CIMA - C3 Fundamentals Of Business Mathematics

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350 Question bank

(b) If ∑X = 240

∑Y = 2,920

∑X

= 5,110

∑Y

= 745,200

∑XY = 61,500

Calculate the correlation coefficient between output and costs, stating your answer correct to 3

decimal places

90 Based on the last 7 periods, the underlying trend of sales is y = 690.24 – 2.75x. If the 8th period has a

seasonal factor of –25.25, assuming an additive forecasting model, then the forecast for that period, in

whole units is

A 643

B 646

C 668

D 671

91 Which of the following are necessary if forecasts obtained from a time series analysis are to be reliable?

I There must be no seasonal variation

II The trend must be increasing

III The model used must fit the past data

IV There must be no unforeseen events

A I and III only

B I and IV only

C II and III only

D III and IV only

92 The results of an additive time series model analysing production are shown below.

Weekly production

'000 units

Week 1 –4

Week 2 +5

Week 3 +9

Week 4 –6

Which of the following statements is/are true in relation to the data shown in the table above?

I Production is on average 9,000 units above the trend in week 3.

II Production is on average 4% below the trend in week 1.

III Production is on average 5% above the trend in week 2.

IV Production in week 4 is typically 6% below the trend.

A I only

B I and II only

C I and III only

D II and IV only

Question bank 351

93 A time series was analysed using a multiplicative model. The seasonal variations given by actual value ÷

trend, are adjusted so that they total 4.

Quarter

1 2 3 4

Unadjusted average 1.09 0.93 1.17 0.78

The correct adjusted average is

A Quarter 1 adjusted average = 1.0975

B Quarter 2 adjusted average = 0.96

C Quarter 3 adjusted average = 1.1400

D Quarter 4 adjusted average = 0.7725

94 In a time series analysis, the multiplicative model is used to forecast sales and the following seasonal

variations apply.

Quarter

1 2 3 4

Seasonal variation 0.45 1.22 1.31 ?

The seasonal variation for quarter 4 is

A 0.02

B 1.02

C 1.98

D 2.98

95 In 20X8, seasonal variations and trend values in quarters 1-4 are as follows.

Quarter Seasonal variation Trend

1 0.6 4,500

2 0.4 4,800

3 1.2 5,200

4 1.0 5,300

Match the sales values forecast with the correct quarters shown below.

Quarter Sales forecast

1 6,591

2 7,489

3 2,364

4 3,358

352 Question bank

96 The accountant at Hopwood Trends Co has carried out a time series analysis of quarterly sales, calculating

the moving average trend and average seasonal variations using the additive method. She has only partially

completed this analysis. The calculations carried out so far are shown in the following table.

Moving Moving

total of average of

4 quarters' 4 quarters' Seasonal

Year Quarter Sales sales sales Trend variation

20X2 1 200

2 110

870 217.5

3 320 219 +101

884 221.0

4 240 222 +18

892 223.0

20X3 1 214 225 –11

906 226.5

2 118 229 –111

926 231.5

3 334 232 +102

932 233.0

4 260 234 +26

938 234.5

20X4 1 220 235 –15

A C

2 124 E F

B D

3 340

4 278

(a) Complete the table by finding the missing values indicated by the letters. All answers should be

correct to the nearest whole number except for C and D which should be correct to one decimal

place.

A =

B =

C =

D =

E =

F =

Question bank 353

(b) Complete the following table to calculate the seasonal components. Find the values represented by

letters, giving your answers to one decimal place throughout.

Quarter

Year

1 2 3 4 Total

20X2 .. ..

20X3 .. .. .. ..

20X4 .. ..

Average seasonal variation .. .. .. .. G

Adjustment H .. .. .. ..

Adjusted seasonal variation I J K L

G =

H =

I =

J =

K =

L =

(d) If the predicted trend for the first quarter in 20X5 is 245, forecast the actual sales.

97 The regression equation of a linear trend is given by T = 52 + 6.3t where time t = 1 in the first quarter of

2006. What is the trend for the third quarter of 2010 giving your answer to three significant figures?

98 A time series for weeks 1 to 12 has been analysed into a trend and seasonal variations, using the additive

model. The trend value is 84 + 0.7w, where w is the week number. The actual value for week 9 is 88.7.

What is the seasonal variation for week 9?

A –1.6

B –0.9

C +0.9

D +1.6

354 Question bank

99 A time series analysis has been performed on data for weeks 1 to 20. The trend line is given by 3,150 +

72X, where X is the week number. The average seasonal variation (using the additive model) for weeks

whose numbers are divisible by 4 (ie weeks 4,8,12 etc) is – 47. The actual figure for week 12 was 4,000.

What was the residual for that week?

A –61

B –14

C +19

D +33

100 Which

one of the following tasks is a spreadsheet not able to perform?

A The presentation of numerical data in the form of graphs and charts

B The application of logical tests to data

C The application of 'What If' scenarios

D Automatic correction of all data entered by the operator into the spreadsheet

101 Spreadsheets are a well-known type of software application. All the following statements about

spreadsheets are true expect one. Which

one of the statements is untrue?

A Spreadsheets can import information from documents created in other applications

B Microsoft Access is a more advanced spreadsheet package than Microsoft Excel

C It is possible to use a spreadsheet to sort data in a variety of ways

D Spreadsheet packages usually include a facility to graph numeric data

102 If the formula =NOW( ) is entered into an Excel spreadsheet which of the following statements is true?

A The spreadsheet author's name will be displayed in the cell

B The current time and date will be displayed in the cell

C The macro operation called 'now' be will now be carried out

D The cell will be formatted according to the current template

355

Answer bank

356

Answer bank 357

1 B

)(x

= x

3) – 6

= x

6 – 6

= x

= 1 (always)

You should have been able to eliminate option A straightaway since you should have been able to

see that the correct answer is x or x to the power of something. Remember, x

always equals 1.

Options C and D are incorrect because

does not equal x or x

2 B The term x

–1

equals

by definition.

3 (a)

$10.80

Workings

Laura's share = $6 = 5 parts

Therefore one part is worth $6

÷ 5 = $1.20

Total of 9 parts shared out originally

Therefore total was 9

× $1.20 = $10.80

(b)

$13.50

Workings

Laura's share = $6 = 4 parts

Therefore one part is worth $6

÷ 4 = $1.50

Therefore original total was 9

× $1.50 = $13.50

$1,150

Workings

23% of $5,000 = 0.23

× $5,000 = $1,150

40%

Workings

$18 as a percentage of $45 =

× 100% =

5.2

× 100% = 40%

$24,390

Workings

Deirdre's salary

before increase (original) 100.0

Salary increase

2.5

Deirdre's salary after increase (final)

102.5

102.5% = $25,000 (final salary)

358 Answer bank

1% =

5.102

000,25$

= $243.90 (to 2 dp)

∴100% (original salary before increase) = $243.90 × 100

= $24,390 (to nearest $)

$190,000

Workings

Purchases – 20X0 (original) 100

Percentage decrease

–5

Purchases – 20X1 (final)

If 100% = $200,000

1% = $2,000

∴ 95% = $2,000 × 95

= $190,000

$200

Workings

Initial fee, X = 100%

Sales tax = 17.5%

Final fee = 117.5% = $235

1% =

5.117

235$

100% =

5.117

235$

× 100

= $200

9 D Putting a value in the cell, such as 2,860, would mean that the cell was not updated to reflect later

changes to the spreadsheet.

10 B In Excel, placing the $ sign in front of a cell reference makes that reference absolute. When you

move or copy a formula absolute cell references do not change.

11 A The correct formula is =D28+D18. Although D18+D28 looks the same, because it has no = sign it is

not treated as a formula. Both of the other options count sub totals as well the cost items.

12 B Formulae, text and numbers can be entered onto a spreadsheet.

13 A Option A shows the correct formula.

14 A Option A shows the correct formula.

15 C The formula would contain the COUNT function.

16 A The absolute sign, '$', should be used on the row and column reference for the cell B15. Also using

the '$' with the column references for C column will give the desired result.

Answer bank 359

17 C Q =

DC2

200 =

000,48402

××

Square both sides

200

000,48402

××

200

000,48402 ××

= $96

If you selected one of the other options, then work through the solution again remembering that if

you do anything to one side of an equation, you must make sure you do the same to the other side

of the equation as well.

18 D If D = 30 – 3P

D – 30 = –3P

3P = 30 – D

P =

−

P = 10 –

Option A is incorrect since you have divided the 30 by 3 but not the D.

Option B is incorrect because you have (incorrectly) calculated that D = 30 – 3P is D = 27P. This

would only be the case if there were brackets as such (D = (30 – 3)P).

Option C is incorrect because you have forgotten to change the sign of the D from positive to

negative when you took it to the other side of the equation.

19 x =

1.7

= 4.913

x = 1.7 (take the cube root of each side).

20 x =

–10.5

34x – 7.6 = (17x – 3.8)

× (x + 12.5)

This one is easy if you realise that 17

× 2 = 34 and 3.8 × 2 = 7.6, so 2(17x – 3.8) = 34x – 7.6

We can then divide each side by 17x – 3.8 to get

2 = x + 12.5

– 10.5 = x (subtract 12.5 from each side).