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**LEVEL II**

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**REVISION KIT**

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**Updated with November 2019 Examination Past paper**

**KASNEB SYLLABUS**

**PAPER NO. 7 BUSINESS MATHEMATICS AND STATISTICS**

**GENERAL OBJECTIVE**

This paper is intended to equip the candidate with the knowledge, skills and attitudes that will enable him/her to apply the principles of management in practice.

**7.0 LEARNING OUTCOMES**

A candidate who passes this paper should be able to:

- Apply linear, quadratic and simultaneous equations to solve business problems
- Solve business problems using matrix algebra
- Solve business problems involving commercial mathematics
- Present statistical data in form of tables, graphs and curves
- Calculate measures of location, dispersion, skewness and kurtosis
- Apply basic probability concepts
- Compute simple, general and weighted index numbers.

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**CONTENT**

**7.1 Equations**

- Linear equations; solving and graphs
- Simultaneous equations; solving
- Quadratic equations; solving and graphs
- Basic calculus; simple differentiation and integration
- Total revenue, total cost and profit equations
- Break-even analysis
- Application of errors; absolute/relative

**7.2 Sequences and series**

- Arithmetic progression(A.P): nth term, sum of first n terms
- Geometric progression (G.P): nth term, sum of first n terms

** ****7.3 Matrices**

- Introduction: order of matrices, types of matrices
- Addition, subtraction and multiplication of matrices
- Determinants of 2×2 matrices
- Inverses of 2×2 matrices
- Application of matrices in solving business problems

**7.4 Commercial mathematics**

- Buying and selling; discounts, profit and loss, margins and mark-ups
- Wages and salaries; piece and hourly rates, commissions, gross and net pay
- Statutory deductions; PAYE, NHIF, NSSF
- Simple and compound interest
- Depreciation and appreciation of assets
- Hire purchase
- Foreign exchange rate transactions

**7.5 Introduction to statistics**

- Introduction: definitions and branches of statistics
- Methods of data collection: primary and secondary data,
- Sampling techniques

**7.6 Presentation of statistical data**

- Tables
- Diagrams: bar charts and pie charts
- Graphs: time series graphs, Z-charts, Lorenz curves and semi-logarithmic graphs
- Frequency distribution tables
- Histogram and frequency polygons
- Cumulative frequency curve (ogive) and its application

**7.7 Descriptive statistics**

- Measures of central tendency: mean: arithmetic mean, weighted arithmetic mean; geometric mean, harmonic mean, median and mode.
- Measures of dispersion: range, quartile, deciles, percentiles, mean deviation, standard deviation and coefficient of variation
- Measures of skewness: pearsons coefficient of skewness, product coefficient of skewness
- Measures of kurtosis: pearsons coefficient of kurtosis, product coefficient of kurtosis.

**7.8 Set theory**

- Introduction to set theory
- Types of sets: universal, empty/null, subsets, finite and infinite
- Operation of sets: unions, intersections, complements and set difference
- Venn diagrams

**7.9 Basic probability theory**

- Introduction to probability: definitions, events, outcomes, sample space
- Types of events: simple, compound, independent, mutually exclusive, mutually inclusive, dependent events
- Rules of probability: additive and multiplicative rules
- Introduction to counting techniques, combinations and permutations
- Baye’s Theorem
- Elementary probability trees

**7.10 Index numbers**

- Construction of index numbers
- Purpose of index numbers
- Simple index numbers; fixed base method and chain base method
- Weighted index numbers; Laspeyre’s, Paasche’s, Fisher’s ideal and Marshall Edgeworth’s methods (both price and quantity index numbers)
- Consumer Price Index (CPI)
- Applications of CPI
- Limitations of index numbers

**7.11 Emerging issues and trend**

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**CONTENT PAGE**

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**Past papers**

- November 2019………………………….7
- May 2019……………………….…………13
- November 2018…………………………18
- May 2018………………………………….23
- November 2017………………………….28
- May 2017……………………………………33
- November 2016……………………………39
- May 2016………………………….…………44
- November 2015……………………………49
- September 2015…………………………..54

**Suggested answers and solutions:**

- November 2019………………………………59
- May 2019………………………….……………77
- November 2018………………………………94
- May 2018………………………………………..112
- November 2017……………………………….127
- May 2017………………………………………..146
- November 2016……………………………….164
- May 2016………………………………………..186
- November 2015……………………………….203
- September 2015………………….……………221

** BUSINESS MATHEMATICS AND STATISTICS REVISION KIT SAMPLE**

**ATD LEVEL II**

**DCM LEVEL II**

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**BUSINESS MATHEMATICS AND STATISTICS**

**TUESDAY: 21 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.**

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**QUESTION ONE**

- Outline four limitations of index numbers. (4 marks)
- The following data relate to the production of sugar (in metric tonnes) in Kenya for the first six months of the year 2019:

**BUSINESS MATHEMATICS AND STATISTICS REVISION KIT SAMPLE**

**ATD LEVEL II**

**DCM LEVEL II**

** **

**BUSINESS MATHEMATICS AND STATISTICS**

**TUESDAY: 21 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**

(a) Differentiate between the following terms with respect to statistical inquiry:

(i) ‘‘Census inquiry” and “sample inquiry”. (2 marks)

(ii) “Open inquiry” and “confidential inquiry”. (2 marks)

**BUSINESS MATHEMATICS AND STATISTICS REVISION KIT SAMPLE**

**ATD LEVEL II**

**DCM LEVEL II**

**BUSINESS MATHEMATICS AND STATISTICS**

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**TUESDAY: 27 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) State four characteristics of a good questionnaire. (4 marks)

(b) Explain three advantages of the interview method of data collection. (6 marks)

(c) Hamisi Ali bought a baking machine at a cash price of Sh. 100,000 on hire purchase terms. He paid an initial deposit of 20% of the cash price. An interest of 15% per annum is charged on the outstanding balance for the period of repayment. The balance plus the interest was to be paid in 24 equal monthly instalments. A customer who purchases the machine on cash basis is given a 15% discount on the cash price.

**BUSINESS MATHEMATICS AND STATISTICS REVISION KIT SAMPLE**

**ATD LEVEL II**

**DCM LEVEL II**

**BUSINESS MATHEMATICS AND STATISTICS**

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**TUESDAY: 22 May 2018.**

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**QUESTION ONE**

(a) Highlight five applications of mathematical functions in business. (5 marks)

(b) State four advantages of a hire purchase system in business. (4 marks)

(c) (i) Willy Bushuti bought a house at the beginning of year 2002 at Sh.40,000,000. The value of the house has been increasing at the rate of 4% per annum.

**BUSINESS MATHEMATICS AND STATISTICS REVISION KIT SAMPLE**

**ATD LEVEL II**

**DCM LEVEL II**

**BUSINESS MATHEMATICS AND STATISTICS**

**TUESDAY: 28 November 2017. Time Allowed: 3 hours.**

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**QUESTION ONE**

(a) Define (he following terms as used in index numbers:

(i) Simple index number. (2 marks)

(ii) Chain base method. (2 marks)

(iii) Stock market index. (2 marks)

(iv) Consumer price index. (2 marks)

**BUSINESS MATHEMATICS AND STATISTICS REVISION KIT SAMPLE**

**ATD LEVEL II**

**DCM LEVEL II**

**BUSINESS MATHEMATICS AND STATISTICS**

** **

**TUESDAY: 23 May 2017. Time Allowed: 3 hours.**

** **

**QUESTION ONE**

(a) Explain the following terms as used in probability:

(i) Addition law of probability. (2 marks)

(ii) Multiplication law of probability. (2 marks)

(iii) Baye’s theorem. (2 marks)

**BUSINESS MATHEMATICS AND STATISTICS REVISION KIT SAMPLE**

**ATD LEVEL II**

**DCM LEVEL II**

**BUSINESS MATHEMATICS AND STATISTICS**

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**TUESDAY: 22 November 2016. Time Allowed: 3 hours.**

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**QUESTION ONE**

(a) Highlight four applications of linear functions. (4 marks)

(b) Distinguish between “marginal cost function” and “marginal revenue function”. (4 marks)

(c) Dorcas and Gladys visited a supermarket to purchase some items. Dorcas bought 9 jackets and 12 sweaters for Sh.2I.000. Gladys bought 14 jackets and 6 sweaters for Sh.900 more than Dorcas.

**BUSINESS MATHEMATICS AND STATISTICS REVISION KIT SAMPLE**

**ATD LEVEL II**

**DCM LEVEL II**

**BUSINESS MATHEMATICS AND STATISTICS**

** **

**TUESDAY: 24 May 2016. Time Allowed: 3 hours.**

**QUESTION ONE**

(a) State four advantages and four disadvantages of closed-ended questions in a questionnaire. (8 marks)

(b) Bundacho Bakery, produces two types of cakes, namely; queen cake and blackforest. The cost of producing 10 queen cakes and 8 blackforest is Sh.4,060. The cost of producing 4 queen cakes and 7 blackforest is Sh.2,840. The bakery makes a mark-up of 20% and 30% on queen cakes and blackforest respectively.

**BUSINESS MATHEMATICS AND STATISTICS REVISION KIT SAMPLE**

**ATD LEVEL II**

**DCM LEVEL II**

**BUSINESS MATHEMATICS AND STATISTICS**

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**WEDNESDAY: 18 November 2015. Time Allowed: 3 hours.**

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**QUESTION ONE**

(a) Explain three challenges that might be faced during statistical sampling. (6 marks)

(b) The cash price of a television set is Sh. 18,000. If the television is bought on hire purchase terms, a deposit of 25% of the cash price is required. A flat interest rate of 15% per annum is charged on the remaining balance for two years.

**Required:**

The amount of monthly instalment on hire purchase terms. (4 marks)

The following information relates to the expenditure of a certain family during the years 2013 and 2014:

**BUSINESS MATHEMATICS AND STATISTICS REVISION KIT SAMPLE**

**ATD LEVEL II**

**DCM LEVEL II**

**BUSINESS MATHEMATICS AND STATISTICS**

**PILOT PAPER**

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**September 2015 Time Allowed: 3 hours.**

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**QUESTION ONE**

(a) A retailer bought a machine with a cash price of Sh.600,000 on hire purchase terms. He paid an initial deposit of 25 percent of the cash price. An interest of 20 percent is charged on the outstanding balance for the period of repayment. The balance plus the interest is payable in 36 equal monthly instalments. A customer who purchases the machine on cash basis is given a 20% discount on the cash price.

**BUSINESS MATHEMATICS AND STATISTICS REVISION KIT SAMPLE**

**NOVEMBER 2019**

**SUGGESTED ANSWERS AND SOLUTIONS**

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**QUESTION ONE**

**Limitations of index numbers**

- The comparisons of changes in variables over long periods are not reliable
- Sampling errors are inevitable and these renders the index numbers subjective
- There is always difficult faced in the choice of the appropriate base period or weights for the proper construction of index numbers
- Construction of index numbers is always time consuming and costly.
- May not be suitable for international comparisons due to changes in qualities or grades of commodities as well as the differences in bases used

**BUSINESS MATHEMATICS AND STATISTICS REVISION KIT SAMPLE**

**SUGGESTED ANSWERS AND SOLUTIONS**

**MAY 2019**

** **

**QUESTION ONE**

**1a) Differences between the following terms with respect to statistical inquiry:**

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**i) “Census inquiry” and Sample inquiry”**

**Census inquiry **– refers to the complete count or enumeration of all individual units/items in the given population, whereas, **Sample Inquiry **refers to the study of enumeration of the selected units/items in a sample, that has been taken/drawn from a population.

**BUSINESS MATHEMATICS AND STATISTICS REVISION KIT SAMPLE**

**SUGGESTED ANSWERS AND SOLUTIONS**

**NOVEMBER 2018**

**QUESTION ONE**

**1a) characteristics of a good questionnaire**

- It should be belief and comprehensive
- Ask well phrased and unambiguous questions that can be answered
- Should be uniform in terms of questions asked from respondent to respondent
- Should have a well designed layout or format
- Should be simple and easy to use as well as understand
- Should guarantee anonymity that is, ensure confidentiality

**BUSINESS MATHEMATICS AND STATISTICS REVISION KIT SAMPLE**

**SUGGESTED ANSWERS AND SOLUTIONS**

**MAY 2018**

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**QUESTION ONE**

**1a) Five applications of mathematical functions in business**

- Estimation of output for profit maximization
- In demand analysis
- In supply analysis
- In bills calculation
- In determination of employee benefits such as commissions
- Estimation of cost of production
- In break-even analysis

**BUSINESS MATHEMATICS AND STATISTICS REVISION KIT SAMPLE**

**SUGGESTED ANSWERS AND SOLUTIONS**

**NOVEMBER 2017**

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**QUESTION ONE**

**1 a) Defining the following terms as used in index numbers**

**i) Simple index numbers**

- It is an index number constructed/Obtained by using only one type of commodity e.g maize only or beans only etc.

**ii) Chain Base method**

- It is a method used to construct simple index numbers. Under this method the base is not fixed but varies from period to period

**BUSINESS MATHEMATICS AND STATISTICS REVISION KIT SAMPLE**

**SUGGESTED ANSWERS AND SOLUTIONS**

**MAY 2017**

** **

**QUESTION ONE**

**1 a) Explain the following terms as used in probability:**

**Additional law of probability**

It’s a rule of probability that is normally applicable on mutually exclusive events. For example, if A and B are mutually exclusive events then the;

**BUSINESS MATHEMATICS AND STATISTICS REVISION KIT SAMPLE**

**SUGGESTED ANSWERS AND SOLUTIONS**

**NOVEMBER 2016**

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**QUESTION ONE**

**1 a) Application of linear function**

- In demand analysis
- In supply analysis
- In break-even analysis
- In bills calculation
- Estimating revenues, profits and costs of a firm
- In calculating commissions

**BUSINESS MATHEMATICS AND STATISTICS REVISION KIT SAMPLE**

**SUGGESTED ANSWERS AND SOLUTIONS**

**MAY 2016**

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** **

**QUESTION ONE**

**1 a) Four advantages and four disadvantages of closed-ended questions in a questionnaire **

**Advantages**

- Are easy to answer since they do not require elaborate explanations
- The researcher is able to obtain quick responses from the respondents
- Are time saving
- They save space and cost in terms of paper materials required in the preparation of questionnaire

**BUSINESS MATHEMATICS AND STATISTICS REVISION KIT SAMPLE**

**SUGGESTED ANSWERS AND SOLUTIONS**

**NOVEMBER 2015**

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**QUESTION ONE**

**1 a) Challenges that might be faced during sampling**

**i) Choice of sampling technique**

There are various methods of sampling such as cluster, stratified, quasi, quota and so on. Hence, choice of an appropriate method of sampling is always difficult.

**ii) Errors and biasness**

Sampling always result in errors and biases since the selected sample may not be a representative of the underlying population

**BUSINESS MATHEMATICS AND STATISTICS REVISION KIT SAMPLE**

**SUGGESTED ANSWERS AND SOLUTIONS**

**SEPTEMBER 2015 **

**PILOT PAPER**

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**QUESTION ONE**

**a) The amount of money the retailer would have saved had he bought the machine on cash basis**

Cash price = sh.600,000

Deposit = 25%x600,000 = sh.150,000

Principal Balance = Cash price – Deposit

= 600,000-150,000

Interest rate = 20% P.a