CIMA | Business Mathematics Fundamentals past papers

© The Chartered Institute of Management Accountants 2001

Foundation Level Business Mathematics

3c FBSM21 May 2001

Day 1 – late afternoon

INSTRUCTIONS TO CANDIDATES

Read this page before you look at the questions

You are allowed TWO hours to answer this question paper.

Ensure that there is graph paper on your desk.

Answer the ONE question in section A (this has 25 sub-questions).

Answer TWO questions ONLY from section B.

Maths Tables and Formulae are provided elsewhere on the website, but were included withinthe printed question paper.

Write your examination number in the boxes provided on the front of the answer book.

Write FBSM on the line marked "Subject" on the front of the answer book.

Write your examination number on the special answer sheet for section A which is on page 3 ofthis question paper booklet.Detach the sheet from the booklet and insert it into your answer book before you hand this in.

Do NOT write your name or your student registration number anywhere on your answer book.

Tick the appropriate boxes on the front of the answer book to indicate which questions you haveanswered.

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FBSM 2 May 2001

SECTION A — 50 MARKS

ANSWER ALL TWENTY-FIVE SUB-QUESTIONS – 2 MARKS EACH

Question One

1.1 The numbers of rejects from 50 samples of the same size is as follows:

Number of rejects in each sample: 0 1 2 3 4 5Number of samples (frequency of rejects): 5 10 10 20 5 0

The arithmetic mean number of rejects per sample is

A 2∙2 B 2∙4 C 3 D 20

1.2 The unit price of Brand X in May 2000 and May 2001 was as follows:

Year 2000 2001Unit price of Brand X £1∙40 £1∙75

The price relative for Brand X in May 2001, with base May 2000 = 100 is

A 80 B 120 C 125 D 135

1.3 On which ONE of the following graphics can the median readily be found without furthercalculation?

A Bar chart

B Cumulative frequency curve

C Histogram

D Pie chart

1.4 A retailer buys a box of a product, which nominally contains Q units. The planned sellingprice of each unit is £P. If both P and Q have been rounded to ± 10%, then the maximumrounding error in total revenue is

A 10% B 20% C 21% D 0∙1Q x 0∙1P

Each of the sub-questions numbered from 1.1 to 1.25 inclusive, given below, has only ONE correctanswer.



M2001 FBSM3

1.5 The telephone costs of a company last year were £10,000, including Value Added Tax(VAT) at 17∙5%. It has been decided to allocate 60% of these telephone costs, excludingVAT, to Central Administration and to allocate 30% of the remainder, excluding VAT, toFinance.

The telephone costs (to the nearest £) to be allocated to Finance will be closest to

A £990 B £1,021 C £1,100 D £1,135

1.4 The formula Q =H

2CDis used in stock control.

When the formula is rearranged, with H as the subject, H equals

A2Q

2CDB

2Q

4CDC

Q

2CD DQ

2CD

1.7 A company’s market for computer supplies has trebled in value in exactly six years. Theannual equivalent percentage growth rate in this market is (to 2 decimal places) closest to

A 12∙25 B 20∙09 C 24∙57 D 33∙33

1.8 The following statements are often made about “simple random sampling”.

(i) It ensures a representative sample.(ii) It eliminates selection bias.

Which one of the following is always true?

A (i) only B (ii) only C Both (i) and (ii) D Neither (i) nor (ii)

1.9 A machine was purchased for £100,000. Depreciation is calculated using the “reducingbalance method” (that is, a constant percentage is applied each year to the written downvalue). In the last balance sheet, the net book value of the machine, exactly four years old,was shown as £50,000.

In the next balance sheet the machine should be shown to have a net book value, rounded to thenearest £100, closest to

A £37,500 B £40,000 C £42,000 D £43,500



FBSM 4 May 2001

1.10 In a particular country, a tax at 40% is payable on any gains on house sales not due toinflation. A house was purchased there for $75,000 and sold for $250,000. Over the sameperiod, the country’s house price (inflation) index rose from 120 to 240.

The tax (to the nearest $) payable on the house sale is

A $28,000 B $37,500 C $40,000 D $70,000

1.11 Each of the following diagrams shows a histogram of data with equal area. The verticaland horizontal scales of each histogram are identical.

Which set of data (histogram) has the largest standard deviation?

A B

Employees Employees

0 Wages 0 Wages

C D

Employees Employees

0 Wages 0 Wages

1.12 The lengths of steel rods are Normally distributed with a mean of 100mm and a standarddeviation of 5mm.

The percentage of steel rods with a length of less than 95mm is closest to

A 5% B 16% C 20% D 34%

1.13 The calculation of a rank correlation coefficient [formula given in the Mathematical Tablessheet 3 on page 19], shows that ten pairs of data are found to be perfectly negativelycorrelated.

Therefore, the value of ∑d² equals

A zero B 165 C 330 D none of these.



M2001 FBSM5

1.14 A £100,000 mortgage, with interest compounded at 11% each year, is to be repaid by 10equal year-end payments of £X, the first being due one year after the mortgage wascontracted.

£X is closest to

A £16,111 B £16,273 C £16,981 D £25,937

1.15 The quarterly sales (units) of a company are given in the table below.

Year Q1 Q2 Q3 Q4

1997 13 52 56 791998 29 43 48 801999 24 55 46 75

Read the following statements.

(i) Annual sales are static.(ii) The fourth quarter, Q4, has the highest quarterly sales in each of the three years.(iii) The mean sales for the second quarter (Q2) equals the mean quarterly sales for the

whole period, 1997-99.

Which is true?

A (i) only B (i) and (ii) only C (ii) and (iii) only D (i), (ii) and (iii)

1.16 An accountant has to check a sample of invoices. The invoices are divided into threegroups, by value: “under £100”, “£100 – £500” and “over £500”. Samples are thenselected randomly from each group.

Which ONE of the following sampling methods is involved?

A cluster B multi-stage C quota D stratified

1.17 The equations of two straight lines are given below:

Y = 7 + X Y = 9 + 3X

These lines intersect where the (X, Y) co-ordinates are equal to

A (–1,6) B (1,6) C (1,8) D none of these

The following information is to be used for sub-questions 1.18 and 1.19

A scatter diagram shows the weekly total costs of production (£) in a certain factory plottedagainst the weekly output (units). A broadly linear pattern is evident, with r = 0∙9. Theregression equation is

COSTS = 1,500 + (15 x OUTPUT).

Fifty data points have been included in the analysis, with output ranging from 100 units to 1,000units. Output next week is planned to be 500 units.



FBSM 6 May 2001

1.18 Read the following statements about estimates.

(i) Weekly fixed costs are approximately £1,500.(ii) Variable costs are approximately £15 per unit on average.(iii) Next week’s production costs are likely to be about £9,000.

Which one of the following is true, all other things being equal?

A (i) and (ii) only B (i) and (iii) only C (ii) and (iii) only D (i), (ii) and (iii)

1.19 Read the following statements:

(i) There is very little correlation between weekly costs of production and productionlevel.

(ii) 90% of the variation in weekly costs is attributable to the amount produced.(iii) Given the information, any forecast using the regression equation is likely to be very

unreliable.

Which one of the following is justified?

A (ii) only B (i) and (iii) only C (ii) and (iii) only D None of them

1.20 Three independent experts have estimated the probability of a company’s future annualsales:

Sales High [£1m] Medium [£0∙5m] Low [£0∙25m]Expert W 0∙2 0∙3 0∙5Expert X 0∙1 0∙4 0∙5Expert Y 0∙1 0∙6 0∙3

The highest expected value for the company’s estimated annual sales is given by

A W only. B X only. C Y only. D Both W and Y.

1.21 Details of an index number are given below:

Group Base Weight IndexFood & Drink 100 50 140Travel & Leisure 100 30 130Housing 100 20 120All items 100 100 ??

The All items index number is closest to

A 130 B 133 C 135 D 146



M2001 FBSM7

1.22 For the following set of ten numbers, the median is 15:

10 11 12 13 14 16 17 18 19 20+X

This statement is false if X equals

A –5 B –4 C –3 D –2

1.23 Which of the following could have a value of –2 (minus 2)?

(i) Correlation coefficient(ii) Slope of a regression line(iii) Variance

A (ii) only B (i) and (ii) only C (i) and (iii) only D (ii) and (iii) only

1.24 The following data represents a time series for the last seven days:

2 6 10 6 10 14 10

Which ONE of the following moving averages would result in a straight-line graph?

A 2-point B 3-point C 4-point D None of these.

1.25 Three people are carrying out independent functions during an internal audit. It is knownthat in each of the three separate areas being investigated there is a serious error. Frompast experience, it is estimated that the (independent) chances of the individuals findingthe serious error in their area are 0∙8, 0∙7 and 0∙6.

The probability that at least one of the serious errors will be found is

A (0∙8 x 0∙3 x 0∙4) + (0∙2 x 0∙7 x 0∙4) + (0∙2 x 0∙3 x 0∙6)

B 1 – (0∙2 x 0∙3 x 0∙4)

C 1 – (0∙8 x 0∙7 x 0∙6)

D none of the above.

Total = 50 marks



FBSM M20018



M2001 FBSM9



FBSM M200110

SECTION B – 50 MARKS

ANSWER TWO QUESTIONS ONLY

Question Two

A Health and Fitness Centre has to buy one of two types of machine, A or B. Machine A wouldcost £200,000, half of which would be due on delivery, the remainder a year later. Machine Bwould cost £240,000, with payment due in the same way as for machine A. Both machines lastfor 6 years and have an expected scrap value of 10% of their original cost price. Taking intoaccount operating costs and maintenance, machine A would produce year-end net operationalcash flows of £40,000 and machine B year-end net operational cash flows of £50,000. In bothcases the relevant cost of capital is 10% each year.

Required:(a) Calculate the net present value of each machine.

(11 marks)

(b) Recommend which machine should be bought, giving your reasons and assumptions.

(4 marks)

(c) Estimate the internal rate of return for your recommended machine, using a graph orcalculation, and state its meaning.

(10 marks)

(Total = 25 marks)



M2001 FBSM11

Question Three

A retailer sells computer games. Tabulated below are the unit sales of one of its games for thelast 13 quarters, together with the computer-generated trend equation and average seasonalvariations. For planning purposes, forecasts of sales are required for the remaining threequarters of this year. (The brand was introduced in 1997.)

Sales Q1 Q2 Q3 Q4

1998 105 95 150 250

1999 80 70 110 180

2000 50 50 70 110

2001 30

Trend equation: S = 180 – 10T

where S = sales units andT = time period in quarters

[For example, T = 1 in Q1 of 1998, T = 2 in Q2 of 1998, T = 3 in Q3 of 1998 ….. T = 5 in Q1

of 1999 and so on.]

Q1 Q2 Q3 Q4Average seasonal variations for the years1998 – 2001 -40% -40% 0 +80%

Required:(a) Plot a time series graph of the unit sales, and include the trend on the same graph.

(10 marks)

(b) Forecast the unit sales for the second, third and fourth quarters of 2001, and comment onthe reliability of these forecasts.

(8 marks)

(c) Interpret the key factors in this game's unit sales, 1998 – 2001.

(7 marks)

(Total = 25 marks)



FBSM M200112

Question Four

A bakery produces fresh cakes each day in anticipation of demand. The variable costs ofproduction are £0∙20 per cake and the retail price is £0∙50 per cake. The daily demand forcakes over the last four months is shown in the table below. At the end of each day, anyunsold cakes are sold to a local pig farmer for £0∙05 per cake.

Daily demand (numberof cakes)

1 – 39 40 – 79 80 – 119 120 – 159 160 – 199

Number of days 10 20 30 30 10

(For practical purposes, you may assume the midpoints of the class intervals to be 20, 60, 100,140, 180.)

Required:(a) Prepare a 5 x 5 contribution table for each production / demand combination and calculate

the expected contribution for each level of production.(20 marks)

(b) Recommend, with reasons and comments, the most suitable production policy for thebakery.

(5 marks)

(Total = 25 marks)

End of paper





3c FBSM19 November 2001




You are allowed TWO hours to answer this question paper.

Ensure that there is graph paper on your desk.

Answer the ONE question in section A (this has 25 sub-questions, and is on pages 2 – 7).

Answer TWO questions ONLY from section B (these questions are on pages 8 – 10).

Maths Tables and Formulae were provided in the printed question paper and are availableelsewhere on the website.

Write your examination number in the boxes provided on the front of the answer book.

Write FBSM on the line marked "Subject" on the front of the answer book.

Write your examination number on the special answer sheet for section A. Detach the sheetfrom the booklet and insert it into your answer book before you hand this in.

Do NOT write your name or your student registration number anywhere on your answer book.

Tick the appropriate boxes on the front of the answer book to indicate which questions you haveanswered.



FBSM 2 November 2001



Question One

1.1 The sales of a product increase at a rate of 1% each month, month on month, for ayear. This is equivalent to an annual percentage rate of expansion closest to

A 11∙3% B 12∙0% C 12∙7% D 13∙0%

1.2 An annual (year-end) income of £10,000 is required in perpetuity. If there is a fixedinterest rate of 8% each year and administrative charges are ignored, the lump suminvestment necessary now is closest to

A £9,260 B £80,000 C £100,000 D £125,000

1.3 The numbers of hours worked last week by a company’s 11 employees were:

P Q R S T U V W X Y Z

35 36 36 36 40 38 40 37 35 42 43

The median number of hours worked last week was

A 36 B 37 C 38 D 39

1.4 The straight lines Y = 2X + 4 and Y = 12 – 2X intersect where (X,Y) equals

A (–2, 0) B (0,12) C (0,4) D (2,8)

1.5 A 1% random sample of mail order customers, each with a serial number, is to beselected. A random number between 00 and 99 is chosen, and turns out to be 29.Customers with serial numbers 29, 129, 229, 329 and so on are then selected to be thesample.

This type of sample is termed

A biased. B multi-stage. C quota. D systematic.

Each of the sub-questions numbered from 1.1 to 1.25 inclusive, given below, has only ONEcorrect answer.



November 2001 3 FBSM

1.6 The following formula is used in loan calculations:

R = 1)B(N

2PC

+

When the formula is rearranged, with N in terms of the other letters, N is equal to

ARB

2PC – 1 B

RB

1 2PC -C 2PC – 1 D none of these

1.7 The formula 11

1

⋅ 2S ÷

⋅−

11

11 simplifies to

A11

S2

⋅ B 2S C11

S10 2

⋅ D 10 2S

1.8 A garage has experienced the following regular weekly demand for its hire cars over thelast 50 weeks:

Weekly demand for hire cars: 0 1 2 3 4 5 or more

Number of weeks (frequency): 10 5 15 15 5 0

The expected value of weekly demand equals

A 2∙0 cars. B 2∙2 cars. C 2∙5 cars. D none of these.

1.9 In the equation C = 6 + 0∙5Q, C denotes the total cost of sales (in thousands of $) and Qdenotes the number of units sold (in thousands).

The total cost of sales for 3,000 units is therefore

A $1,506∙00 B $6,001∙50 C $7,500∙00 D $19,500∙00

1.10 The rank correlation coefficient between the ages and the scrap values of a certain typeof machine equals –1.

This value means that

A no correlation exists between the ages and the scrap values of these machines.

B perfect correlation exists.

C weak negative correlation exists.

D a calculation error has been made.




1.11 The lengths of a very large batch of metal rods are Normally distributed with a meanlength of 300 millimetres and a standard deviation of 10 millimetres.

The percentage of the batch which is longer than 285 millimetres is closest to

A 43% B 57% C 84% D 93%

1.12 A $20,000 new car depreciates in value by 20% ± 2% each year (year-end). (The cardepreciates by the “reducing balance method”, which means that a constant percentageis applied each year to the written down value.)

Therefore, after 3 years, the car’s value is most accurately estimated by

A between $9,491 and $11,027

B $10,240 ± $1,024

C $10,240 ± $205

D between $12,168 and $13,448

1.13 A trader’s weekly costs, TC, are less than or equal to $100. Weekly revenue, R, is aminimum of $120.

Which ONE of the following statements is true?

A TC < $100 and R > $120 and R > TC

B TC ≥ $100 and R ≤ $120 and TC > R

C TC ≤ $100 and R > $120 and R < TC

D TC ≤ $100 and R ≥ $120 and R > TC

1.14 A company has to repay a mortgage by making 10 year-end payments of $50,000. Thecompound interest rate is fixed at 8% each year.

Therefore, the size of the mortgage is closest to

A $266,750 B $307,250 C $335,500 D $356,900




The next two sub-questions, 1.15 and 1.16 are based on the following data.

1998 1999 2000 2001

Weekly money wages index (1998 = 100) 100 105 110 115

Index of inflation (1990 = 100) 180 190 200 210

1.15 Read the following statements about the period 1998 to 2001:

(i) Inflation has increased by more than money wages.

(ii) Money wages have increased by 5% each year, year on year.

Which ONE of the following is true?

A (i) only B (ii) only C Both (i) and (ii) D Neither (i) nor (ii)

1.16 “Real wages” are money wages that have been adjusted for inflation, that is, “deflated”.Over the period 1998 to 2001, real wages have (approximately)

A remained unchanged.

B decreased by 1∙43%.

C decreased by 1∙67%.

D increased by 1∙45%.

1.17 If aX² + bX + c = 0, then X = a2

)ac4b(b 2 −±−

If X² – 2X – 24 = 0, then X equals

A2

102 ±−B

2

922 ±−C

2

962 ± D2

102 ±




The next three sub-questions, 1.18 – 1.20, are based on the following data.

A multiplicative time series model should be assumed.

Quarterly sales (units) of Brand X, 2001

Q1 Q2 Q3

Sales (units) 1,600 4,400 1,680

Seasonal variation –20% +100% –30%

1.18 The trend value for Q1 sales (units) is

A 1,280 B 1,920 C 2,000 D none of these.

1.19 The seasonal variation for Q4 in 2001 is

A –50% B 0% C +50% D none of these.

1.20 The forecast for the fourth quarter’s sales (units), Q4, in 2001, assuming the trendpattern continues, is closest to

A 1,300 B 2,300 C 3,800 D 5,200

1.21 The staff in the Complaints Department of an airline are available to answer thetelephone at random times, which amount to 20% of the working day on average.

The probability that a customer’s call is answered for the first time, on their fifth attempt is

A (0∙2)5B (0∙2)4 ∗ (0∙8) C (0∙8)4 ∗ (0∙2) D 1




The next four sub-questions, 1.22 – 1.25, are based on the following table of data.

Mail order buyers of Brand X, classified by area and age (years)

Area \ Age Under 25 25 – 44 45 – 64 65+

North 400 350 300 250South 600 550 500 450East 200 150 100 50West 400 350 300 250

Totals 1,600 1,400 1,200 1,000

1.22 The probability that a randomly-selected Brand X buyer is from the North and under 25years of age is (to 2 decimal places)

A 0∙08 B 0∙25 C 0∙31 D 0∙56

1.23 The probability that a randomly-selected Brand X buyer is from the West or under 25years of age is (to 2 decimal places)

A 0∙08 B 0∙48 C 0∙56 D none of these.

1.24 The probability that a randomly-selected Brand X buyer, who is under 25 years of age,is from the South is (to 3 decimal places)


1.25 The probability that two randomly-selected Brand X buyers are both under 25 years ofage is (to 2 decimal places)


(Total = 50 marks)



FBSM November 20018


ANSWER TWO QUESTIONS ONLY

Question Two

A factory's monthly production costs and output from a production line for circuit boards are asfollows:

Jan Feb Mar April May June July Aug Sept Oct

Output X (units) 200 150 400 450 50 500 150 350 100 250

Costs Y (£000) 10 9 12 14 5 16 10 14 6 10

∑X = 2,600 ∑Y = 106 ∑X² = 895,000 ∑Y² = 1,234 ∑XY = 32,200

Required:(a) (i) Draw on graph paper a scatter diagram of costs against output.

[Do not draw in your "line of best fit".](6 marks)

(ii) Comment on your diagram.

(2 marks)

(b) (i) Calculate the least-squares regression of costs on output and plot this line on thediagram.

(6 marks)

(ii) Explain the meaning of your regression line.

(3 marks)

(c) Estimate approximate values for the correlation coefficient, and r-squared, and explain theirmeanings.[Do not calculate the value of r.]

(3 marks)

(d) The planned output of the factory for November is 300 circuit boards.

(i) Forecast the costs for November.

(2 marks)

(ii) Discuss the reliability of your forecast.

(3 marks)

(Total = 25 marks)



November 2001 FBSM9

Question Three

The Technical Support department of a software company has received the following number oftelephone enquiries each day to its Help Line over the last (typical) fifty days:

15 7 11 25 9 23 8 19 12 27

8 13 2 14 16 20 8 11 8 19

13 34 6 18 26 6 14 17 12 6

9 5 21 7 18 11 3 33 0 14

24 9 18 29 9 20 7 5 9 22

Required:(a) Tabulate these data as a frequency distribution, using seven class intervals of equal width.

(7 marks)

(b) Plot an ogive (a "less than" cumulative frequency curve) for your distribution on graphpaper, and clearly label the positions (locations) of the median and the quartiles.

(8 marks)

(c) From the graph, estimate the numerical values of the median and the quartiles in (b) andbriefly explain their meaning.

(6 marks)

(d) The cost of the Help Line service to the Technical Support department is £5 each call.Assume there are 300 working days in the year.Calculate an estimate of the annual cost of the Help Line, and comment on the reliability ofyour estimate.

(4 marks)

(Total = 25 marks)



FBSM November 200110

Question Four

(a) A company needs to have a cash balance of £500,000 in exactly three years from now. Itplans to achieve this by putting 12 equal quarterly sums into a Fund. The first sum will bedeposited in three months from now. The Fund attracts compound interest of 2∙5% eachquarter.

[Formulae are provided on page 19.]

Required:(i) Calculate the size of the quarterly sum required for the Fund.

(8 marks)

(ii) Demonstrate simply why your answer is reasonable.(2 marks)

(b) A company is considering the purchase of one of two machines, A or B, for £180,000. Theterms of payment for each machine are £90,000 on delivery and £90,000 a year later. Themachines are expected to produce year-end net cash flows as follows:

Time (end of year) 1 2 3 4 5

Net cash flow of A (£000) 60 50 40 30 20

Net cash flow of B (£000) 40 40 40 40 40

At the end of year 5, either machine would be sold for £20,000. The annual cost of capitalis 9% for each year.

Required:(i) Calculate the net present value of each machine.

(12 marks)

(ii) Recommend which machine should be purchased, and explain why.(3 marks)

(Total = 25 marks)

End of paper



ExaminationQuestion andAnswer Book

Write here your full examination number

Centre Code:

Hall Code:

Desk Number:


3c FBSM20 May 2002




THIS QUESTION PAPER BOOKLET IS ALSO YOUR ANSWER BOOKLET.Sufficient space has been provided for you to write your answers and also for workings where questionsrequire them. For section B questions, you must write your answers in the shaded space provided.Additional blank sheets (pages 18-20) are included if you require more space for notes or workings.Please note that you will NOT receive marks for your notes or workings. Do NOT remove any sheets fromthis booklet: cross through neatly any work that is not to be marked. Avoid the use of correction fluid.

You are allowed two hours to answer this question paper. All questions are compulsory.

Answer the ONE question in section A (this has 25 sub-questions and is on pages 2-11)

Answer the THREE questions in section B (these are on pages 12-17)

Maths Tables and Formulae are provided on pages 21-26

You are advised to spend 10 minutes reading through the paper before starting to answer the questions.

You should spend no more than 55 minutes on answering the ONE question in section A, which has 25sub-questions.

You should spend no more than 55 minutes on answering the THREE questions in section B.

Hand this entire booklet to the invigilators at the end of the examination. You are NOT permitted to leavethe examination hall with this booklet.

Do NOT write your name or your student registration number anywhere on this booklet.

TURN OVER

For office use only Total One Two Three Four

Marks awarded (First marker) for each question

Marks awarded (Second marker) for each question




F



Q

1

A

1

A

B

C

D

FMM


REQUIRED:Place a circle “O” around the letter A, B, C or D that gives the correct answer to each sub-question.

If you wish to change your mind about an answer, block out your first answer completely and then circleanother letter. You will NOT receive marks if more than one letter is circled.

Please note that you will NOT receive marks for any workings to these sub-questions. Sufficient spacehas been provided for you to do your workings where these sub-questions require them.

BSM 2 May 2002

uestion One

.1 An index number increases each year by 10% of its value in the previous year. If its value in 1999 was120, its value in 2002 is closest to

150. B 156. C 160. D 162.

Space for workings to 1.1

.2 In a time series of the unit sales of shoes, random variation could be caused by

a general trend.

seasonal effects due to the weather.

cyclical effects resulting from a change in fashion.

unexplained or freak events.

or office use only Total 1.1 1.2

arks awarded (First marker) for each sub-questionarks awarded (Second marker) for each sub-question



May 2002 3 FBSM

1.3 An annual year-end income of £15,000 is required in perpetuity. Assuming a fixed rate of interest of9% each year, and ignoring administrative charges, the sum required now to purchase the annuity isclosest to

A £13,650. B £135,000. C £150,000. D £167,000.


1.4 Which ONE of the following describes a qualitative variable?

A The number of invoices selected for an internal audit.

B The number of errors discovered in batches of invoices.

C The $ value of the error made in invoices in a batch.

D The type of error made in invoices.

1.5 For a certain group of students, the coefficient of rank correlation between their performance inAccounting and their performance in Law is –1. The coefficient of rank correlation between theirperformances in Law and FBSM is also –1. Therefore, the coefficient of rank correlation between theirperformance in Accounting and their performance in FBSM is

A –2

B zero

C +1

D impossible to determine from the information given.


TURN OVER

For office use only Total 1.3 1.4 1.5

Marks awarded (First marker) for each sub-questionMarks awarded (Second marker) for each sub-question



FBSM 4 May 2002

1.6 An accountant has marked some performance criteria out of 20 and found the mean to be 10 marksand the standard deviation to be 2 marks. The marks now have to be expressed as a percentage.

What would be the new value of the standard deviation?

A √10% B √20% C 10% D 20%

1.7 An index number is made up of two items, food and non-food.

Sub-group Weight IndexNon-food 7 130Food 3 ?All items 10 127

The index number for the sub-group Food is closest to

A 120. B 122. C 124. D 126.


1.8 The diagram below shows an ogive (cumulative frequency) for a sample of 400 items.

400

300

Cumulativefrequency

0 X K

The point K on the X-axis represents the value

A which 75% of the sample take.

B below which 75% of the sample values lie.

C which 25% of the sample take.

D above which 75% of the sample values lie.

For office use only Total 1.6 1.7 1.8Marks awarded (First marker) for each sub-questionMarks awarded (Second marker) for each sub-question



May 2002 5 FBSM

1.9Sample 1: 2, 5, 5, 12Sample 2: 1, 3, 5, 8, 8

Which of the following statistics has the same value in both samples?

A Arithmetic mean B Standard deviation C Median D Mode


1.10 A company’s market value has fallen from £32 billion to £2 billion in four years. The average annualpercentage decline in market value is closest to

A 20%. B 40%. C 50%. D 100%.


1.11 Y8 x

x x6 x x

x x4 x x x

x x2 x x

x x

0 4 8 12 X

On the basis of the scatter diagram above, which of the following equations would best represent theregression line of Y on X?

A Y = –X + 8 B Y = X + 8 C Y = X – 8 D Y = –X – 8

TURN OVER




FBSM 6 May 2002

1.12 A sample of 10% of CIMA students is required. Which ONE of the following methods would providethe best simple random sample?

A Select every tenth CIMA student to arrive at their college/institute on one specific day.

B Select randomly, using random number tables, one in ten of every CIMA class.

C Select 10% of colleges/institutions providing CIMA courses, then from these choose all students whoare registered with CIMA.

D Select 10% of all students registered with CIMA, giving each a chance of 0∙1 of being picked.

1.13 Two groups of stock, K and L, are valued. The first group, K, is valued at £10,000 ± 5% and thesecond group, L, is valued at £20,000 ± 10%.

The maximum percentage error in the combined (K + L) stock valuation of £30,000 is closest to

A 7∙5%. B 8∙3%. C 10∙0%. D 15∙0%.


1.14 The sales of a product are recorded monthly for 24 months. The four-point (centred) moving averagesare calculated and plotted on a graph.

How many moving average points are plotted?

A 20 B 21 C 22 D 24





May 2002 7 FBSM

1.15 In a single throw of a pair of fair (six-sided) dice, what is the probability that the result is two numberswhich sum to 7?

A12

1 B6

1 C4

1 D2

1


The following data should be used for 1.16 and 1.17

In an internal audit of 200 invoices, the following numbers of errors were discovered:

Number of errors: 0 1 2 3 4 5 6 or more

Number of invoices: 60 30 40 40 20 10 0

1.16 The percentage of invoices with errors is

A 30%. B 70%. C 80%. D none of these.


1.17 The expected value of the number of errors per invoice is

A 1∙8 B 2 C 2∙1 D 3


TURN OVER




FBSM 8 May 2002

1.18 The number of daily complaints to a railway company has an average (arithmetic mean) of 12 and astandard deviation of 3 complaints.

The coefficient of variation, measured as a percentage, is therefore

A 0∙25%. B 4%. C 25%. D 400%.


1.19 The following formula is used in the financial analysis of dividends:

GP

VR +

=

When the formula is rearranged, with P in terms of the other variables, P is equal to

A GV

R −

B

( )V

GR−C G

R

V −

D ( )GR

V−


For office use only Total 1.18 1.19Marks awarded (First marker) for each sub-questionMarks awarded (Second marker) for each sub-question



May 2002 9 FBSM

1.20 The length of telephone calls to a Software Support line is approximately Normally distributed with amean of 20 minutes and a standard deviation of 5 minutes.

The percentage of calls lasting under 30 minutes is closest to

A 2%. B 48%. C 83%. D 98%.


1.21 A fixed-interest $200,000 mortgage, with annual interest compounded at 6% each year, is to be repaidby 15 equal year-end repayments of $R.

The annual repayment $R will be closest to

A $14,133. B $20,593. C $31,954. D $83,400.



TURN OVER



FBSM 10 May 2002

1.22 A company’s security system is made up of three separate electronic alarms, which operateindependently. The security system operates provided that at least one of the three alarms is working.The probability of an alarm failing at any time is 1 in 100.

The probability of the security system failing is

A 1 in 100. B 3 in 100. C 1 in 10,000. D 1 in 1,000,000.


1.23 You borrow £3,000 and pay 10% each year interest. Ignoring capital, if you pay this interest at theend of each year, what is the present value of the interest payable at the end of the third year?

A ( )103 x £300 x 3 B ( )10

7 x £300 C ( )31110 x £300 D ( )310

11 x £400





May 2002 11 FBSM

1.24 A manufacturer supplies components in boxes of 10, stating that there is a (independent) chance of10% of any one component being faulty.

In a large batch, the percentage of boxes containing no faulty components will be closest to

A 10%. B 35%. C 50%. D 90%.


1.25 A new lake is to be stocked with fish, according to the numbers in the table below.

Type of fish A B C DNumber of fish 400 300 200 100Annual % increase 10 20 30 40

After one year, the percentage of fish of Type D in the lake will be closest to

A 10%. B 12%. C 14%. D 20%.


(Total = 50 Marks)

End of Section A

Section B starts overleaf

TURN OVER




FBSM 12 May 2002


ANSWER ALL THREE QUESTIONS

IMPORTANTMARKS ARE AWARDED FOR CORRECTLY COMPLETING THE SHADED BOXES WITH THECORRECT ANSWER WHERE A MARK IS INDICATED IN THE RIGHT-HAND COLUMN.

THERE ARE NO MARKS FOR COMPLETING THE MISSING FIGURES WHERE NO MARK ISINDICATED, BUT COMPLETING THESE WILL HELP YOU OBTAIN THE CORRECT ANSWERS.

DO NOT WRITE IN THE MARGINS NOR IN THE COLUMNS FOR USE BY MARKERS.

Question Two

In two years from now, some equipment in your company will need replacing. You estimate that £400,000 incash, then, will be required to do this. Your company has three alternative options for achieving this sum.The rate of interest will be 3∙5% per quarter over the next 2 years, in all three options. Interest will becompounded every quarter.

Option (1) Invest £X now, so that the investment grows to £400,000 in two years.

Option (2) Put £25,000 into a Reserve Fund (RF1) every quarter, starting now (that is, 9 deposits aremade), and borrow the shortfall (the amount by which the Reserve Fund (RF1) falls short of itstarget of £400,000).

Option (3) Put £Y into a Reserve Fund (RF2) at the end of every quarter for two years, to achieve thetarget of £400,000 exactly.

A geometric series of n terms, with first term A and common ratio R, is denoted by:

A + AR + AR2 + AR3 + AR4 + … + ARn-1.

The sum of this series is given by: Sn = 1)(R

1)(RA n

−−

Required

Write your answers in the shaded boxes below Marksavailable

For useby thesecondmarker

For useby the

firstmarker

(a) Calculate the value of X, to the nearest £. 2

(b) Calculate the effective annual rate of interest, to 2decimal places. 2

(c) Calculate the amount of money that will be in theReserve Fund (RF1) after 2 years, to the nearest £.

4

(d) Calculate the discount factor that you would use tofind the present value of the shortfall in the ReserveFund (RF1) to 4 decimal places.

1

(e) Calculate the present value of the shortfall in theReserve Fund (RF1) implied by your answer to part(c), to the nearest £100.

2

(f) Calculate the value of £Y, for the Reserve Fund(RF2), to the nearest £.

4

sub-total:15

Part (g) of Question Two is on page 13

Do not write in thesecolumns below



May 2002 13 FBSM

Question Two continued

Required Marksavailable


For useby the

firstmarker

(g) Explain, in no more than 20 words, (in the shaded area below) themeaning of the term “present value”.

2

Sub-total:2

Space for workings and/or notes for Question Two

Total for Question Two = 17 Marks

TURN OVER




FBSM 14 May 2002

Question Three

The unit sales of a toy for the last nine quarters are given below:

Year 2000 2001 2002Quarter Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1

Unit sales 45 170 200 130 85 205 235 170 120

The (moving-average) trend in unit sales is approximately linear and described by the equation

Sales = 110 + 10T

where T = 1 denotes the first quarter, Q1, of 2000, T = 2 denotes the second quarter, Q2, of 2000, and so on.

The unit sales of the toy over the last few years have been analysed in two different ways: firstly, using theadditive model and, secondly, using the multiplicative model. The average seasonal variations for the twomodels are as follows:

Quarter Q1 Q2 Q3 Q4

Additive model (units) -80 +40 +60 -20Multiplicative model -40% +20% +30% -10%

The underlying business conditions are not expected to change during thenext two quarters.

Required



For useby the

firstmarker

(a) Calculate the percentage increase in the total annualsales between 2000 and 2001, to 1 decimal place. 1

(b) Predict the trend value for the second quarter,Q2, of2002. 1

Sub-total:2

Space for workings and/or notes for Question Three

Parts (c) to (f) of Question Three are on page 15




May 2002 15 FBSM

Question Three continued

Required



For useby the

firstmarker

Using the additive model, calculate the forecasts forthe second quarter, Q2, of 2002; AND

1(c)

the third quarter, Q3, of 2002. 1

sub-total:2

(d) Using the multiplicative model, calculate the forecastsfor the second quarter, Q2, of 2002; AND

2

the third quarter, Q3, of 2002. 2

sub-total:4

(e) Based on the sales information given, identify three features of theunit sales of this toy in no more than 20 words each (in the shadedareas below).

1

2

2

2

3

2

Sub-total:6

(f) Explain when it is appropriate to use a multiplicative model forforecasting in no more than 30 words (in the shaded area below).

2

Sub-total:14

Total for Question Three = 16 Marks

TURN OVER




FBSM 16 May 2002

Question Four

The mail-order sales (units) of Brand X in a certain country are shown below. In this country, the populationsof all the twenty sub-groups are equal. Each customer buys one unit. Ages are given in years.

Mail-order sales of Brand X (units) by region and age in 2001

Region\Age 21 – 29 30 – 39 40 – 49 50 – 59 60 + TotalNorth 100 80 50 40 30 300South 55 50 45 30 20 200East 65 60 65 60 50 300West 20 30 40 50 60 200

Space for workings and/or notes for Question Four

Required:



For useby the

firstmarker

(a) Calculate the arithmetic mean sales per sub-group 1

(b) Calculate the median sales per sub-group 1

(c) A customer is to be randomly selected for a holidayprize. What is the probability that this customer is“from the East and over 39 years of age”? 2

(d) A customer is to be randomly selected for a cashprize. Assuming that the winning of two prizes isallowed, what is the probability that this customer is“from the North or under 40 years of age”? 2

sub-total:6

Parts (e) to (h) of Question Four are on page 17




May 2002 17 FBSM

Question Four continued

Required:



For useby the

firstmarker

(e) Without calculation, state the region with the largest standarddeviation in sales (across age groups) and give a reason for youranswer in no more than 20 words.

2

(f) For the North and South, what is the rank correlationcoefficient between sales and age? 2

(g) A chain-base index number system for total saleswas introduced in 1999 with a base figure of 100. Iftotal sales have increased by 10% each year sincethen, what is the chain-base index number for totalsales in 2001 (2000 = 100)? 1

(h) Identify three features shown by the sales data in the table in no morethan 20 words each (in the shaded areas below).

1

2

2

2

3

2

Sub-total:11

Total for Question Four = 17 Marks

End of Question Paper

Maths Tables and Formulae are on pages 21 - 26

TURN OVER FOR ADDITIONAL SPACE FOR NOTES AND WORKINGS




FBSM 18 May 2002

You may use this sheet for workings(no marks are awarded for workings)



May 2002 19 FBSM




FBSM 20 May 2002




May 2002 21 FBSM



FBSM 22 May 2002



May 2002 23 FBSM



FBSM 24 May 2002



May 2002 25 FBSM



FBSM 26 May 2002



May 2002 27 FBSM

DO NOT WRITE ON THIS SHEET



FBSM 28 May 2002

3c

FBSM

Business Mathematics





ExaminationQuestion and AnswerBook






THIS QUESTION PAPER BOOKLET IS ALSO YOUR ANSWER BOOKLET.Sufficient space has been provided for you to write your answers, and also for workings where questions requirethem. For section B questions, you must write your answers in the shaded space provided. Additional blanksheets (pages 16 – 19) are included if you require more space for notes or workings. Please note that you willNOT receive marks for your notes or workings. Do NOT remove any sheets from this booklet: cross through neatlyany work that is not to be marked. Avoid the use of correction fluid.


Answer the ONE question in section A (this has 25 sub-questions and is on pages 2 – 9).

Answer the THREE questions in section B (these are on pages 10 – 15).

Maths Tables and Formulae wee provided within the question paper and are available elsewhere on the website.


You should spend no more than 55 minutes on answering the ONE question in section A, which has 25 sub-questions.


Hand this entire booklet to the invigilators at the end of the examination. You are NOT permitted to leave theexamination hall with this booklet.





SECTION A — 50 MARKSANSWER ALL TWENTY-FIVE SUB-QUESTIONS – 2 MARKS EACH

Each of the sub-questions numbered from 1.1 to 1.25 inclusive, given below, has only ONE correct answer.



Please note that you will NOT receive marks for any workings to these sub-questions. Sufficient space hasbeen provided for you to do your workings where these sub-questions require them.

Question One

1.1The expression y2

x2

aa simplifies to

A a2x/y B a(x-y)/2 C a2(x-y) D a2(x+y)

1.22

QH = Q

DS

The formula above can be re-arranged so that Q equals

A2

DS2H

BH

2DSC

2DSH D

2

HDS2

1.3 The total profit, P, of an organisation is related to output (x units) by the expression:

P = 40 + 11x – 2x2

The organisation will break even (that is, P = 0) with an output of

A 2·5 units. B 4 units. C 5·5 units. D 8 units.

Space for workings for sub-questions 1.1 to 1.3




1.4 3x + 2y = 6 x – 2y = 2

The solution, in the form (x,y), to the above simultaneous equations is

A (0,3) B (2,3) C (2,0) D (3,2)

Space for workings for sub-question 1.4


The following time series represents the weekly sales (£000) of a particular product:

Week Sales£000

1 2002 2403 2504 2205 2306 260

1.5 The 2nd four-point centred moving average for the sales data will be

A 235·5 B 237·5 C 239·5 D none of these.

1.6 Assuming an additive model, and based on the information given, the seasonally-adjusted sales figure(£000) for week 4 will be

A 237·5 B 222·5 C 220·0 D 202·5

Space for workings for sub-questions 1.5 and 1.6





The numbers of houses sold by an estate agent in the last 8 weeks were:

4, 3, 2, 0, 0, 10, 1, 4

1.7 The median number of houses sold per week was

A 0 B 2·5 C 3·0 D 5·0

1.8 The arithmetic mean number of houses sold per week was

A 0 B 2·5 C 3·0 D 5·0


1.9 The following information shows the daily sales revenue (£000) of a company producing a particularitem of clothing, over a period of two years:

Sales£000

Frequency%

0 to under 10 510 to under 20 2020 to under 30 6030 to under 40 1040 to under 50 5

The expected daily sales (in £000) is

A 22 B 24 C 26 D none of these.





1.10 The estimated total cost of each unit of a product is £12 (± £1), and the estimated selling price of eachunit is £20 (± £3). The estimated profit per unit will be

A £8 (± £4) B £8 (± £3) C £8 (± £2) D £8 (± £1)


1.11 In order to carry out a survey into the spending habits of the population living in a certain region of theUnited Kingdom, a sample of individuals is to be selected. The population can be categorisedaccording to age group ("under 18", "18 to under 30", "30 to under 60", "60 and above"). The samplewill consist of 0·5% of the membership of each age group. This method of sampling is an example of

A stratified. B quota. C systematic. D random.

1.12 For a set of six pairs of observations for the variables X (number of employees in hundreds) and Y(product sales in thousands of units), the following results were obtained:

ΣX = 1 ΣY = 15 ΣX2 = 15 ΣY2 = 65 ΣXY = 7

The correlation coefficient is nearest to

A 0·22 B 0·47 C 0·90 D - 0·32






The following table shows the index of prices (1995 = 100) for a certain commodity over theperiod 1995 – 2000:

1995 1996 1997 1998 1999 2000100 105 115 127 140 152

1.13 The percentage increase in the price between 1997 and 1999 is nearest to


1.14 It has been decided to rebase the index so that 1998 = 100. The index for 2000 will now be nearest to

A 193·1 B 139·4 C 125·0 D 119·7





The following data should be used for 1.15 to 1.17

The total overtime cost of a small company varies from week to week, and is found to beNormally distributed with a mean of £800 and a standard deviation of £200.

1.15 In any given week, the probability that the overtime cost will exceed £1,000 is


1.16 In any given week, the probability that the overtime cost will be between £700 and £900 is


1.17 In 10% of weeks, the overtime cost will approximately fall below

A £366 B £455 C £544 D £633






£2,000 is invested in a bank account. The account earns compound interest at 5% per year.

1.18 The cash value of the account, to the nearest £, at the end of five years will be

A £2,680 B £2,553 C £2,431 D £2,335

1.19 The investment will have almost doubled in value after

A 11 years. B 12 years. C 13 years. D 14 years.


1.20 An individual who expects to retire in five years' time, estimates that his company pension will be£15,000 per year. Each year's pension will be paid as a lump sum at the end of the year. If currentinterest rates are 6%, then the present value of the first year's pension, to the nearest £5, will be

A £10,575 B £10,975 C £11,190 D £11,205


1.21 A credit card company states that its nominal annual interest rate is 18%. If interest is chargedmonthly at 1·5%, then the annual percentage rate (APR), correct to 2 decimal places, will be

A 19·56%. B 19·25%. C 18·81%. D none of these.





The following data should be used for 1.22 to 1.25

Two components, A and B, operate independently as part of a computer system. The probabilitiesthat A and B will work correctly are 0·9 and 0·8 respectively.

1.22 The probability that both components will work correctly is

A 0·81 B 0·72 C 0·28 D 0·17

1.23 The probability that both components will not work correctly is


1.24 The probability that only one component will work correctly is

A 0·98 B 0·81 C 0·74 D 0·26

1.25 The probability that at least one component will work correctly is



Total = 50 Marks




SECTION B – 50 MARKSANSWER ALL THREE QUESTIONS

IMPORTANTMARKS ARE AWARDED FOR CORRECTLY COMPLETING THE SHADED BOXES WITH THECORRECT ANSWER WHERE A MARK IS INDICATED IN THE RIGHT-HAND COLUMN.



ADDITIONAL SPACE FOR WORKINGS OR NOTES IS AVAILABLE ON PAGES 16 – 19.

Question Two

At the close of business on the last working day of each month, the Manager of a branch of a bankrequires his staff to produce a brief summary of the account balances. These monthly figures areintended to form the basis of the Manager's quarterly report which is then used by the head office forplanning purposes. To provide this information, the accounts of a randomly selected sample of 100customers are examined. The details for one month are shown in the table below.

Account balance£000

Classmid-point

x

Classfrequency

ffx fx2

0 to less than 2 1 102 to less than 4 3 40 A B4 to less than 6 5 30

6 to 8 7 20Total (∑) 100 420 2,100

Do not write in thesecolumns belowRequired:

Write your answers in the shaded boxes below: Marksavailable

For useby firstmarker

For useby second

marker(a) Fill in the appropriate numerical value as indicated by the letters in the

table above:A 2

B 2

(b) The arithmetic mean of the account balances is 2

(c) The standard deviation of the account balances is 2sub-total:

8

Space for workings





(d) Answer the questions below: Marksavailable


For useby second

marker(i) From the data given in the table on the previous page, construct a

cumulative "less than" frequency ogive.

Summary of the end-of-day account balances

0102030405060708090

100

2 4 6 8

Account balance (£000)

Cum

ulat

ive

Freq

uenc

y

2

(ii) The median of the account balances is 2

(iii) The semi-interquartile range of the accountbalances is

2

(e) Giving your reasons, explain whether the mean and standard deviation,or the median and semi-interquartile range, would be the mostappropriate summary measures for this set of data.(Do not exceed 50 words)

3

sub-total:9

Total Marks for Question Two = 17

Space for workings (additional space for workings is available on pages 16 – 19)


0 2 4 6 8




Question Three

The Production Manager of a large manufacturing company is concerned about the apparent increasingmaintenance costs of the production machinery. There is a feeling that there may be a relationshipbetween the ages of the individual machines and their annual maintenance costs.

In order to examine this theory in more detail, the following information has been collected for arandomly selected sample of 8 machines currently in operation:

Machine A B C D E F G HAge in years (X) 2 5 8 2 3 7 4 10Maintenance costs (£000) (Y) 3 8 12 5 7 10 8 13

ΣX = 41 ΣY = 66 ΣX2 = 271 ΣY2 = 624 ΣXY = 405


Required: Marksavailable


For useby second

marker(a) Plot a scatter diagram of the above data.

Scatter Diagram

0123456789

1011121314

0 1 2 3 4 5 6 7 8 9 10 11Age (years)

Mai

nten

ance

cos

ts (£

000)

2

Required: Write your answers in the shaded boxes below:(b) Describe two important features that are evident from the scatter

diagram. (Do not exceed 20 words for each.)(i)

1

(ii)

1

sub-total:4







For useby second

marker

(c) Calculate the least-squares regression line of maintenance costs(£000) on machine age (years) in the form Y = a + bX.

a = 3

b = 2

(d) In relation to this particular situation, explain the meanings of a and b inthe formula above. (Do not exceed 20 words each.)

a:

2

b:

2

(e) A similar sample, in terms of age range of machines, was selected atone of the company's other factories, yielding the least-squaresregression line:

Y = 3 + 1·5X

(i) Forecast the annual maintenance costs that would beexpected for a 12-year old machine. 2

(ii) Comment on the reliability of your forecast. (Do not exceed 30 words.)

2

sub-total:13

Total Marks for Question Three = 17

Space for workings (additional space for workings is available on pages 16 – 19)





Question Four

(a) A company borrowed £50,000 to buy some new equipment. Interest on this loan is compoundedannually at 9%. The company is required to pay off the loan by making a single payment after fiveyears.

In order to have the cash available to make this payment, it has decided that annual payments will bemade into a sinking fund that compounds interest annually at 5%. The first payment into the fund will bemade one year after the loan was taken out, and the last payment will be made on the day the loan isrepaid.

The table below shows how the debt and sinking fund will grow during the five years:

LOAN SINKING FUND

Year end Interestcharged (£)

Outstandingdebt (£)

Interestearned (£)

Payment(£)

Amount in fund(£)

1 0 13,922·61 13,922·612 A D34 C5 B




For useby second

markerCalculate the appropriate numerical value to go in the space indicatedby the letters in the table above:

A 2

B 2

C 3

D 3sub-total:

10

Space for workings for question four (a)




(b) The Manager of a sports centre has forecast that the sports centre will need £80,000 incash in four years' time so that it can buy some new equipment. In order to have the necessarycash available at that date, the Manager has decided to put £X every quarter into a sinking fund.The payments will start immediately (and therefore 17 payments will be made). Interest on thefund will be compounded at 3·5% per quarter.


Required:

Write your answers in the shaded box below. Marksavailable


For useby second

marker

(i) Calculate the value of £X (that is, the quarterlypayment into the fund). 4

(ii) What is the present value of the £80,000 (assuming aninterest rate of 3·5% per quarter)? 2

sub-total:6

Total Marks for Question Four = 16

Note: A geometric series of n terms, with first term A and common ratio R, is denoted by:A + AR + AR2 + AR3 + … + ARn – 1

The sum of this series is given by: Sn = 1)(R

1)A(Rn

−

−

Space for workings for question four (b)





The Chartered Institute of Management Accountants 2003


Write here your full examination number

Centre Code:

Hall Code:

Desk Number:


3c FBSM19 May 2003

Monday late afternoon



THIS QUESTION PAPER BOOKLET IS ALSO YOUR ANSWER BOOKLET.Sufficient space has been provided for you to write your answers and also for workings where questionsrequire them. For section B questions, you must write your answers in the shaded space provided. Pleasenote that you will NOT receive marks for your notes or workings. Do not exceed the stated number ofwords. Do NOT remove any sheets from this booklet: cross through neatly any work that is not to bemarked. Avoid the use of correction fluid.


Answer the ONE question in section A (this has 25 sub-questions and is on pages 2-13)

Answer the THREE questions in section B (these are on pages 14-20)

Maths Tables and Formulae were provided with the printed question paper, and are available elsewhereon the website








FBSM 2 May 2003



Question One

The following information is required for sub-questions 1.1 and 1.2

The Economic Order Quantity (EOQ) for a particular stock item is given by the expression:

EOQ =h

o

CD2C

1.1 If Co = £2 per order, D = 1,000 items and Ch = £0⋅25 per item, then EOQ (rounded to the nearestwhole number) will be

A 400 B 320 C 160 D 126

1.2 If, for a different stock item, EOQ = 200 items, Co = £4 per order and D = 1,000 items, then Ch (in £ peritem) will be

A 0⋅05 B 0⋅10 C 0⋅15 D 0⋅20







May 2003 3 FBSM

1.3 If the demand for a particular product is x (hundred units per week), then the weekly profit (£P) isgiven by the expression

P = 30 + 4x – 2x2

The break-even demand (that is when P = 0) will be

A 500 units per week.

B 400 units per week.

C 300 units per week.

D 200 units per week.

1.4 The production costs per unit of a certain commodity are £20 (± £2) and the selling price per unit is£35 (± £3). In any given week, the sales are 90 (± 10) units. On the basis of this information, themaximum profit per week is

A £1,000 B £1,600 C £1,800 D £2,000


On a particular day, a company’s finance department received 20 invoices, of which 3 containederrors.

1.5 If two of the invoices are selected at random, then the probability (correct to 2 decimal places) thatneither of them will contain an error is

A 0⋅72 B 0⋅63 C 0⋅42 D 0⋅40

1.6 If two of the invoices are selected at random, then the probability (correct to 2 decimal places) that atleast one of them will contain an error is

A 0⋅60 B 0⋅58 C 0⋅36 D 0⋅28



FBSM 4 May 2003


The following frequency distribution shows the number of days of absence due to sickness, during thelast year, of a randomly selected sample of 50 employees of a large manufacturing company.

Days of absence Number of employees0 – 2 153 – 5 106 – 9 9

10 – 12 813 – 15 6

More than 15 2

1.7 The median number of days of absence due to sickness per employee will be nearest to

A 3 days. B 4 days. C 5 days. D 6 days.

1.8 If the upper quartile is 11 days, and the lower quartile is 1 day, then the quartile deviation will be

A 12 days. B 10 days. C 6 days. D 5 days.

1.9 In the current financial year, an employee’s net income is £15,360, after total deductions of 40% fromher gross income. In the last financial year, her gross income was £23,400. In percentage terms, theincrease in her gross income is

A 9⋅4% B 8⋅6% C 7⋅5% D 6⋅7%

1.10 The following table of index numbers shows how the production of a particular model of motorboat at aboat builders has changed over the period August 2002 to February 2003, with January 2002 = 100:

Aug Sep Oct Nov Dec Jan Feb

Production index 110 119 115 108 102 98 95

If the actual production figure for August was 140 motorboats, then the number of motorboats produced inFebruary 2003 was closest to

A 105 B 121 C 133 D 162



May 2003 5 FBSM

1.11 The following table shows the price of a certain commodity over the years 1998 to 2001:

Year 1998 1999 2000 2001

Price(£) 2⋅70 3⋅11 3⋅42 3⋅83

If a chain-based index is used, the price index number for 2000 will be closest to

A 110 B 117 C 120 D 127

1.12 A broker has estimated the profits or losses for a particular investment and their respectiveprobabilities as follows:

Profit(£000) -1 1 3 5

Probability 0⋅1 0⋅3 0⋅4 0⋅2

The expected profit (£000) on this investment will be

A 2⋅1 B 2⋅2 C 2⋅3 D 2⋅4

1.13 The Personnel Department of a large manufacturing company wishes to measure the correlationbetween the performance of its employees on an aptitude test, and their ability to carry out a specificwork-related task.

The following table shows the rankings of 7 employees at both the test and the task:

Employee A B C D E F GTest Rank 2 5 7 4 1 6 3

Task Rank 2 6 7 4 3 5 1

Spearman’s rank correlation coefficient for this data is

A 0⋅62 B 0⋅72 C 0⋅82 D 0⋅92



FBSM 6 May 2003


A company uses regression analysis to examine the relationship between its total weekly costs (£C)and its weekly production level (P units). The following model was found to be a suitable description ofthis relationship:

C = 1500 + 300P

1.14 If, in a particular week, the production level is 500 units, then the predicted costs will be

A £150,000 B £150,300 C £151,000 D £151,500

1.15 The average variable cost per unit is estimated as

A £300 B £1,500 C £1,800 D £3,030

1.16 A graphical presentation of classified data in which the number of items in each class is representedby the area of the bar is called

A an ogive.

B a histogram.

C a bar chart.

D a compound bar chart.

1.17 A pie chart is to be drawn to represent the following data, which shows the breakdown by departmentof the number of employees working on a particular project:

Department Number of EmployeesMarketing 7Finance 5Personnel 8Sales 10

The angle of the sector (slice), in degrees, of the pie chart representing “Finance” will be

A 30° B 45° C 60° D 90°

1.18 A survey is to be carried out into the spending habits of the population of a large town in the NorthEast of England. It has been decided that five small areas are to be randomly chosen, two close to thetown centre and three in more outlying areas. In these areas, ten interviewers are each required tointerview a randomly selected sample of 30 people.

This system of sampling is an example of

A multi stage. B cluster. C quota. D stratified.



May 2003 7 FBSM

1.19 On one particular checkout in a supermarket, the service times in minutes of five customers were:

3, 2, 1, 5, 4

The standard deviation of these service times, correct to 1 decimal place, is closest to

A 3⋅5 minutes B 2⋅0 minutes C 1⋅5 minutes D 1⋅0 minutes

1.20 At a second checkout in the same supermarket as in sub-question 1.19, the service time has anarithmetic mean of 5 minutes and a standard deviation of 1 minute.

The coefficient of variation will be

A 50% B 20% C 5% D 2%

1.21 The underlying trend in the demand for a particular product is constant (flat), and is subject toquarterly seasonal variations as follows:

Quarter Q1 Q2 Q3 Q4

Seasonality +50% +50% -50% -50%

Assume a multiplicative model is appropriate.

If the demand for the last quarter, Q2, was 240 units, then the forecasted demand for the next quarter, Q3, is

A 80 units. B 100 units. C 120 units. D 140 units.

1.22 A bank offers investors a nominal annual interest rate of 4% with interest paid quarterly.

The effective annual rate of interest is

A 4⋅06% B 4⋅04% C 4⋅02% D 4⋅01%

1.23 If £10,000 is invested now, at an interest rate of 6% compounded annually, then after 5 years thevalue of the investment will be closest to

A £13,226 B £13,382 C £13,562 D £13,598



FBSM 8 May 2003

1.24 A company pays rent of £50,000, annually in advance, on a building for a period of 5 years. Theannual interest rate is 10%. The total present value of the rental repayments will be closest to

A £212,650 B £210,800 C £208,500 D £189,550

1.25 An annuity requires the deposit of £100 per year for 5 years. The deposits are made at the beginningof each year and earn interest at 8% per year. At the end of the 5 years, the investment will be worthclosest to

A £633 B £645 C £654 D £660

(Total = 50 Marks)

End of Section A



May 2003 9 FBSM


ANSWER ALL THREE QUESTIONS

IMPORTANTMARKS ARE AWARDED FOR COMPLETING THE SHADED BOXES WITH THE CORRECTANSWER WHERE A MARK IS INDICATED IN THE RIGHT-HAND COLUMN.



Question Two

As part of its expansion plans, a large financial services organisation is examining the feasibility of updatingand expanding its IT facilities. One proposal is the purchase of a new server costing £7,500. This wouldreduce the operating costs over the next five years as shown below:

End of year 1 2 3 4 5Net cash savings £1,000 £2,000 £3,000 £3,000 £2,000

It is anticipated that the cost of capital to the organisation will be 10% per year over this period.

Required:Write your answers in the shaded boxes below Marks

available

For useby the

secondmarker

For useby thefirst

marker

Complete the table by calculating the appropriate numerical valuesfor the spaces indicated by the letters A-E:

Year endNet cash flow

£Discount factor Present value

£

Now (7,500)

1 1,000 A B

2 2,0003 3,000

4 3,000

1 each

5 2,000 C D11/2

each

(a)

Net Present Value E 2

sub-total: 7




FBSM 10 May 2003


Required:Marks

available

For useby the

secondmarker

For useby thefirst

marker

Explain, in the shaded area below, what is meant by the term“internal rate of return (IRR)”.

(b)

Maximum of 20 words 3

Calculate the approximate internal rate of return (IRR) of the aboveproject, correct to the nearest whole percentage point.

(c)

4

(d) On the basis of your calculations, explain, in the shaded area below,whether or not you would recommend the purchase of the server.

Maximum of 30 words 3





May 2003 11 FBSM

Question Three

A large manufacturing company, with factories throughout Europe, employs a large force of travellingsalespeople. Records show that for salespeople in the UK, the weekly distance travelled per person isapproximately Normally distributed with a mean of 1,000 kilometres and a standard deviation of300 kilometres.

The company’s Head of Marketing and Sales thinks that salespeople whotravel more than 750 kilometres per week should be eligible for a luxurycompany car.

Required:Write your answers in the shaded areas below Marks

available

For useby the

secondmarker

For useby thefirst

marker

The stages in the calculation of the probability that a particularsalesperson in the UK is eligible for a luxury car are shown below.You are required to state the numerical values indicated by the lettersA, B and C. Give your answers correct to 2 decimal places.

(Note: Z denotes the standard normal variable)

P (salesperson is eligible for a luxury car)

= P (weekly distance travelled > A) A 1

= P (Z > B) B 2

(a)

= C C 3The company intends to introduce an incentive scheme in the UKwhich would give an additional payment of £1,000 to each of the10% of salespeople who travel the greatest distances.

Calculate the numerical values indicated by the letters in the followingcalculations, giving your answers correct to 2 decimal places.

From the Normal Tables, the Z-value, which is exceeded by 10% of

Normal values, is D . 2

(b)

Salespeople travelling more than E kilometres

per week should be paid the additional £1,000.

3

(c) In France, where 200 salespeople are employed, the mean distancetravelled is 1,000 kilometres per week, but there is less variability inthe weekly distances. The standard deviation is estimated as 200kilometres.Calculate the number of salespeople in France who travel

(i) less than 1,250 kilometres per week

2

(ii) between 750 kilometres and 1,250 kilometres per week

3





FBSM 12 May 2003

Question Four

A newspaper publisher is promoting the sales of a new local daily newspaper. The following table shows thedaily sales of the newspaper over a recent three-week period:

Day Sales(00s)

Monday 27Tuesday 41Wednesday 45Thursday 53Friday 65Monday 30Tuesday 42Wednesday 50Thursday 57Friday 66Monday 34Tuesday 48Wednesday 53Thursday 59Friday 72

Required:Marks

available

For useby the

secondmarker

For useby thefirst

marker

(a) Plot the above time series data using the following axes:

Sales of newspaper

80

70

60

50

40

30

20

10

0

M T W Th F M T W Th F M T W Th F

Sales,00’s

per day

Day 2




May 2003 13 FBSM



available

For useby the

secondmarker

For useby thefirst

marker

State two features of the time series shown by the graph.

(1)

Maximum of 15 words

(2)

(b)

Maximum of 15 words

1

1

(c) The following table shows the stages in the calculation of the 5-daymoving average trend line. State which values would arise at A, Band C.

* indicates the cell is blank

DaySales(00’s)

(Y)

5-daymoving total

5-daymovingaverage

(T)

Trend(Y – T)

Monday 27

Tuesday 41

Wednesday 45 A * * 2

Thursday 53 234 46⋅80 6⋅20

Friday 65 235 47⋅00 18⋅00

Monday 30 240 48⋅00 -18⋅00

Tuesday 42 244 48⋅80 -6.80

Wednesday 50 245 49⋅00 1⋅00

Thursday 57 249 B 7.20 2

Friday 66 255 51⋅00 15⋅00

Monday 34 258 51⋅60 C

Tuesday 48 260 52⋅00 -4⋅00

Wednesday 53 266 53⋅20 -0⋅20

Thursday 59

Friday 72

2

sub-total: 8




FBSM 14 May 2003



available

For useby the

secondmarker

For useby thefirst

marker

(d) Explain the purpose of the moving average calculation and why, inthis case, it is based on a 5-day period.

maximum of 20 words 2

(e) Using the available data in the table in requirement (c) and assumingan additive model, calculate the seasonal component for Monday,giving your answer correct to two decimal places.

2

(f) For the Tuesday of next week the trend forecast for the sales is 6,600newspapers. What is the forecast for the overall sales for that day?

3

sub-total: 7






The Chartered Institute of Management Accountants 2003


Write your full examination number,your contact ID and your name on adouble-sided card, which must beattached to this booklet here.




INSTRUCTIONS TO CANDIDATESRead this page before you look at the questions

THIS QUESTION PAPER BOOKLET IS ALSO YOUR ANSWER BOOKLET.Sufficient space has been provided for you to write your answers and also for workings where questionsrequire them. For section B questions, you must write your answers in the shaded space provided. Pleasenote that you will NOT receive marks for your notes or workings. Do not exceed the stated number ofwords. Do NOT remove any sheets from this booklet: cross through neatly any work that is not to bemarked. Avoid the use of correction fluid.


Answer the ONE question in section A (this has 25 sub-questions and is on pages 2 – 12)

Answer the THREE questions in section B (these are on pages 14 – 21)

Maths Tables and Formulae are provided on pages 22 – 27





Do NOT write your name or your contact ID anywhere on this booklet.

TURN OVER

For office use only Total One Two Three Four

Marks awarded (First marker) for each question

Marks awarded (Second marker) for each question



F

SECTION A — 50 MARKSANSWER ALL TWENTY-FIVE SUB-QUESTIONS – 2 MARKS EACH

Q

1

A

FMM


REQUIRED:Place a circle "O" around the letter A, B, C or D that gives the correct answer to each sub-question.



BSM 2 November 2003

uestion One

.1 A large department store wishes to carry out a survey by issuing a questionnaire to a sample of 100 ofits 2,000 account holders. The sample is to be selected as follows:

Each customer will be allocated a number from 1 to 2000. A table of random numbers from 1 to 20 willthen be used to select the first member of the sample. Every succeeding 20th member of thepopulation of account holders will then be selected.

This form of sampling is called

stratified. B multi-stage. C systematic. D quota.

or office use only Total 1.1arks awarded (First marker) for each sub-questionarks awarded (Second marker) for each sub-question




1.2 The yearly sales of a particular product from three factories are represented by the following diagram:

��

��

��

��

��

��

��

��

��

Yearly Sales

010002000300040005000600070008000

2000 2001 2002

$000

��Factory C��

�� Factory B�� Factory A

This diagram is an example of

A a Histogram.

B a multiple Bar Chart.

C a Component Bar Chart.

D an Ogive.

1.3 The solution to the simultaneous equations:

4x + 3y = 262x - y = 8

in the form (x,y) is

A (2, 5) B (-5, 2) C (-2, 5) D (5, 2)


TURN OVER





1.4

02468

101214161820

0 2 4 6 8 10X

Y

xxx

xx x x

xx x

xx x

x x

x

x

Which of the following equations best represents the above scatter diagram:

A Y = 2X + 3 B Y = 3X + 2 C Y = 3X - 2 D Y = 2 - 3X


1.5 A customer paid $230 for a television which had been reduced by 15%. The original price of thetelevision before the price reduction was closest to

A $243. B $265. C $271. D $276.






1.6 If the rank correlation coefficient between the performances of two groups of fifteen people performingthe same task was -0⋅1, which ONE of the following statements is true?

A There is perfect agreement between the performances of the two groups.

B There is moderate agreement between the performances of the two groups.

C There is no agreement between the performances of the two groups.

D This is an impossible result.

1.7 Since 1995, the average annual salaries for a group of workers have been index-linked to prices. Thetable below shows the price index since 1997:

(1995 = 100)

Year 1997 1998 1999 2000 2001 2002Price Index 112 118 122 125 127 130

If the average salaries were $30,000 in 1997, then the average salaries of the workers in 2002 would havebeen closest to

A $31,800. B $33,600. C $34,821. D $36,000.


TURN OVER




FBSM

1.8 A toy manufacturer sells 3 ranges of toys. The following table shows sales information for the last twoyears:

Range: Price($/unit)

A 10B 15C 30

A relatives quantity index, to the nearest whole numbe

A 144 B 141


1.9 The sum, S, of the first n terms of a geometricthe formula:

The sum of the first 8 terms of a geometric series wi

The first term of this series is

A 7 B 6


For office use onlyMarks awarded (First marker) for each sub-quesMarks awarded (Second marker) for each sub-qu

FOR FREE CIMA, ACCA & CAT RESOUR

Quantity(000 units)

6 November 2003

2001 2002

30 4050 7010 15

ber, for the year 2002, with 2001 as the base year, will

C 139 D 69

series with first term a and common ratio r, is given by

1)(r1)a(rS

n

−−

=

th common ratio 3 is 19,680.

C 5 D 4

Total 1.8 1.9tionestion

CES VISIT: http://kaka-pakistani.blogspot.com



The following data are to be used to answer questions 1.10 and 1.11 below.A cell phone retailer conducts a survey of 200 cell phone purchasers, and obtains the following resultsrelating to their ages in years:

Age Under 25 25 to 50 Over 50Male 40 30 40Female 60 20 10

1.10 The probability that a randomly selected purchaser is male and aged 50 or under is

A 0⋅15 B 0⋅27 C 0⋅35 D 0⋅64

1.11 If the selected purchaser is female, the probability that she is aged 25 to 50 is

A 0⋅10 B 0⋅22 C 0⋅25 D 0⋅35

Space for workings to 1.10 and 1.11

1.12 The following table shows the number of cars of a particular model sold by a dealer over the last fiveweeks:

Week 1 2 3 4 5Cars sold 8 3 7 9 4

The expected number of cars of this model to be sold in the year (50 weeks) is

A 300 B 310 C 325 D 350


TURN OVER





1.13 A car insurance company estimates that in a given year, each policyholder will make a "small" claim of$500 with a probability of 0⋅1, a "moderate" claim of $1,000 with a probability of 0⋅05, or a "large" claimof $2,000 with a probability of 0⋅01.

In order to break even, between premiums taken in and claims paid out, the company should set the annualpremium for each policy at

A $100. B $120. C $140. D $160.


The following data are to be used to answer questions 1.14 to 1.16 below.

Flights arriving at an airport are subject to delays. The length of the delays is normallydistributed with a mean of 20 minutes and a standard deviation of 8 minutes.

1.14 The probability that a flight will be delayed by less than 10 minutes is nearest to

A 0⋅894 B 0⋅494 C 0⋅250 D 0⋅106

1.15 The probability that a flight will be delayed by between 15 and 25 minutes is nearest to

A 0⋅268 B 0⋅465 C 0⋅535 D 0⋅732

1.16 Approximately 20% of the flight delays are less than

A 11 minutes B 13 minutes C 15 minutes D 17 minutes

Space for workings to 1.14 to 1.16

For office use only Total 1.13 1.14 1.15 1.16Marks awarded (First marker) for each sub-questionMarks awarded (Second marker) for each sub-question




The following data are to be used to answer questions 1.17 and 1.18 below.

The records of a supplier of an automobile part show that the quarterly demand over the pastthree years was as follows:

2000 2001 2002Quarter 1 2 3 4 1 2 3 4 1 2 3 4Demand(000 units)

142 54 162 206 130 50 174 198 126 42 162 186

1.17 Using a 4-point centred moving average, the trend component of the demand (000 units) for Quarter 4of the year 2000 will be closest to

A 206. B 166. C 160. D 138.

1.18 If an additive model is assumed, and the seasonal components of the demand for quarters 2,3 and 4are -88, 30 and 66 respectively, the seasonal component of the demand (000 units) for Quarter 1 willbe

A 8⋅0 B -8⋅0 C 2⋅7 D -2⋅7


1.19 A small manufacturing company owns two machines, A and B. Machine A is valued at $15,000 ± 10%,and machine B is valued at $25,000 ± 5%.

The maximum percentage error in the combined value of the two machines is closest to

A 7⋅0% B 7⋅5% C 10⋅0% D 15⋅0%


TURN OVER





1.20 Which ONE of the following statements regarding sample measures is INCORRECT?

A The arithmetic mean is always distorted by extreme values.

B The median will not be distorted by extreme values.

C The mode can be distorted by extreme values.

D The standard deviation can be distorted by extreme values.

The following data are to be used to answer questions 1.21 and 1.22 below.

$20,000 is invested at an interest rate of 4%, which is compounded annually.

1.21 After 10 years, the investment will have a value, to the nearest $, of

A $23,798. B $25,408. C $27,398. D $29,605.

1.22 The investment will have approximately doubled after

A 18 years. B 20 years. C 22 years. D 25 years.






1.23 An individual has taken out a mortgage of $150,000, at a fixed interest rate of 5% per annum over 20years. Repayments will commence one year after the mortgage is taken out.

The annual repayments will be closest to

A $12,276. B $12,036. C $11,796. D $11,076.


1.24 If the annual rate of interest is 4⋅75%, the amount (to the nearest $) that should be invested now inorder to receive $5,000 per annum in perpetuity, with receipts starting one year from now, is

A $100,653. B $102,365. C $103,526. D $105,263.


TURN OVER





1.25 An item of machinery that was purchased 5 years ago for $100,000 now has a value of $50,000.Assuming the reducing balance method of calculation, the annual rate of depreciation to the nearestwhole percentage point will be

A 17%. B 15%. C 13%. D 11%.


(Total for Question One= 50 Marks)

End of Section A

For office use only Total 1.25Marks awarded (First marker) for each sub-questionMarks awarded (Second marker) for each sub-question




Section B starts on the next page

TURN OVER




SECTION B – 50 MARKSANSWER ALL THREE QUESTIONS

IMPORTANTMARKS ARE AWARDED FOR COMPLETING THE SHADED BOXES WITH THE CORRECTANSWER WHERE A MARK IS INDICATED IN THE RIGHT-HAND COLUMN.



Question Two

Because of an increasing population, the executive committee of a local community centre is planning tobuild an extension to its main building. In order to fund this building project, the centre will need to have$300,000 available at the beginning of January 2005.

To achieve this, the centre intends to make 8 equal quarterly instalments of $X into a sinking fund whichpays a quarterly compound interest rate of 1%. The first of the instalments was paid at the beginning of April2003.

Required:Write your answers to (a) and (b) in the shaded boxes below Marks

available

For useby thefirst

marker


(a) Calculate the annual effective interest rate. 2(b) Calculate the value of the quarterly instalments, $X. 4

Sub-total: 6

Note:The sum of the first n terms of a geometric series with first term A and common ratio R, is:

1)(R1)A(RS

n

n −−

=

Space for workings for question two

Question Two continues on the next page






The executive committee has estimated that the project will take one year to complete, and will be ready foruse in January 2006. The increased cash flows that will be generated by the centre’s extended facilities andfundraising activities during the construction period have been estimated to be $50,000 for each of the firstfive years, and then $30,000 for each of the next five years.

Required:Write your answers to parts (c) to (e) in the shaded boxes below Marks

available

For useby thefirst

marker


(c) The following table shows the calculations necessary to evaluate the NetPresent Value (NPV) of the project, assuming a constant discount rate of5% per year. Complete the table by replacing the letters with theappropriate numerical values:

YearCash flow

($)Discount

factorPresentvalue ($)

2005 = 0 (300,000)1 50,0002 50,000 A 23 50,0004 50,0005 50,0006 30,0007 30,0008 30,000 B 29 30,00010 30,000

NPV 18,290(d) An alternative way of calculating the NPV would have been to use the

following formula:

NPV = -300,000 + (50,000 x C) + 30,000 x (D - C)

The values that should be inserted for C and D are:C 2D 2

(e) Comment on the NPV of the project.


(Total for Question Two = 16 Marks)

Question Three starts on the next page

TURN OVER





Question Three

Airport Catering Ltd provides catering services at airports throughout Europe. Each month, the SalesManager is required to produce a statistical report that summarises the company’s performance.

The table below shows October's sales figures ($000) at 50 of its branches:

Sales($000) Frequency

Less than 30 330 < 60 560 < 90 790 < 120 9

120 < 150 11150 < 180 8180 < 210 5210 < 240 2

Total 50

Required:Write your answers to part (a) in the shaded boxes below Marks

available

For useby thefirst

marker


(a) The following table shows the workings leading to the calculation ofthe mean and standard deviation of October’s sales.Calculate the numerical values that would occupy the spaces in thetable shown as A, B and C.

Sales($000)

Frequency(f)

Class Mid-point(x)

f.x f.x2

< 30 3 30 < 60 5 60 < 90 7 A 2

90 < 120 9 B 2

120 < 150 11 C 2

150 < 180 8180 < 210 5210 < 240 2

Total 50 5,970 859,050(b) For October, calculate

(i) The mean sales ($000) 2

(ii) The standard deviation of the monthly sales ($000) 2

Sub-total: 10

Question Three continues on the next page






Required:Write your answer to part (c) in the shaded box below Marks

available

For useby thefirst

marker


For September, the mean and standard deviation of the monthlysales figures were $120,100 and $34,450 respectively.Compare the two months’ sales figures.

(c)

maximum of 30 words 2(d) Use the following axes to draw an ogive for October’s sales figures:

AIRPORT CATERING Ltd

0102030405060708090

100

30 60 90 120 150 180 210 240

SALES($000)

%

3

sub-total: 5

Space for workings to question three

Question Three continues on the next page

TURN OVER






Required:Write your answer to part (e) in the shaded box below Marks

available

For useby thefirst

marker


(e) The company operates a bonus scheme under which each one of the10 branches with the highest sales is given a free flight, which canthen be allocated to a member of staff at the branch manager’sdiscretion. Based on your ogive, estimate the monthly sales figureneeded to qualify for the bonus in October.The estimated monthly figure is $ 2

Space for workings to question three

(Total for Question Three = 17 marks)





Question Four

Each year, a large company, which manufactures domestic electrical appliances, pays its employees anannual bonus. The Company Accountant wishes to assess the effect of the previous year’s bonus on thecompany’s output for the following year.

Data relating to bonus paid (as a percentage of annual salary) and total output (tens of thousands of unitssold) over an 8-year period are given in the following table:

Previous years bonus (%) 0 1 2 3 4 5 6 7Following years output (0,000s) 3 6 14 15 20 18 24 25

Required:Marks

available

For useby thefirst

marker


(a) Plot a scatter diagram of the above data on the axes provided:

Scatter Diagram

30

25

20

15

10

5

0Out

put (

0,00

0 un

its)

0 1 2 3 4 5 6 7 8

Bonus (%)

2

(b) Comment on the relationship shown by your scatter diagram in theshaded box below.


Sub-total: 4

Question Four continues on the next page

TURN OVER






Required:Write your answers to parts (c) and (d) in the shaded boxes below Marks

available

For useby thefirst

marker


If Bonus (%) is represented by X, and Output (0,000s) is representedby Y, the following totals have been calculated from the data given inthe table on page 19:

ΣX = 28, ΣY = 125, ΣX2 = 140, ΣY2 = 2391, ΣX.Y = 568Calculate the correlation coefficient between Bonus and Output,giving your answer correct to 2 decimal places.

(c)

4

(d) The least squares regression equation relating the previous year'sannual bonus to the following year’s output is:

Output (0,000s) = 4⋅75 + 3⋅11 x Bonus (%)In the above equation, what does the value 4⋅75 represent?


Sub-total: 7

Space for workings to question four

Question Four continues on the next page






Required:Write your answers to parts (e) to (g) in the shaded boxes below Marks

available

For useby thefirst

marker


(e) If the annual bonus paid last year was 10%, predict the output for thecurrent year.

2

(f) Comment on the reliability of the prediction that you made in part (e)


(g) Another similar manufacturing company has found that the coefficientof determination between Bonus and Output is 0⋅86. Explain what thismeans.


(Total for Question Four = 17 Marks)

Space for workings to question four


Maths Tables and Formulae are on pages 22 – 27























3c

FBSM

Business Mathematics




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