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1 Examination Question and Answer Book Foundation Level 3c Business Mathematics FBSM 18 November 00 Day 1 late afternoon INSTRUCTIONS TO CANDIDATES Read 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 questions require them. For section B questions, you must write your answers in the shaded space provided. Additional blank sheets (pages 16 19) 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 from this 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 5 sub-questions and is on pages 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 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 5 subquestions. 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 leave the examination hall with this booklet. Do NOT write your name or your student registration number anywhere on this booklet. The Chartered Institute of Management Accountants 00

2 SECTION A 50 MARKS ANSWER ALL TWENTY-FIVE SUB-QUESTIONS MARKS EACH Each of the sub-questions numbered from 1.1 to 1.5 inclusive, given below, has only ONE correct answer. 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 circle another 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 space has been provided for you to do your workings where these sub-questions require them. Question One 1.1 a The expression a x y simplifies to A a x/y B a (x-y)/ C a (x-y) D a (x+y) 1. QH DS = Q The formula above can be re-arranged so that Q equals A H DS B DS H C H DS D DS H 1.3 The total profit, P, of an organisation is related to output (x units) by the expression: P = x x The organisation will break even (that is, P = 0) with an output of A 5 units. B 4 units. C 5 5 units. D 8 units. Space for workings for sub-questions 1.1 to 1.3 FBSM November 00

3 1.4 3x + y = 6 x y = The solution, in the form (x,y), to the above simultaneous equations is A (0,3) B (,3) C (,0) D (3,) Space for workings for sub-question 1.4 The following data should be used for 1.5 and 1.6 The following time series represents the weekly sales ( 000) of a particular product: Week Sales The nd four-point centred moving average for the sales data will be A 35 5 B 37 5 C 39 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 37 5 B 5 C 0 0 D 0 5 Space for workings for sub-questions 1.5 and 1.6 November 00 3 FBSM

4 The following data should be used for 1.7 and 1.8 The numbers of houses sold by an estate agent in the last 8 weeks were: 4, 3,, 0, 0, 10, 1, The median number of houses sold per week was A 0 B 5 C 3 0 D The arithmetic mean number of houses sold per week was A 0 B 5 C 3 0 D 5 0 Space for workings for sub-questions 1.7 and The following information shows the daily sales revenue ( 000) of a company producing a particular item of clothing, over a period of two years: The expected daily sales (in 000) is Sales 000 Frequency % 0 to under to under to under to under to under 50 5 A B 4 C 6 D none of these. Space for workings for sub-question 1.9 FBSM 4 November 00

5 1.10 The estimated total cost of each unit of a product is 1 (± 1), and the estimated selling price of each unit is 0 (± 3). The estimated profit per unit will be A 8 (± 4) B 8 (± 3) C 8 (± ) D 8 (± 1) Space for workings for sub-question In order to carry out a survey into the spending habits of the population living in a certain region of the United Kingdom, a sample of individuals is to be selected. The population can be categorised according to age group ("under 18", "18 to under 30", "30 to under 60", "60 and above"). The sample will 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. 1.1 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 ΣX = 15 ΣY = 65 ΣXY = 7 The correlation coefficient is nearest to A 0 B 0 47 C 0 90 D Space for workings for sub-question 1.1 November 00 5 FBSM

6 The following data should be used for 1.13 and 1.14 The following table shows the index of prices (1995 = 100) for a certain commodity over the period : The percentage increase in the price between 1997 and 1999 is nearest to A 5 0 B 3 C 1 7 D none of these It has been decided to rebase the index so that 1998 = 100. The index for 000 will now be nearest to A B C 15 0 D Space for workings for sub-questions 1.13 and 1.14 FBSM 6 November 00

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 be Normally distributed with a mean of 800 and a standard deviation of In any given week, the probability that the overtime cost will exceed 1,000 is A B C D none of these In any given week, the probability that the overtime cost will be between 700 and 900 is A B C D none of these In 10% of weeks, the overtime cost will approximately fall below A 366 B 455 C 544 D 633 Space for workings for sub-questions 1.15 to 1.17 November 00 7 FBSM

8 The following data should be used for 1.18 and 1.19,000 is invested in a bank account. The account earns compound interest at 5% per year The cash value of the account, to the nearest, at the end of five years will be A,680 B,553 C,431 D, The investment will have almost doubled in value after A 11 years. B 1 years. C 13 years. D 14 years. Space for workings for sub-questions 1.18 and 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 current interest 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 11,05 Space for workings for sub-question A credit card company states that its nominal annual interest rate is 18%. If interest is charged monthly at 1 5%, then the annual percentage rate (APR), correct to decimal places, will be A 19 56%. B 19 5%. C 18 81%. D none of these. Space for workings for sub-question 1.1 FBSM 8 November 00

9 The following data should be used for 1. to 1.5 Two components, A and B, operate independently as part of a computer system. The probabilities that A and B will work correctly are 0 9 and 0 8 respectively. 1. The probability that both components will work correctly is A 0 81 B 0 7 C 0 8 D The probability that both components will not work correctly is A 0 0 B 0 03 C 0 3 D none of these. 1.4 The probability that only one component will work correctly is A 0 98 B 0 81 C 0 74 D The probability that at least one component will work correctly is A 0 64 B 0 81 C 0 98 D none of these. Space for workings for sub-questions 1. to 1.5 Total = 50 Marks November 00 9 FBSM

10 SECTION B 50 MARKS ANSWER ALL THREE QUESTIONS IMPORTANT MARKS ARE AWARDED FOR CORRECTLY COMPLETING THE SHADED BOXES WITH THE CORRECT ANSWER WHERE A MARK IS INDICATED IN THE RIGHT-HAND COLUMN. THERE ARE NO MARKS FOR COMPLETING THE MISSING FIGURES WHERE NO MARK IS INDICATED, BUT COMPLETING THESE WILL HELP YOU OBTAIN THE CORRECT ANSWERS. DO NOT WRITE IN THE MARGINS NOR IN THE COLUMNS FOR USE BY MARKERS. ADDITIONAL SPACE FOR WORKINGS OR NOTES IS AVAILABLE ON PAGES Question Two At the close of business on the last working day of each month, the Manager of a branch of a bank requires his staff to produce a brief summary of the account balances. These monthly figures are intended to form the basis of the Manager's quarterly report which is then used by the head office for planning purposes. To provide this information, the accounts of a randomly selected sample of 100 customers are examined. The details for one month are shown in the table below. Required: Account balance 000 Class mid-point x Class frequency f fx fx 0 to less than 1 10 to less than A B 4 to less than to Total ( ) ,100 Write your answers in the shaded boxes below: (a) Fill in the appropriate numerical value as indicated by the letters in the table above: Do not write in these columns below Marks available A B by first by second (b) The arithmetic mean of the account balances is (c) The standard deviation of the account balances is Space for workings sub-total: 8 FBSM 10 November 00

11 Required: (d) Answer the questions below: Marks available (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 Do not write in these columns below by first by second Cumulative Frequency Account balance ( 000) (ii) The median of the account balances is (iii) The semi-interquartile range of the account balances is (e) Giving your reasons, explain whether the mean and standard deviation, or the median and semi-interquartile range, would be the most appropriate 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) Total for Question Two = 17 Marks November FBSM

12 Question Three The Production Manager of a large manufacturing company is concerned about the apparent increasing maintenance costs of the production machinery. There is a feeling that there may be a relationship between 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 a randomly selected sample of 8 machines currently in operation: Machine A B C D E F G H Age in years (X) Maintenance costs ( 000) (Y) ΣX = 41 ΣY = 66 ΣX = 71 ΣY = 64 ΣXY = 405 Required: (a) Plot a scatter diagram of the above data. Do not write in these columns below Marks available by first by second Scatter Diagram Maintenance costs ( 000) Age (years) (b) (i) Required: Write your answers in the shaded boxes below: Describe two important features that are evident from the scatter diagram. (Do not exceed 0 words for each.) 1 (ii) 1 sub-total: 4 FBSM 1 November 00

13 Required: Write your answers in the shaded boxes below: (c) Calculate the least-squares regression line of maintenance costs ( 000) on machine age (years) in the form Y = a + bx. Do not write in these columns below Marks available by first by second a = 3 b = (d) In relation to this particular situation, explain the meanings of a and b in the formula above. (Do not exceed 0 words each.) a: b: (e) (i) A similar sample, in terms of age range of machines, was selected at one of the company's other factories, yielding the least-squares regression line: Y = X Forecast the annual maintenance costs that would be expected for a 1-year old machine. (ii) Comment on the reliability of your forecast. (Do not exceed 30 words.) sub-total: 13 Total Marks for Question Three = 17 Space for workings (additional space for workings is available on pages 16 19) Total for Question Three = 17 Marks November FBSM

14 Question Four (a) A company borrowed 50,000 to buy some new equipment. Interest on this loan is compounded annually at 9%. The company is required to pay off the loan by making a single payment after five years. In order to have the cash available to make this payment, it has decided that annual payments will be made into a sinking fund that compounds interest annually at 5%. The first payment into the fund will be made one year after the loan was taken out, and the last payment will be made on the day the loan is repaid. The table below shows how the debt and sinking fund will grow during the five years: LOAN SINKING FUND Year end Interest Outstanding Interest Payment Amount in fund charged ( ) debt ( ) earned ( ) ( ) ( ) , ,9 61 A D 3 4 C 5 B Required: Write your answers in the shaded boxes below: Calculate the appropriate numerical value to go in the space indicated by the letters in the table above: Do not write in these columns below Marks available by first by second A B C 3 D 3 sub-total: 10 Space for workings for question four (a) FBSM 14 November 00

15 (b) The Manager of a sports centre has forecast that the sports centre will need 80,000 in cash in four years' time so that it can buy some new equipment. In order to have the necessary cash 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 the fund will be compounded at 3 5% per quarter. Required: Write your answers in the shaded box below. (i) Calculate the value of X (that is, the quarterly payment into the fund). Do not write in these columns below Marks available 4 by first by second (ii) What is the present value of the 80,000 (assuming an interest rate of 3 5% per quarter)? 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 + AR + AR AR n 1 The sum of this series is given by: S n = Space for workings for question four (b) A(R n 1) (R 1) Total for Question Four = 16 Marks End of Question Paper November FBSM

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