foundation level business mathematics 3c fbsm level business mathematics 3c fbsm 17 november 2003...

The Chartered Institute of Management Accountants 2003

ExaminationQuestion andAnswer Book

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

Foundation Level Business Mathematics

3c FBSM17 November 2003

Monday late afternoon

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.

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 – 12)

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

Maths Tables and Formulae are provided on pages 22 – 27

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 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

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

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 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

November 2003 3 FBSM

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)

Space for workings to 1.3

TURN OVER

For office use only Total 1.2 1.3Marks awarded (First marker) for each sub-questionMarks awarded (Second marker) for each sub-question

FBSM 4 November 2003

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

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


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

For office use only Total 1.10 1.11 1.12Marks awarded (First marker) for each sub-questionMarks awarded (Second marker) for each sub-question


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.

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

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

For useby thesecondmarker

(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

Do not write in thesecolumns below


Question Two continued

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.

maximum of 20 words 2

(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



Question Three continued

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



Question Three continued

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



Question Four continued

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



Question Four continued

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

End of Question Paper

Maths Tables and Formulae are on pages 22 – 27



3c

FBSM

Business Mathematics

Monday late afternoon

foundation level business mathematics 3c fbsm level business mathematics 3c fbsm 17 november 2003...

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