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C03-Fundamentals of business mathematicsSaSample Exam PaperQuestion 1A 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.B.C.D.10%20%21%0.1Q x 0.1PQuestion 2The 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, excluding VAT, toCentral Administration and to allocate 30% of the remainder, excluding VAT, to Finance. Thetelephone costs (to the nearest ) to be allocated to Finance will be closest to:Question 3The following formula is used in the financial analysis of dividends:R (V/P) GWhen the formula is rearranged, with P in terms of the other variables, P is equal to:A.B.C.D.(R/V)-G(R-G)/V(V/R)-GV/R-GQuestion 4A company’s market value has fallen from 32 billion to 2 billion in four years. The averageannual percentage decline in market value is closet to:A.B.C.D.20%40%50%100%Question 5If 3x 2y 6 and x – 2y 2. The solution in the form (x,y), to the above simultaneousequations is1Updated: October 2013

C03-Fundamentals of business mathematicsSaQuestion 6The estimated total cost of each unit of a product is 12 ( 1), and the estimated sellingprice of each unit is 20 ( 3). The estimate profit per unit will be:A.B.C.D. 8 ( 4) 8 ( 3) 8 ( 2) 8 ( 1)Question 7A 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.B.C.D.TC 100 and R 120 and R TCTC 100 and R 120 and TC RTC 100 and R 120 and R TCTC 100 and R 120 and R TCQuestion 8In a group of 100 players, 30 are male, 55 are a pro level, and 6 of the males are at beginnerlevel. A player chosen at random is female. What is the probability that she is not a prolevel?A.B.C.D.80.56.44.20Question 9Three people are carrying out independent functions during an internal audit. It is known thatin each of the three separate areas being investigated there is a serious error. From pastexperience, it is estimated that the (independent) chances of the individuals finding theserious error in their area are 0.8, 0.7 and 0.6The probability that at least one of the serious errors will be found is:A.B.C.D.(0.8 x 0.3 x 0.4) (0.2 x 0.7 x 0.4) (0.2 x 0.3 x 0.6)1- (0.2 x 0.3 x 0.4)1- (0.8 x 0.7 x 0.6)None of the above2Updated: October 2013

C03-Fundamentals of business mathematicsSaQuestion 10Mail order buyers of Brand X, classified by area and age (years)Area/AgeUnder 2525-4445-6465 est400350300250Total1,6001,4001,2001,000The probability that a randomly-selected Brand X buyer is from the North and under 25 yearsof age is (to 2 decimal places)A.B.C.D.0.080.250.310.56Question 11Mail order buyers of Brand X, classified by area and age (years)Area/AgeUnder 2525-4445-6465 est400350300250Total1,6001,4001,2001,000The probability that a randomly-selected Brand X buyer is from the West or under 25 yearsof age is (to 2 decimal places).A.B.C.D.0.080.480.56None of these3Updated: October 2013

C03-Fundamentals of business mathematicsSaQuestion 12In an internal audit of 200 invoices, the following numbers of errors were discovered:Number of ErrorsNumber of Invoices0601302403404205106 or more0The expected value of the number of errors per invoice is:A.B.C.D.1.822.13Question 13The following information shows the daily sales revenue ( 000) of a company producing aparticular item of clothing, over a period of two years:Sales 000Frequency %0 to under 10510 to under 202020 to under 306030 to under 401040 to under 505The expected daily sales in ( 000) is4Updated: October 2013

C03-Fundamentals of business mathematicsSaQuestion 14A broker has estimated the profits or losses for a particular investment and their respectiveprobabilities as follows:Profit ( 000)Probability-1.11.33.45.2The expected profit ( 000) on this investment will beQuestion 15A cumulative frequency distribution of weekly spending is as follows:Weekly spendingCumulative frequencyLess than 7550Less than 100140Less than 150180Less than 200200Less than 300220A. How many spent between 150 to 200B. How many spent less than 300 and more than 200Question 16In 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 same5Updated: October 2013

C03-Fundamentals of business mathematicsSaperiod, the country’s house price (inflation) index rose from 120 to 240. The tax (to thenearest ) payable on the house sale is?Question 17The number of rejects from 50 samples of the same size is as follows:Number of rejects in each sampleNumber of samples (frequency of reject)051102103204550The arithmetic mean number of rejects per sample is:A.B.C.D.2.22.4320Question 18For the following set of ten numbers, the median is 15:10 11 12 13 14 16 17 18 19 20 XThis statement is false of X equals:A.B.C.D.-5-4-3-26Updated: October 2013

C03-Fundamentals of business mathematicsSaQuestion 19Details of an index number are given below:GroupBaseWeightIndexFood & Drink10050140Travel & Leisure10030130Housing10020120All items100100?The All items index number is closest to:A.B.C.D.130133135146Question 20Weekly moneywages index1998 100Index of inflation1990 1001998100199910520001102001115180190200210Read 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 yearWhich one of the following is true?A.B.C.D.(i) only(ii) onlyBoth (i) and (ii)Neither (i) or (ii)7Updated: October 2013

C03-Fundamentals of business mathematicsSaQuestion 21An index number is made up of two items, food and non-food.Sub-groupWeightIndexNon-food7130Food3?All items10127The index number for the sub-group Food is closest to:Question 22On the basis of the scatter diagram above, which of the following equations would bestrepresent the regression line of Y on X?A.B.C.D.Y -X 8Y X 8Y X-8Y -X -8Question 23For a certain group of students, the coefficient of rank correlation between their performancein Accounting and their performance is Law is -1. The coefficient of rank correlation betweentheir performances in Law and FBSM is also -1. Therefore, the coefficient of rank correlationbetween their performance in Accounting and their performance in FBSM is8Updated: October 2013

C03-Fundamentals of business mathematicsA.B.C.D.Sa-2Zero 1Impossible to determine from the information givenQuestion 24The number of daily complaints to a railway company has an average (arithmetic mean) of12 and a standard deviation of 3 complaints. The coefficient of variation, measured as apercentage, is therefore;A.B.C.D.0.25%4%25%400%Question 25For 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: X 1 Y 15 X2 15 Y2 65 XY 7The correlation coefficient is nearest to:A.B.C.D.0.220.470.90-0.32Question 26The Personnel department of a large manufacturing company wishes to measure thecorrelation between the performance of its employees on an aptitude test, and their ability tocatty out a specific work-related task.The following table shows the rankings of 7 employees at both the test and the task:Employee ABCDEFGTest Rank2574163Test Rank2674351Spearman’s rank correlation coefficient for this data is:Question 279Updated: October 2013

C03-Fundamentals of business mathematicsSaOn one particular checkout in a supermarket, the service times in minutes of five customerswere:3, 2, 1, 5, 4The standard deviation of these service times, correct to 1 decimal place, is closest to:Question 28At a second checkout in the same supermarket as in question 27, the service time has anarithmetic mean of 5 minutes and a standard deviation of 1 minute. The coefficient ofvariation will be:A.B.C.D.50%20%5%2%Question 29The sales of a product are recorded monthly for 24 months. The four-point (centred) movingaverages are calculated and plotted on a graph. How many moving average points areplotted?A.B.C.D.20212224Question 30If a company has sales value of 1,800 at a certain point and the seasonal factor is 1.13,using the multiplicative model the adjusted figure to the nearest 00 will be?Question 31The underlying trend in the demand for a particular product is constant (flat), and is subjectto quarterly seasonal variations as follows:QuarterQ1Q2Q3Q4Seasonality 50% 50%-50%-50%Assume a multiplicative model is appropriate. If the demand for the last quarter, Q2, was 240units, then the forecasted demand for the next quarter, Q3 is:A. 80 unitsB. 100 unitsC. 120 units10Updated: October 2013

C03-Fundamentals of business mathematicsSaD. 140 unitsQuestion 32A product has a constant trend in its sales and is subject to the following periodical seasonalvariations.PeriodP1P2P3P4Seasonality 45% 65%-50%-35%Assuming a multiplicative model for the time series, what should be the sale for the Period 3,if the sales in the last period, P2 were 350?Question 33A multiplicative time series model should be assumed.Quarterly sales (units) of Brand X, 2001Q1Q2Q3Sales (units)1,6004,4001,680Seasonal variation-20% 100%-30%The trend value for Q1 sales (units) is:A.B.C.D.1,2801,9202,000None of theseQuestion 34A multiplicative time series model should be assumed.Quarterly sales (units) of Brand X, 2001Sales (units)Seasonal variationQ11,600-20%Q24,400 100%Q31,680-30%The seasonal variation for Q4 is:A. -50%B. 0%11Updated: October 2013

C03-Fundamentals of business mathematicsSaC. 50%D. None of theseQuestion 35A multiplicative time series model should be assumed.Quarterly sales (units) of Brand X, 2001Sales (units)Seasonal variationQ11,600-20%Q24,400 100%Q31,680-30%The forecast for the fourth quarter’s sales (units), Q4, in 2001, assuming the trend patterncontinues, is closet to:A. 1,300B. 2,300C. 3,800D. 5,200Question 36An annual (year-end) income of 10,000 is required in perpetuity. If there is a fixed interestrate of 8% each year and administrative charges are ignored, the lump sum investmentnecessary now is closest to:A.B.C.D. 9,260 80,000 100,000 125,000Question 37An annual (year-end) income of 15,000 is required in perpetuity. Assuming a fixed rate ofinterest of 9% each year, and ignoring administrative charges, the sum required now topurchase the annuity is closest to:A.B.C.D. 13,650 135,000 150,000 167,000Question 38 2,000 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:12Updated: October 2013

C03-Fundamentals of business mathematicsSaA.B.C.D. 2,680 2,553 2,431 2,335Question 39 2,000 is invested in a bank account. The account earns compound interest at 5% per year.The investment will have almost doubled in value after:A.B.C.D.11 years12 years13 years14 yearsQuestion 40A 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. The first payment X is closest to?Question 41A fixed-interest 200,000 mortgage, with annual interest compounded at 6% each year, is tobe repaid by 15 equal year-end repayments of R. The annual repayment R will be closestto:A.B.C.D. 14,133 20,593 31,954 83,400Question 42You borrow 3,000 and pay 10% each year interest. Ignoring capital, if you pay this interestat the end of each year, what is the present value of the interest payable at the end of thethird year?A.B.C.D.(3/10) x 300 x 3(7/10) x 300(10/11) 3 x 300 3,000 x (11/10) 3Question 4313Updated: October 2013