and profit of marginal unit
• Use of second order derivatives; maxima, minima and point of inflexion.

### Matrices and determinants:

• Fundamentals of matrices, addition, subtraction, multiplication, inverse of matrices
• Solution of simultaneous linear equations using Cramer’s Rule and Matrix Inverse method

## Statistics:

### Presentation and use of data:

• Collection and tabulation of data
• Presentation through graphs, charts and diagrams, including stem and leaf display, box and whisker plot
• Measures of central tendencies and measures of dispersion

### Index numbers:

• Index numbers, weighted index numbers, concept of purchasing power and deflation of income

### Methods of least square and regression:

• Scatter diagram, linear relationship, simple linear regression lines by method of least square
• Simple linear correlation
• Coefficient of correlation and determination
• Rank correlation

### Probability and probability distribution:

• Counting techniques
• probability
• Addition law for mutually exclusive and non-mutually exclusive events
• Multiplicative laws for dependent and independent events
• Binomial distribution
• Poisson distribution
• Hyper-geometric distribution
• Normal distribution

### Sampling and decision making:

• Simple random sampling
• Sampling distribution of mean
• Standard error of mean
• Sampling with and without replacement
• Testing of hypothesis for population means, difference between population means and population proportion and difference between two population proportions
• Single population variance based on test of chi-square
• Confidence interval for estimating population means, proportions and variance, and differences between proportion means, proportion and variance
• Problems of determination of sample size for the study of population mean and proportion

## Course Content:

Here is the detailed Syllabus of AFC Quantitative Methods for Winter 2021.

## Elementary Mathematical operations:

### Elementary mathematical operations:

• Basic techniques
•  Brackets
•  Parts of a whole – fractions
•  Operations involving fractions
•  Other ways of describing parts of a whole
•  Common uses of percentages

### Costs:

• Cost behavior
• Contribution

## Coordinate system and equation of straight line:

### Coordinate system:

• The coordinate system
• Coordinates

### Equations of straight line:

• Slope – intercept form of the equation of a straight line
• Other forms of equations of the straight line

## Solving equations:

### Solving simultaneous equations:

• Introduction
• Solving

• Introduction
• Solving quadratic equations by factorisation
• Solving quadratic equations by completing the square
• Solving quadratic equations by using a formula
• Dividing equations

### Exponential and logarithmic functions :

• Indices
• Laws of indices (exponents)
• Exponential and logarithmic functions
• Using logs
• Laws of logs
• Solving equations

## Mathematical Progression:

### Arithmetic progression:

• Introduction to numerical progressions
• Arithmetic progression
• Value of any term in an arithmetic progression
• Sum of number of terms in an arithmetic progression
• Problem of a more complex nature

### Geometric progression:

• Introduction
• Value of any term in a geometric progression
• Sum of number of terms in a geometric series
• Infinite series

## Financial mathematics: Compounding

### Simple interest:

• Interest
• Simple interest

### Compound interest:

• Compound interest
• Compound interest for non-annual periods
• Nominal and effective rates
• Solving for duration
• Alternative approach to finding the final value of a series of payments receipts

### Annuities:

• Annuities
• Calculating the final value of an annuity
• Sinking funds

## Financial mathematics: Discounting

### Discounting:

• The time value of money
• Discounting
• Discounting tables

### Net present value (NPV) method of investment appraisal:

• Introduction to Discounted Cash Flow (DCF) analysis
• Calculating the NPV of an investment project

### Discounting annuities and perpetuities:

• Annuities
• Perpetuities
• Application of annuity arithmetic

### Internal rate of return (I.R.R):

• Internal rate of return
• Calculating the IRR of an investment project

## Linear programming

Linear inequalities:

•  Linear inequalities
• Boundaries and feasibility regions

Linear programming:

•
• Introduction
• Plotting constraints
• Maximising (or minimising) the objective function
• Slope of the objective function
• Terminology

•  Introduction
• Formulating constraints
• The objective function

## Calculus: Differentiation

Calculus:

•
• Differential calculus (differentiation)
• Slope of curved lines (lines of non-linear equations)
• Estimating the slope
• Differentiating sums

Differentiation of functions which are more complex :

•  Differentiating products
• Differentiating quotients
• Differentiating a function of a function
• Differentiating exponential and logarithmic functions

## Calculus: Turning points, maxima, minima and point of inflexion

Turning points maxima minima and point of inflexion:

•
• Maxima or minima?
• Local maxima and minima
• Points of inflection

Marginal functions:

•  Introduction
• Demand curves in imperfect competition
• Profit maximization

## Matrices and determinants:

### Fundamentals of matrices

•  Introduction to matrices
• Multiplication of matrices
• Properties of specific matrices

Determinants and inverse matrices (2 by 2 matrices):

• Determinant of a matrix
• Inverse of a matrix

Solving simultaneous linear equations with two variables:

• Introduction – basic algebraic solution
• Matrix inverse method
• Cramer’s rule

Determinants and inverse matrices (3 by 3 matrices):

• Determinant of a 3 by 3 matrix
• Inverse of a 3 by 3 matrix

Solving simultaneous linear equations with more than two variables:

• Cramer’s rule

## Collection, tabulation and presentation of data:

### Collection and tabulation of data:

• Introduction
• Different types of data
• Data collection
• Organising and summarising data
• Frequency distributions
• Tally
• Class boundaries

### Graphics charts and diagrams:

• Introduction
• Bar charts and pie charts
• Plots of grouped frequency distributions
• Graphical representations of data

## Statistical measures of data:

### Measures of central tendency:

• Introduction
• Mean, median and mode – ungrouped data
• Mean, median and mode – grouped data (frequency distributions)
• Combined arithmetic mean
• Weighted arithmetic mean
• Geometric mean
• Harmonic mean
• Measures of central tendency compared

### Measures of dispersion:

• Introduction
• Range and semi inter-quartile range
• Standard deviation and variance
• Measures of dispersion compared

### Skew:

• Symmetry and skewness
• Direction of skew
• Degree of skew

## Regression and Correlation:

### Linear regression analysis:

• Introduction
• Scatter diagrams
• Linear regression analysis

### Correlation and correlation coefficient:

• Correlation
• Degrees of correlation
• Correlation coefficient, r
• Coefficient of determination, r2
• Spearman’s rank correlation coefficient

## Indices:

### Index numbers:

• The purpose of index numbers
• Base of 100 or 1,000
• Price indices and quantity indices
• Constructing index numbers
• Index numbers with more than one item

### Weighted indices:

• Introduction
• Price indices
• Laspeyre and Paasche – comments
• Fisher index
• Quantity indices
• Chained index series

### Inflating and deflating data:

• Impact of inflation
• Dealing with inflation

## Counting methods and probability:

### Counting the number of possible outcomes:

• mn counting rule
• Permutations
• Permutations of a selection from a larger group
• Combinations of a selection from a larger group (order does not matter)

### Probability:

• Basic probability
• Addition law (OR law) – Mutually exclusive events
• Multiplication law (AND law) – Independent events
• Addition law – Non-mutually exclusive events
• Multiplication law – Dependent events (conditional probability)
• Conditional probability revisited
• Complementary probabilities
• Introduction to probability distributions

## Probability Distributions:

### Binomial distribution:

• Introduction
• The distribution
• Formulae

### Hyper- Geometric distribution:

• Introduction
• Hyper-geometric distribution formula

### Poisson distribution:

• Introduction
• Formulae
• Poisson distribution tables
• Problems of a more complex nature
• Poisson as an approximation for the binomial distribution

### Normal distribution:

• Introduction
• Properties of a normal distribution
• using the normal distribution

### Normal approximations:

• Introduction
• Normal approximation to the binomial distribution
• Normal approximation to the Poisson distribution
• Summary

## Sampling:

• Introduction
• Random sampling
• Systematic sampling
• Stratified sampling
• Other sampling methods
• An introduction to sampling theory

## Sampling distribution of mean:

• Sampling distribution of the mean
• Standard error
• Estimating population means
• Confidence levels
• Improving accuracy

## Sampling distribution of proportion:

• Introduction and standard error
• Estimating population proportion
• Improving accuracy

## Small samples:

• Introduction
• Estimation of population mean
• Confidence intervals- summary

## Introduction to significance testing:

• Significance testing
• Overall approach
• Alternate hypothesis type of test

## Significance tests of means:

• Significance testing
• Types of error
• One tailed test

## Significance test of difference between two means :

• Sampling distribution of the difference between two means
• Significance test – Example

• Examples

## Significance test involving differences of proportions:

• Sampling distribution of difference between population proportions

## Significance tests of small samples:

• Significance tests

## Chi Square testing:

### Chi square testing:

• Introduction
• Goodness of fit
• Tests of association
• 2 × 2 contingency tables

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