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

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Examination Question and Answer Book Write here your full examination number Centre Code: Hall Code: Desk Number: Foundation Level 3c Business Mathematics FBSM 0 May 00 Day 1 late afternoon

1 Examination Question and Answer Book Write here your full examination number Centre Code: Hall Code: Desk Number: Foundation Level 3c Business Mathematics FBSM 0 May 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 18-0) 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 -11) Answer the THREE questions in section B (these are on pages 1-17) Maths Tables and Formulae are provided on pages 1-6 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 sub-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 leave the 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 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 An index number increases each year by 10% of its value in the previous year. If its value in 1999 was 10, its value in 00 is closest to A 150. B 156. C 160. D 16. Space for workings to In a time series of the unit sales of shoes, random variation could be caused by A B C D a general trend. seasonal effects due to the weather. cyclical effects resulting from a change in fashion. unexplained or freak events. For office use only Total Marks awarded (First marker) for each sub-question Marks awarded (Second marker) for each sub-question FBSM May 00

3 1.3 An annual year-end income of 15,000 is required in perpetuity. Assuming a fixed rate of interest of 9% each year, and ignoring administrative charges, the sum required now to purchase the annuity is closest to A 13,650. B 135,000. C 150,000. D 167,000. Space for workings to Which ONE of the following describes a qualitative variable? A B C D The number of invoices selected for an internal audit. The number of errors discovered in batches of invoices. The $ value of the error made in invoices in a batch. The type of error made in invoices. 1.5 For a certain group of students, the coefficient of rank correlation between their performance in Accounting and their performance in Law is 1. The coefficient of rank correlation between their performances in Law and FBSM is also 1. Therefore, the coefficient of rank correlation between their performance in Accounting and their performance in FBSM is A B zero C +1 D impossible to determine from the information given. Space for workings to 1.5 For office use only Total Marks awarded (First marker) for each sub-question Marks awarded (Second marker) for each sub-question TURN OVER May 00 3 FBSM

4 1.6 An accountant has marked some performance criteria out of 0 and found the mean to be 10 marks and the standard deviation to be marks. The marks now have to be expressed as a percentage. What would be the new value of the standard deviation? A 10% B 0% C 10% D 0% 1.7 An index number is made up of two items, food and non-food. Sub-group Weight Index Non-food Food 3? All items The index number for the sub-group Food is closest to A 10. B 1. C 14. D 16. Space for workings to The diagram below shows an ogive (cumulative frequency) for a sample of 400 items Cumulative frequency 0 X K The point K on the X-axis represents the value A B C D which 75% of the sample take. below which 75% of the sample values lie. which 5% of the sample take. above which 75% of the sample values lie. For office use only Total Marks awarded (First marker) for each sub-question Marks awarded (Second marker) for each sub-question FBSM 4 May 00

5 1.9 Sample 1:, 5, 5, 1 Sample : 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 Space for workings to A company s market value has fallen from 3 billion to billion in four years. The average annual percentage decline in market value is closest to A 0%. B 40%. C 50%. D 100%. Space for workings to Y 8 x x x 6 x x x x 4 x x x x x x x x x X On the basis of the scatter diagram above, which of the following equations would best represent the regression line of Y on X? A Y = X + 8 B Y = X + 8 C Y = X 8 D Y = X 8 For office use only Total Marks awarded (First marker) for each sub-question Marks awarded (Second marker) for each sub-question TURN OVER May 00 5 FBSM

6 1.1 A sample of 10% of CIMA students is required. Which ONE of the following methods would provide the best simple random sample? A B C D Select every tenth CIMA student to arrive at their college/institute on one specific day. Select randomly, using random number tables, one in ten of every CIMA class. Select 10% of colleges/institutions providing CIMA courses, then from these choose all students who are registered with CIMA. Select 10% of all students registered with CIMA, giving each a chance of 0 1 of being picked Two groups of stock, K and L, are valued. The first group, K, is valued at 10,000 ± 5% and the second group, L, is valued at 0,000 ± 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%. Space for workings to The sales of a product are recorded monthly for 4 months. The four-point (centred) moving averages are calculated and plotted on a graph. How many moving average points are plotted? A 0 B 1 C D 4 Space for workings to 1.14 For office use only Total Marks awarded (First marker) for each sub-question Marks awarded (Second marker) for each sub-question FBSM 6 May 00

7 1.15 In a single throw of a pair of fair (six-sided) dice, what is the probability that the result is two numbers which sum to 7? A 1 B 1 1 C 6 1 D 4 1 Space for workings to 1.15 The following data should be used for 1.16 and 1.17 In an internal audit of 00 invoices, the following numbers of errors were discovered: Number of errors: or more Number of invoices: The percentage of invoices with errors is A 30%. B 70%. C 80%. D none of these. Space for workings to The expected value of the number of errors per invoice is A 1 8 B C 1 D 3 Space for workings to 1.17 For office use only Total Marks awarded (First marker) for each sub-question Marks awarded (Second marker) for each sub-question TURN OVER May 00 7 FBSM

8 1.18 The number of daily complaints to a railway company has an average (arithmetic mean) of 1 and a standard deviation of 3 complaints. The coefficient of variation, measured as a percentage, is therefore A 0 5%. B 4%. C 5%. D 400%. Space for workings to The following formula is used in the financial analysis of dividends: A V R = + G P When the formula is rearranged, with P in terms of the other variables, P is equal to R G V B ( R G) V C V G R D ( R V G) Space for workings to 1.19 For office use only Total Marks awarded (First marker) for each sub-question Marks awarded (Second marker) for each sub-question FBSM 8 May 00

9 1.0 The length of telephone calls to a Software Support line is approximately Normally distributed with a mean of 0 minutes and a standard deviation of 5 minutes. The percentage of calls lasting under 30 minutes is closest to A %. B 48%. C 83%. D 98%. Space for workings to A fixed-interest $00,000 mortgage, with annual interest compounded at 6% each year, is to be repaid by 15 equal year-end repayments of $R. The annual repayment $R will be closest to A $14,133. B $0,593. C $31,954. D $83,400. Space for workings to 1.1 For office use only Total Marks awarded (First marker) for each sub-question Marks awarded (Second marker) for each sub-question TURN OVER May 00 9 FBSM

10 1. A company s security system is made up of three separate electronic alarms, which operate independently. 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. Space for workings to You borrow 3,000 and pay 10% each year interest. Ignoring capital, if you pay this interest at the end of each year, what is the present value of the interest payable at the end of the third year? A ( 3 10) x 300 x 3 B ( 7 10) x 300 C ( 10 ) 3 x 300 D ( ) 3 Space for workings to x 400 For office use only Total Marks awarded (First marker) for each sub-question Marks awarded (Second marker) for each sub-question FBSM 10 May 00

11 1.4 A manufacturer supplies components in boxes of 10, stating that there is a (independent) chance of 10% 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%. Space for workings to A new lake is to be stocked with fish, according to the numbers in the table below. Type of fish A B C D Number of fish Annual % increase After one year, the percentage of fish of Type D in the lake will be closest to A 10%. B 1%. C 14%. D 0%. Space for workings to 1.5 (Total = 50 Marks) End of Section A Section B starts overleaf For office use only Total Marks awarded (First marker) for each sub-question Marks awarded (Second marker) for each sub-question TURN OVER May FBSM

12 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. Question Two In two years from now, some equipment in your company will need replacing. You estimate that 400,000 in cash, 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 years, in all three options. Interest will be compounded every quarter. Option (1) Option () Option (3) Invest X now, so that the investment grows to 400,000 in two years. Put 5,000 into a Reserve Fund (RF1) every quarter, starting now (that is, 9 deposits are made), and borrow the shortfall (the amount by which the Reserve Fund (RF1) falls short of its target of 400,000). Put Y into a Reserve Fund (RF) at the end of every quarter for two years, to achieve the target of 400,000 exactly. A geometric series of n terms, with first term A and common ratio R, is denoted by: A + AR + AR + AR 3 + AR AR n-1. The sum of this series is given by: S n = n A (R 1) (R 1) Do not write in these columns below Required Write your answers in the shaded boxes below Marks available (a) Calculate the value of X, to the nearest. (b) Calculate the effective annual rate of interest, to decimal places. (c) 4 (d) (e) (f) Calculate the amount of money that will be in the Reserve Fund (RF1) after years, to the nearest. Calculate the discount factor that you would use to find the present value of the shortfall in the Reserve Fund (RF1) to 4 decimal places. Calculate the present value of the shortfall in the Reserve Fund (RF1) implied by your answer to part (c), to the nearest 100. Calculate the value of Y, for the Reserve Fund (RF), to the nearest. 1 4 sub-total: 15 For use by the second marker For use by the first marker Part (g) of Question Two is on page 13 FBSM 1 May 00

13 Question Two continued Do not write in these columns below (g) Required Explain, in no more than 0 words, (in the shaded area below) the meaning of the term present value. Marks available For use by the second marker For use by the first marker Sub-total: Space for workings and/or notes for Question Two Total for Question Two = 17 Marks TURN OVER May FBSM

14 Question Three The unit sales of a toy for the last nine quarters are given below: Year Quarter Q 1 Q Q 3 Q 4 Q 1 Q Q 3 Q 4 Q 1 Unit sales The (moving-average) trend in unit sales is approximately linear and described by the equation Sales = T where T = 1 denotes the first quarter, Q 1, of 000, T = denotes the second quarter, Q, of 000, and so on. The unit sales of the toy over the last few years have been analysed in two different ways: firstly, using the additive model and, secondly, using the multiplicative model. The average seasonal variations for the two models are as follows: Quarter Q 1 Q Q 3 Q 4 Additive model (units) Multiplicative model -40% +0% +30% -10% The underlying business conditions are not expected to change during the next two quarters. Do not write in these columns below Required Write your answers in the shaded boxes below Marks available (a) Calculate the percentage increase in the total annual sales between 000 and 001, to 1 decimal place. 1 (b) Predict the trend value for the second quarter,q, of Sub-total: For use by the second marker For use by the first marker Space for workings and/or notes for Question Three Parts (c) to (f) of Question Three are on page 15 FBSM 14 May 00

15 Question Three continued Do not write in these columns below Required Write your answers in the shaded boxes below (c) (d) Using the additive model, calculate the forecasts for the second quarter, Q, of 00; AND Marks available 1 the third quarter, Q 3, of sub-total: Using the multiplicative model, calculate the forecasts for the second quarter, Q, of 00; AND For use by the second marker For use by the first marker (e) the third quarter, Q 3, of 00. Based on the sales information given, identify three features of the unit sales of this toy in no more than 0 words each (in the shaded areas below). sub-total: (f) Explain when it is appropriate to use a multiplicative model for forecasting in no more than 30 words (in the shaded area below). Sub-total: 6 Sub-total: 14 Total for Question Three = 16 Marks TURN OVER May FBSM

16 Question Four The mail-order sales (units) of Brand X in a certain country are shown below. In this country, the populations of 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 001 Region\Age Total North South East West Space for workings and/or notes for Question Four Do not write in these columns below Required: Write your answers in the shaded boxes below Marks available (a) Calculate the arithmetic mean sales per sub-group 1 (b) Calculate the median sales per sub-group 1 (c) (d) A customer is to be randomly selected for a holiday prize. What is the probability that this customer is from the East and over 39 years of age? A customer is to be randomly selected for a cash prize. Assuming that the winning of two prizes is allowed, what is the probability that this customer is from the North or under 40 years of age? Parts (e) to (h) of Question Four are on page 17 sub-total: 6 For use by the second marker For use by the first marker FBSM 16 May 00

17 Question Four continued Do not write in these columns below Required: Write your answers in the shaded boxes below (e) Without calculation, state the region with the largest standard deviation in sales (across age groups) and give a reason for your answer in no more than 0 words. Marks available For use by the second marker For use by the first marker (f) (g) (h) For the North and South, what is the rank correlation coefficient between sales and age? A chain-base index number system for total sales was introduced in 1999 with a base figure of 100. If total sales have increased by 10% each year since then, what is the chain-base index number for total sales in 001 (000 = 100)? 1 Identify three features shown by the sales data in the table in no more than 0 words each (in the shaded areas below). 1 3 Sub-total: 11 Total for Question Four = 17 Marks End of Question Paper Maths Tables and Formulae are on pages 1-6 TURN OVER FOR ADDITIONAL SPACE FOR NOTES AND WORKINGS May FBSM

18 You may use this sheet for workings (no marks are awarded for workings) FBSM 18 May 00

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28 3c FBSM Business Mathematics Day 1 late afternoon FBSM 8 May 00

GRADE 12 SEPTEMBER 2012 MATHEMATICS P1

Province of the EASTERN CAPE EDUCATION NATIONAL SENIOR CERTIFICATE GRADE 12 SEPTEMBER 2012 MATHEMATICS P1 MARKS: 150 TIME: 3 hours *MATHE1* This question paper consists of 8 pages, 3 diagram sheets and