**CPA**

**CIFA**

**CCP**

** **

**PART II**

**SECTION 4**

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**REVISION KIT**

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** **

**PAST EXAMINATION PAST PAPERS WITH SUGGESTED ANSWERS**

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** **

** **** **

**Updated with November 2019 Examination Past paper**

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** To buy this revision kit, CALL / TEXT / WHATSAPP 0728 776 317**

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Email: info@masomomsingi.com

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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.

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**

**12.1.1 Functions**

- Functions, equations and graphs: Linear, quadratic, cubic,

exponential and logarithmic - Application of mathematical functions in solving business problems

- 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
- Sensitivity analysis and economic meaning of shadow prices in business

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**

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**CONTENT PAGE**

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**Past papers**

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- November 2019…………………….…9
- May 2019…………………………..……16
- November 2018………………………21
- May 2018……………………………….26
- November 2017………………………32
- May 2017………………………………….39
- November 2016…………………………45
- May 2016………………………………….51
- November 2015…………………………57
- September 2015…………………………63

**Suggested answers and solutions:**

** **

- November 2019………………………….69
- May 2019……………………………..…….91
- November 2018……………………….…107
- May 2018……………………………………121
- November 2017……………………….…139
- May 2017…………………………………..165
- November 2016……………………….…183
- May 2016……………………………………..199
- November 2015………………………….…219
- September 2015……………………………237

Tables…………………………………………….……257

**QUANTITATIVE ANALYSIS REVISION KIT SAMPLE**

**QUESTION PAPERS**

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**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.**

** **

**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.**

** **

**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.**

** **

**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.**

** **

**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.**

** **

**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.**

** **

**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:

**SUGGESTED ANSWERS AND SOLUTIONS**

**QUANTITATIVE ANALYSIS REVISION KIT SAMPLE**

**KASNEB**

**CPA PART II SECTION 4**

**QUANTITATIVE ANALYSIS**

**NOVEMBER 2019**

**SUGGESTED ANSWERS**

**QUESTION ONE**

**Description of ‘Business analytics’**

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:

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

**QUANTITATIVE ANALYSIS REVISION KIT SAMPLE**

**SUGGESTED ANSWERS AND SOLUTIONS**

**KASNEB**

**CPA PART II SECTION 4**

**QUANTITATIVE ANALYSIS**

**MAY 2019**

**SUGGESTED ANSWERS**

**QUESTION ONE**

**The profit Function**

**QUANTITATIVE ANALYSIS REVISION KIT SAMPLE**

**SUGGESTED ANSWERS AND SOLUTIONS**

**KASNEB**

**CPA PART II SECTION 4**

**QUANTITATIVE ANALYSIS**

**NOVEMBER 2018**

**SUGGESTED ANSWERS**

**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**

**SUGGESTED ANSWERS AND SOLUTIONS**

**KASNEB**

**CPA PART II SECTION 4**

**QUANTITATIVE ANALYSIS**

**MAY 2018**

**SUGGESTED ANSWERS**

**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**

**SUGGESTED ANSWERS AND SOLUTIONS**

**KASNEB**

**CPA PART II SECTION 4**

**QUANTITATIVE ANALYSIS**

**DECEMBER 2017**

**SUGGESTED ANSWERS**

** **

**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**

**SUGGESTED ANSWERS AND SOLUTIONS**

**KASNEB**

**CPA PART II SECTION 4**

**QUANTITATIVE ANALYSIS**

**MAY 2017**

**SUGGESTED ANSWERS**

** **

**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**

**SUGGESTED ANSWERS AND SOLUTIONS**

**CPA PART II SECTION 4**

**QUANTITATIVE ANALYSIS**

**NOVEMBER 2016**

**SUGGESTED ANSWERS**

** **

**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**

**SUGGESTED ANSWERS AND SOLUTIONS**

**KASNEB**

**CPA PART II SECTION 4**

**QUANTITATIVE ANALYSIS**

**MAY 2016**

**SUGGESTED ANSWERS**

** **

**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**

**SUGGESTED ANSWERS AND SOLUTIONS**

**KASNEB**

**CPA PART II SECTION 4**

**QUANTITATIVE ANALYSIS**

**NOVEMBER 2015**

**SUGGESTED ANSWERS**

** **

**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**

**SUGGESTED ANSWERS**

** **

**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**

How much is Quantitative analysis / Techniques revision kit / question and answer

Sh 500 in hard copy and it covers 2015 to November 2019. Call | Text or Whatsapp 0728 776 316 for delivery arrangements