KASNEB – QUANTITATIVE ANALYSIS REVISION KIT ( KASNEB PAST PAPERS WITH ANSWERS )

CPA

CIFA

CCP

PART II

SECTION 4

REVISION KIT

PAST EXAMINATION PAST PAPERS WITH SUGGESTED ANSWERS

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PAPER NO.12 QUANTITATIVE ANALYSIS

GENERAL OBJECTIVE
This paper is intended to equip the candidate with knowledge, skills and attitudes that
will enable him/her to use quantitative analysis tools in business operations and
decision making.

12.0    LEARNING OUTCOMES

A candidate who passes this paper should be able to:

• Use mathematical techniques in solving business problems
• Apply set theory in business decision making
• Apply operation research techniques in decision making
• Apply simulation techniques in analysing business situations.

CONTENT

12.1    Mathematical techniques

12.1.1 Functions

• Functions, equations and graphs: Linear, quadratic, cubic,
exponential and logarithmic
• Application of mathematical functions in solving business problems

12.1.2 Matrix algebra

• Types and operations (addition, subtraction, multiplication,
transposition and inversion)
• Application of matrices: statistical modelling, Markov analysis, inputoutput analysis and general applications

12.1.3 Calculus

Differentiation

• Rules of differentiation (general rule, chain, product, quotient)
• Differentiation of exponential and logarithmic functions
• Higher order derivatives: turning points (maxima and minima)
• Ordinary derivatives and their applications
• Partial derivatives and their applications
• Constrained optimisation; Lagrangian multipliers

Integration

• Rules of integration
• Applications of integration to business problems

12.2    Probability

12.2.1 Set theory

• Types of sets
• Set description: enumeration and descriptive properties of sets
• Operations of sets: union, intersection, complement and difference
• Venn diagrams

12.2.2 Probability theory and distribution

Probability theory

• Definitions: event, outcome, experiment, sample space
• Types of events: elementary, compound, dependent, independent,
mutually exclusive, exhaustive, mutually inclusive
• Laws of probability: additive and multiplicative rules
• Baye’s Theorem
• Probability trees
• Expected value, variance, standard deviation and coefficient of
variation using frequency and probability

Probability distributions

• Discrete and continuous probability distributions (uniform, normal,
binomial, poisson and exponential)
• Application of probability to business problems

12.3 Hypothesis testing and estimation

• Hypothesis tests on the mean (when population standard deviation is
unknown)
• Hypothesis tests on proportions
• Hypothesis tests on the difference between means (independent samples)
• Hypothesis tests on the difference between means (matched pairs)
• Hypothesis tests on the difference between two proportions

12.4 Correlation and regression analysis

Correlation analysis

• Scatter diagrams
• Measures of correlation –product moment and rank correlation coefficients
(Pearson and Spearman)
• Regression analysis
• Simple and multiple linear regression analysis
• Assumptions of linear regression analysis
• Coefficient of determination, standard error of the estimate, standard error
of the slope, t and F statistics
• Computer output of linear regression
• T-ratios and confidence interval of the coefficients
• Analysis of Variances (ANOVA)

12.5 Time series

• Definition of time series
• Components of time series (circular, seasonal, cyclical, irregular/ random,
trend)
• Application of time series
• Methods of fitting trend: free hand, semi-averages, moving averages, least
squares methods
• Models – additive and multiplicative models
• Measurement of seasonal variation using additive and multiplicative
models
• Forecasting time series value using moving averages, ordinary least
squares method and exponential smoothing
• Comparison and application of forecasts for different techniques
• Trend projection methods: linear, quadratic and exponential

12.6 Linear programming

• Definition of decision variables, objective function and constraints
• Assumptions of linear programming
• Solving linear programming using graphical method
• Solving linear programming using simplex method
situations
• Interpretation of computer assisted solutions
• Transportation and assignment problems

12.7 Decision theory

• Decision making process
• Decision making environment: deterministic situation (certainty)
• Decision making under risk – expected monetary value, expected
opportunity loss, risk using coefficient of variation, expected value of
perfect information
• Decision trees – sequential decision, expected value of sample information
• Decision making under uncertainty – maximin, maximax, minimax regret,
Hurwicz decision rule, Laplace decision rule

12.8 Game theory

• Assumptions of game theory
• Zero sum games
• Pure strategy games (saddle point)
• Mixed strategy games (joint probability approach)
• Dominance, graphical reduction of a game
• Value of the game
• Non-zero sum games
• Limitations of game theory

12.9 Network planning and analysis

• Basic concepts – network, activity, event
• Activity sequencing and network diagram
• Critical path analysis (CPA)
• Float and its importance
• Crashing of activity/project completion time
• Project evaluation and review technique (PERT)
• Resource scheduling (leveling) and Gantt charts
• Advantages and limitations of CPA and PERT

12.10 Queuing theory

• Components/elements of a queue: arrival rate, service rate, departure,
customer behaviour, service discipline, finite and infinite queues, traffic
intensity
• Elementary single server queuing systems
• Finite capacity queuing systems
• Multiple server queues

12.11 Simulation

• Types of simulation
• Variables in a simulation model
• Construction of a simulation model
• Monte Carlo simulation
• Random numbers selection
• Simple queuing simulation: single server, single channel “first come first
served” (FCFS) model
• Application of simulation models

12.12 Emerging issues and trends

CONTENT                                                    PAGE

Past papers

1. November 2019…………………….…9
2. May 2019…………………………..……16
3. November 2018………………………21
4. May 2018……………………………….26
5. November 2017………………………32
6. May 2017………………………………….39
7. November 2016…………………………45
8. May 2016………………………………….51
9. November 2015…………………………57
10. September 2015…………………………63

1. November 2019………………………….69
2. May 2019……………………………..…….91
3. November 2018……………………….…107
4. May 2018……………………………………121
5. November 2017……………………….…139
6. May 2017…………………………………..165
7. November 2016……………………….…183
8. May 2016……………………………………..199
9. November 2015………………………….…219
10. September 2015……………………………237

Tables…………………………………………….……257

QUANTITATIVE ANALYSIS REVISION  KIT SAMPLE

QUESTION PAPERS

CPA PART II SECTION 4

CIFA PART II SECTION 4

CCP PART II SECTION 4

QUANTITATIVE ANALYSIS

FRIDAY: 28 November 2019.                                                 Time Allowed: 3 hours.

Answer ALL questions. Marks allocated to each question are shown at the end of the question. Show ALL your workings.

QUESTION ONE

(a) Business analytics is today emerging as a critical component of driving and sustaining business growth, particularly in the face of rising competition and other market dynamics.

Required:

In the context of the above statement, describe what “business analytics” entails.   (6 marks)

(b) Six consultants work for XYZ Ltd. A consultant has a 20% chance of being absent from work in a given day. The company needs to establish the probability of more than two consultants being absent from work.

QUANTITATIVE ANALYSIS REVISION  KIT SAMPLE

QUESTION PAPERS

CPA PART II SECTION 4

CIFA PART II SECTION 4

CCP PART II SECTION 4

QUANTITATIVE ANALYSIS

FRIDAY: 24 May 2019.                                                               Time Allowed: 3 hours.

Answer ALL questions. Marks allocated to each question are shown at the end of the question. Show ALL your workings.

QUESTION ONE

The marginal revenue and average cost functions of Biashara Limited are given as follows:

KASNEB

CPA PART II SECTION 4

CIFA PART II SECTION 4

CCP PART II SECTION 4

QUANTITATIVE ANALYSIS

FRIDAY: 30 November 2018.                                                 Time Allowed: 3 hours.

Answer ALL questions. Marks allocated to each question are shown at the end of the question. Show ALL your workings.

QUESTION ONE

(a) Explain the following terms as used in decision theory:

(i) Opportunity loss.         (1 mark)

(ii) Expected value of perfect information.             (1 mark)

(b) Outline three assumptions of the transportation model.         (3 marks)

QUANTITATIVE ANALYSIS REVISION  KIT SAMPLE

KASNEB

CPA PART II SECTION 4

CIFA PART II SECTION 4

CCP PART II SECTION 4

QUANTITATIVE ANALYSIS

FRIDAY: 25 May 2018.                                                               Time Allowed: 3 hours.

Answer ALL questions. Marks allocated to each question are shown at the end of the question. Show ALL your workings.

QUESTION ONE

(a) Enumerate four assumptions that are implied in the application of the linear programming model.   (4 marks)

(b) The unit price and total cost functions associated with the production and sale of a certain electric component are given the following equations:

QUANTITATIVE ANALYSIS REVISION  KIT SAMPLE

KASNEB

CPA PART II SECTION 4

CIFA PART II SECTION 4

CCP PART II SECTION 4

QUANTITATIVE ANALYSIS

FRIDAY: 1 December 2017.                                                 Time Allowed: 3 hours.

Answer ALL questions. Marks allocated to each question are shown at the end of the question. Show ALL your workings.

QUESTION ONE

(a) Outline four applications of mathematical functions in business.    (4 marks)

(b) Highlight the four components of a time series.     (4 marks)

(c) A survey was conducted on 800 households to determine their    preference for three consumer      goods, namely Fex, Gex and Mex. The results of the survey were as follows:

QUANTITATIVE ANALYSIS REVISION  KIT SAMPLE

KASNEB

CPA PART II SECTION 4

CIFA PART II SECTION 4

CCP PART II SECTION 4

QUANTITATIVE ANALYSIS

FRIDAY: 25 November 2016.                                                    Time Allowed: 3 hours.

Answer ALL questions. Marks allocated to each question are shown at the end of the question. Show ALL your workings.

QUESTION ONE

(a) Explain the following terms as used in linear programming:

(i) Infeasibility.          (1 mark)

(ii) Unboundedness.          (1 mark)

(iii) Alternate optimality.      (1 mark)

QUANTITATIVE ANALYSIS REVISION  KIT SAMPLE

KASNEB

CPA PART II SECTION 4

CIFA PART II SECTION 4

CCP PART II SECTION 4

QUANTITATIVE ANALYSIS

FRIDAY: 27 May 2016.                                                       Time Allowed: 3 hours.

Answer ALL questions. Marks allocated to each question are shown at the end of the question. Show ALL your workings.

QUESTION ONE

(a) Explain four differences between the project evaluation and review technique (PERT) and the critical path analysis (CPA).                                                                   (8 marks)

(b) A certain audit firm has two categories of employees, auditors and assistant auditors. The total monthly salary of 1 auditor and 5 assistant auditors amount to Sh.456,755 whereas the total monthly salary of 3 auditors and 9 assistant auditors amount to Sh.985,005. The firm has a total of 6 auditors and 14 assistant auditors. The employees contribute 12 per cent of their monthly salaries towards their sacco society

QUANTITATIVE ANALYSIS REVISION  KIT SAMPLE

KASNEB

CPA PART II SECTION 4

CIFA PART II SECTION 4

CCP PART II SECTION 4

QUANTITATIVE ANALYSIS

FRIDAY: 27 November 2015.                                                Time Allowed: 3 hours.

Answer ALL questions. Marks allocated to each question are shown at the end of the question. Show ALL your workings.

QUESTION ONE

(a) Star Manufacturers Limited specialises in the production of two products, A and B. The manufacturer sells the products at a fixed selling price to its customers. The following table shows the requirements for production of products A and B:

QUANTITATIVE ANALYSIS REVISION  KIT SAMPLE

CPA PART II SECTION 4

CIFA PART II SECTION 4

CCP PART II SECTION 4

QUANTITATIVE ANALYSIS

PILOT PAPER

September 2015.                                                                          Time Allowed: 3 hours.

Answer ALL questions. Marks allocated to each question are shown at the end of the question. Show ALL your workings.

QUESTION ONE

(a) Highlight any four assumptions of Markov Analysis.     (4 marks)

(b) The research industry in your country has three market research firms namely X, Y and Z which provide research services. The following data has been collected in relation to the flow of clients among the three firms:

QUANTITATIVE ANALYSIS REVISION  KIT SAMPLE

KASNEB

CPA PART II SECTION 4

QUANTITATIVE ANALYSIS

NOVEMBER 2019

QUESTION ONE

Business analytics – refers to the skills, technologies applications and practices for the continuous exploration of data to gain insight that drive business decisions.

Business analytics help organisations to cope with competition and sustain future growth prospects, in many ways such as:

1. Allowing business to create environments which are receptive to innovation for devising strategies
2. Help organizations to anticipate and predict outcomes and trade-offs more proactively.

QUANTITATIVE ANALYSIS REVISION  KIT SAMPLE

KASNEB

CPA PART II SECTION 4

QUANTITATIVE ANALYSIS

MAY 2019

QUESTION ONE

The profit Function

QUANTITATIVE ANALYSIS REVISION  KIT SAMPLE

KASNEB

CPA PART II SECTION 4

QUANTITATIVE ANALYSIS

NOVEMBER 2018

QUESTION ONE

Explaining the following terms as used in decision theory

i) Opportunity loss is the short fall between the best possible value in the state and actual result.

ii) Expected value of perfect information refers to the difference between the profits obtainable from having perfect knowledge and the expected outcomes without perfect knowledge.

QUANTITATIVE ANALYSIS REVISION  KIT SAMPLE

KASNEB

CPA PART II SECTION 4

QUANTITATIVE ANALYSIS

MAY 2018

QUESTION ONE

a) Assumptions that are implied in the application of the linear programming model

• Assumes that the decision variables are continuous
• All variables are restricted to non negative values
• Only one decision is required for the planning period
• Technology remain fixed
• The relationship between variables and the resources available is linear
• It is assumed that the decision maker is completely certain
• It is assumed that the profit contribution of a product remains constant irrespective of the level of production and sales.

QUANTITATIVE ANALYSIS REVISION  KIT SAMPLE

KASNEB

CPA PART II SECTION 4

QUANTITATIVE ANALYSIS

DECEMBER 2017

QUESTION ONE

A) Applications of mathematics functions in business.

• In even analysis
• In supply analysis
• In demand analysis
• Bills calculations
• Cost estimation
• Profit determination
• Linear programming

QUANTITATIVE ANALYSIS REVISION  KIT SAMPLE

KASNEB

CPA PART II SECTION 4

QUANTITATIVE ANALYSIS

MAY 2017

QUESTION ONE

Describing four types of sets as used in set theory

Null set

Set without members. i.e an empty set. Examples include: empty crate of soda, Empty tray of eggs, class without students’ e.t.c

Overlapping sets

Sets with some common members

Disjoint sets

Sets with different members

QUANTITATIVE ANALYSIS REVISION  KIT SAMPLE

CPA PART II SECTION 4

QUANTITATIVE ANALYSIS

NOVEMBER 2016

QUESTION ONE

Explanation of the following terms as used in Linear programming

(i)Infeasibility:

• Occurs when linear programming constrains can’t be met at the same time. It stams from the following:-
• Incorrect formulation of constraints
• Certain requirements need to be adjusted or altered all together
• Need for extra resources if problem is to be resolved.

QUANTITATIVE ANALYSIS REVISION  KIT SAMPLE

KASNEB

CPA PART II SECTION 4

QUANTITATIVE ANALYSIS

MAY 2016

QUESTION ONE

Project evaluation and review technique is a technique adopted firms to represent and anylyses the activity in a project and to illustrate the flow of events in a project. Pert is a method to evaluate and estimate the time required to complete a task within deadlines. Critical path anylysis (CPA) is a project management technique that requires mapping out every key task that is necessary to complete a project differences between CPA and PERT as detailed below

QUANTITATIVE ANALYSIS REVISION  KIT SAMPLE

KASNEB

CPA PART II SECTION 4

QUANTITATIVE ANALYSIS

NOVEMBER 2015

QUESTION ONE

The total expected revenue

Assume A are units of A produced

Assume B are units of B produced

QUANTITATIVE ANALYSIS REVISION  KIT SAMPLE

KASNEB

CPA PART II SECTION 4

QUANTITATIVE ANALYSIS

SEPTEMBER 2015

QUESTION ONE

Highlighting any four assumptions of marker analysis

• There are limited or finite number of possible states
• The probability of changing states remains the same over time
• The size and make up of the system for example the number of firms and clients do not change during the analysis, that is remains constant.
• Any future state can be predicted from the previous state and the matrix of transition probabilities.

QUANTITATIVE ANALYSIS REVISION  KIT SAMPLE

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