-
C03-Fundamentals of business mathematics
Sa
1 Updated: October 2013
Sample Exam Paper
Question 1
A retailer buys a box of a product, which nominally contains Q
units. The planned selling price of each unit is P. If both P and Q
have been rounded to 10%, then the maximum rounding error in total
revenue is:
A. 10% B. 20% C. 21% D. 0.1Q x 0.1P
Question 2
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, excluding VAT, to Central
Administration and to allocate 30% of the remainder, excluding VAT,
to Finance. The telephone costs (to the nearest ) to be allocated
to Finance will be closest to:
Question 3
The following formula is used in the financial analysis of
dividends: R= (V/P)+G When the formula is rearranged, with P in
terms of the other variables, P is equal to:
A. (R/V)-G B. (R-G)/V C. (V/R)-G D. V/R-G
Question 4
A companys market value has fallen from 32 billion to 2 billion
in four years. The average annual percentage decline in market
value is closet to:
A. 20% B. 40% C. 50% D. 100%
Question 5
If 3x + 2y = 6 and x 2y = 2. The solution in the form (x,y), to
the above simultaneous equations is
-
C03-Fundamentals of business mathematics
Sa
2 Updated: October 2013
Question 6
The estimated total cost of each unit of a product is 12 ( 1),
and the estimated selling price of each unit is 20 ( 3). The
estimate profit per unit will be:
A. 8 ( 4) B. 8 ( 3) C. 8 ( 2) D. 8 ( 1)
Question 7
A traders weekly costs, TC, are less than or equal to $100.
Weekly revenue, R, is a minimum 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
Question 8
In a group of 100 players, 30 are male, 55 are a pro level, and
6 of the males are at beginner level. A player chosen at random is
female. What is the probability that she is not a pro level?
A. .80 B. .56 C. .44 D. .20
Question 9
Three people are carrying out independent functions during an
internal audit. It is known that in each of the three separate
areas being investigated there is a serious error. From past
experience, it is estimated that the (independent) chances of the
individuals finding the 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
-
C03-Fundamentals of business mathematics
Sa
3 Updated: October 2013
Question 10
Mail order buyers of Brand X, classified by area and age
(years)
Area/Age Under 25 25-44 45-64 65+
North 400 350 300 250
South 600 550 500 450
East 200 150 100 50
West 400 350 300 250
Total 1,600 1,400 1,200 1,000
The probability that a randomly-selected Brand X buyer is from
the North and under 25 years of age is (to 2 decimal places)
A. 0.08 B. 0.25 C. 0.31 D. 0.56
Question 11
Mail order buyers of Brand X, classified by area and age
(years)
Area/Age Under 25 25-44 45-64 65+
North 400 350 300 250
South 600 550 500 450
East 200 150 100 50
West 400 350 300 250
Total 1,600 1,400 1,200 1,000
The probability that a randomly-selected Brand X buyer is from
the West or under 25 years of age is (to 2 decimal places).
A. 0.08 B. 0.48 C. 0.56 D. None of these
-
C03-Fundamentals of business mathematics
Sa
4 Updated: October 2013
Question 12
In an internal audit of 200 invoices, the following numbers of
errors were discovered:
Number of Errors Number of Invoices
0 60
1 30
2 40
3 40
4 20
5 10
6 or more 0
The expected value of the number of errors per invoice is:
A. 1.8 B. 2 C. 2.1 D. 3
Question 13
The following information shows the daily sales revenue (000) of
a company producing a particular item of clothing, over a period of
two years:
Sales 000 Frequency %
0 to under 10 5
10 to under 20 20
20 to under 30 60
30 to under 40 10
40 to under 50 5
The expected daily sales in (000) is
-
C03-Fundamentals of business mathematics
Sa
5 Updated: October 2013
Question 14
A broker has estimated the profits or losses for a particular
investment and their respective probabilities as follows:
Profit (000) Probability
-1 .1
1 .3
3 .4
5 .2
The expected profit (000) on this investment will be
Question 15
A cumulative frequency distribution of weekly spending is as
follows:
Weekly spending Cumulative frequency
Less than $75 50
Less than $100 140
Less than $150 180
Less than $200 200
Less than $300 220
A. How many spent between $150 to $200 B. How many spent less
than $300 and more than $200
Question 16
In a particular country, a tax at 40% is payable on any gains on
house sales not due to inflation. A house was purchased there for
$75,000 and sold for $250,000. Over the same
-
C03-Fundamentals of business mathematics
Sa
6 Updated: October 2013
period, the countrys house price (inflation) index rose from 120
to 240. The tax (to the nearest $) payable on the house sale
is?
Question 17
The number of rejects from 50 samples of the same size is as
follows:
Number of rejects in each sample Number of samples (frequency of
reject)
0 5
1 10
2 10
3 20
4 5
5 0
The arithmetic mean number of rejects per sample is:
A. 2.2 B. 2.4 C. 3 D. 20
Question 18
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 of X equals:
A. -5 B. -4 C. -3 D. -2
-
C03-Fundamentals of business mathematics
Sa
7 Updated: October 2013
Question 19 Details of an index number are given below: Group
Base Weight Index
Food & Drink 100 50 140
Travel & Leisure 100 30 130
Housing 100 20 120
All items 100 100 ?
The All items index number is closest to:
A. 130 B. 133 C. 135 D. 146
Question 20 1998 1999 2000 2001 Weekly money wages index 1998 =
100
100 105 110 115
Index of inflation 1990 = 100
180 190 200 210
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) or
(ii)
-
C03-Fundamentals of business mathematics
Sa
8 Updated: October 2013
Question 21
An index number is made up of two items, food and non-food.
Sub-group Weight Index
Non-food 7 130
Food 3 ?
All items 10 127
The index number for the sub-group Food is closest to:
Question 22
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
Question 23
For a certain group of students, the coefficient of rank
correlation between their performance in Accounting and their
performance is 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
-
C03-Fundamentals of business mathematics
Sa
9 Updated: October 2013
A. -2 B. Zero C. +1 D. Impossible to determine from the
information given
Question 24 The number of daily complaints to a railway company
has an average (arithmetic mean) of 12 and a standard deviation of
3 complaints. The coefficient of variation, measured as a
percentage, is therefore;
A. 0.25% B. 4 % C. 25% D. 400%
Question 25
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:
X = 1 Y = 15 X2 = 15 Y2 = 65 XY = 7 The correlation coefficient
is nearest to:
A. 0.22 B. 0.47 C. 0.90 D. -0.32
Question 26
The Personnel department of a large manufacturing company wishes
to measure the correlation between the performance of its employees
on an aptitude test, and their ability to catty out a specific
work-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 G
Test Rank 2 5 7 4 1 6 3
Test Rank 2 6 7 4 3 5 1
Spearmans rank correlation coefficient for this data is:
Question 27
-
C03-Fundamentals of business mathematics
Sa
10 Updated: October 2013
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: Question 28
At a second checkout in the same supermarket as in question 27,
the service time has an arithmetic 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%
Question 29 The sales of a product are recorded monthly for 24
months. The four-point (centred) moving averages are calculated and
plotted on a graph. How many moving average points are plotted?
A. 20 B. 21 C. 22 D. 24
Question 30 If 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
31
The underlying trend in the demand for a particular product is
constant (flat), and is subject to quarterly 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
-
C03-Fundamentals of business mathematics
Sa
11 Updated: October 2013
D. 140 units
Question 32
A product has a constant trend in its sales and is subject to
the following periodical seasonal variations.
Period P1 P2 P3 P4
Seasonality +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 33
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%
The trend value for Q1 sales (units) is:
A. 1,280 B. 1,920 C. 2,000 D. None of these
Question 34 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% The
seasonal variation for Q4 is:
A. -50% B. 0%
-
C03-Fundamentals of business mathematics
Sa
12 Updated: October 2013
C. +50% D. None of these
Question 35
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% The forecast for the
fourth quarters sales (units), Q4, in 2001, assuming the trend
pattern continues, is closet to:
A. 1,300 B. 2,300 C. 3,800 D. 5,200
Question 36 An annual (year-end) income of 10,000 is required in
perpetuity. If there is a fixed interest rate of 8% each year and
administrative charges are ignored, the lump sum investment
necessary now is closest to:
A. 9,260 B. 80,000 C. 100,000 D. 125,000
Question 37 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
Question 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:
-
C03-Fundamentals of business mathematics
Sa
13 Updated: October 2013
A. 2,680 B. 2,553 C. 2,431 D. 2,335
Question 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. 11 years B. 12 years C. 13 years D. 14 years
Question 40 A 100,000 mortgage, with interest compounded at 11%
each year, is to be repaid by 10 equal year-end payments of X, the
first being due one year after the mortgage was contracted. The
first payment X is closest to? Question 41 A fixed-interest
$200,000 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. $20,593 C. $31,954 D. $83,400
Question 42 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. (10/11)^3 x 300 D. 3,000
x (11/10)^3
Question 43
-
C03-Fundamentals of business mathematics
Sa
14 Updated: October 2013
A group of 10 people share the cost of a new years eve for 40
friends. The price of the meal per person is 20 plus 4 for wine and
2 for coffee. Calculate the amount each of the 10 will need to pay.
Write down a formula which could be input into one cell in Excel to
calculate the amount that the 10 will need to pay. Question 44
Enter the formula required in Excel to perform the following
calculation to the specified decimal places in each case: 37/9 x
4.34 (to two decimal places) Question 45 Below is an extract from
an Excel spreadsheet
For the given data, give the Excel formulae that would be
required in Excel to calculate the ROI and NPV in cells B10 and B11
respectively.
-
C03-Fundamentals of business mathematics
Sa
15 Updated: October 2013
C03-Answers
Question Answer Question Answer
1 C 24 C25%
2 1,021 25 A
3 D 26 .82
4 50% 27 1.4
5 X=2, Y=0 28 B
6 A 29 B
7 D 30 1,593
8 B 31 A
9 B 32 106
10 A 33 C
11 B 34 A
12 A 35 A
13 24 (000) 36 D
14 2.4 37 D
15 A20 B20 38 B
16 40,000 39 D
17 A 40 16,981
18 A 41 B
19 B 42 C
20 A 43 40* (20+4+2)/10)
21 120 44 ROUND(37/9*4.34,2)
22 A 45 ROI= Average(B2:B5)/B1 NPV = NPV(B7,B2:B5)-B1
23 C
-
C03-Fundamentals of business mathematics
Sa
16 Updated: October 2013
Explanations:
1. 21%. The maximum rounding error in the total revenue is the
error that is most deviated from the error free revenue. Error free
revenue R=PQ Deviation +10% in P and Q. R=1.1PX1.1Q R= 1.21PQ this
is 21% higher than the error free revenue. Deviation -10% in P and
Q. R=.9PX.9Q R=.81PQ this is 19% lower than the error free
revenue.
2. 1,021. Steps 1 collate the data. Total Costs 10,000. Vat
17.5%. 60% cost to central admin. 30% cost to Finance. Step 2
Exclude the Vat figure. 10,000/1.175 = 8510.63 Step 3 split figure
in to 60% & 40% 60%= 5106 40%= 3404 Steps 4 30% or the 40%
3404X.3 = 1021.
3. Re arrangement of the formula.
4. 50% Using the Future value formula calculate the negative
growth rate.
5. X=2 , Y=0 3X + 2Y = 6 X-2Y = 2 4X = 8 X = 8/4 X=2 (i) Replace
the value of x in any equation. 3X+2Y = 6 replace and X= 2 3(2) +2y
= 6 6+2y = 6 2y= 6-6 y =0
-
C03-Fundamentals of business mathematics
Sa
17 Updated: October 2013
X-2y =2
6. Estimate SP 20 ( 3). Estimate CP 12 ( 1). Estimated Profit =
8 ( 4)
(ii) 4X = 8
7. Basic understating of the signs in Mathematics.
8. Eliminate the distracters from the question, only deal with
the female number
of students. Total no of Female = 70 Total no of Female at
beginner level = 39 If a female is not at pro level she has to be
from beginner level. Chances are 39/70.
9. Sum of probability is 1. The problem is to find at least one
serious error is 1- probability of finding no error at all. The
independent chances of each of the error not to occur (0.2 x 0.3 x
0.4)
10. The probability of the buyer being under 25 and from north.
Multiplication of the probabilities. No of buyers under 25 and from
North is 400 Total number of buyers 5200 Chances are as 400/5200
.0769 rounded up to two decimal 0.08
11. 1. The probability of the buyer being under 25 is 1600/5200
2. The probability of the buyer being from west is 1300/5200 3. The
probability of the buyer being under 25 or from west is [1600/5200
+1300/5200] [1600/5200 X 1300/5200]
12. fx/ f 360/200 1.8
13. 24,000 Take average of class interval and multiply with the
relevant frequency percentage. Take sum of all the expected values
to calculate the final .
Sales 000 Frequency % X 000 EV
-
C03-Fundamentals of business mathematics
Sa
18 Updated: October 2013
0 to under 10 5 5 .25
10 to under 20 20 15 3
20 to under 30 60 25 15
30 to under 40 10 35 3.5
40 to under 50 5 45 2.25
Sum of expected values = 24 24000
14. 2.4 Multiply the profit with estimated probability. Take sum
of all the expected values to calculate the final .
Profit (000) Probability EV
-1 .1 -.1
1 .3 .3
3 .4 1.2
5 .2 1
Sum of expected value 2.4
15. A20:B20 Identify the right group of people by keenly looking
at the range values in each row. .
16. 40,000 Step 1. Adjust the price according to the rise in
index. Step2. Calculate the taxable profit and apply tax rate to
it. Price according to new index is $75000 x 240/120 $150,000
Profit on index adjusted cost is $250,000- $150,000 $100,000 Tax
rate 40% , Hence the tax figure is $40,000
-
C03-Fundamentals of business mathematics
Sa
19 Updated: October 2013
17. Application of the formula 110/ 50
18. Replace X with the given values as option A, B, C, D.
Arrange a new range of values. Apply the definition of median.
An example 10 11 12 13 14 16 17 18 19 20+X 10 11 12 13 14 16 17
18 19 20+ (-3) 10 11 12 13 14 16 17 17 18 19 (14+16)/2 15 repeat
this for other values of X. Note: when the sample is in even number
to find the value of the median middle number of values
19. Weighted average =Wx/ W 13,300/100 133
Group Base Weight Index (X) WX
Food & Drink
100 50 140 7000
Travel & Leisure
100 30 130 3900
Housing 100 20 120 2400
All items 100 100 ? 13,300
Number of rejects in each sample
Number of samples (frequency of reject)
fx
0 5 0
1 10 10
2 10 20
3 20 60
4 5 20
5 0 0
f = 50 fx = 110
-
C03-Fundamentals of business mathematics
Sa
20 Updated: October 2013
20. Wages inflation has been 15%. 15% inflation on the inflation
index would have
given 207. The actual index is 210, confirming that inflation is
higher than wages. Wage inflation is 5 index points year on year,
not 5%.
21. 120 Step1 Use the weighted average formula Step 2 represent
the missing value with X Step 3 Calculate the value by solving the
equation for X
127 = (7x130 + 3X )/10 1270 = 910 +3x 360=3x X= 120
Sub-group Weight Index
Non-food 7 130
Food 3 ?
All items 10 127
22. The graph represents the inverse relationship between two
variables. As the
value of X increases the Value of Y decreases.
23. Both Accounting and Maths are perfectly
negatively correlated with Law which suggests that their
behaviour is 100% predictable. Therefore, Accounting and Maths must
behave predictably and in the same way as each other meaning
another perfect correlation, this time positive.
24. 25% Cv = Standard Deviation / Mean 3/12 = .25 25%
25. Formula for correlation coefficient is provided with the
mathematics table.
26. .82
Use the formula for Rank correlation.
-
C03-Fundamentals of business mathematics
Sa
21 Updated: October 2013
27. 1.4 Calculate the mean value. Use the standard deviation
formula,
=(10/5-1) 1.4
28. Cv = Standard Deviation / Mean 1/5 .2 20%
29. Tabulate 24 month sales, deduce the four point moving
average, count the number of averages deduced.
30. 1600
31. Calculate the value eliminating the seasonal factor in Q2.
Apply the seasonal factor of Q3. Demand in Q2 240. Q2 seasonality
was +50% Elimination of the seasonality 240/1.5 =160 Q3 seasonality
-50% Demand in Q3 = 160(.5) = 80 Units
32. 106 Eliminate the seasonal factor from P2. Adjust the P3
figure according to the new period factor. Sales in P2 350
Seasonality +65% Eliminate the seasonality 350/1.65 = 212. P3
Seasonality -50% 212(.5) 106 Units
33. Trend = 1,600 / (1.00 - 0.20)= 2,000
34. Seasonalities should be balanced to zero. Hence the Q4
should be -50%.
35. Trend calculation Q1Trend = 1,600 / (1.00 - 0.20)= 2,000
Q2Trend = 4,400 / (1.00 + 1.00)= 2,200 Q3Trend = 1,680 / (1.00 -
0.30)= 2,400 If same trend continues then Q4 trend is 2,600 Q4
Forecast = 2,600* 0.50= 1,300
36. Use perpetuity formula. Required investment = 10,000/.08
125,000
-
C03-Fundamentals of business mathematics
Sa
22 Updated: October 2013
37. Use the perpetuity formula. 15,000/.09 The absolute value we
get by calculations 166,666.667 this is closest to 167,000.
38. Use 2000 as present value and apply the future value formula
for the calculation. FV= PV (1+r)^n FV = 2000 (1.05) ^5 2,553
39. Use 2000 as present value and 4000 as future value. Use
compound rate as provided in the data and calculate the value of T
by solving the whole equation. FV= PV (1+r)^t 4000= 2000(1+.05) ^t
2=(1.05) ^t Apply logarithm t= 14 years.
40. 16,981 Use the annuity function/formula to calculate the
equal instalments. C=Pr(1+r) ^n/(1+r) ^n-1 C=
[(100,000)(.11)(1+.11) ^10]/ (1+.11) ^10 -1 C= 16,981
41. Use the annuity function/formula to calculate the equal
instalments. C=Pr(1+r) ^n/(1+r) ^n-1 C= [(200,000)(.06)(1+.06)
^10]/ (1+.06) ^15 -1 C= $20,593.
42. FV= PV(1+r) ^n PV= FV/ (1+r) ^n PV = 300 X( 1/1+r) ^3 PV=
300 X (1/1.11)^3 PV= 300X (10/11) ^3
43. 40* (20+4+2)/10
44. ROUND(37/9*4.34,2)
45. ROI= Average(B2:B5)/B1 NPV = NPV(B7,B2:B5)-B1
-
C03-Fundamentals of business mathematics
Sa
23 Updated: October 2013