The Association of Business Executives Certificate

Answer any FOUR questions


Q1 (a) Express:

1. 
   458,000 in standard form A × 10ⁿ, where 1 ≤ A < 10 and n is an integer
   

(ii)	9
	— as a percentage correct to 2 decimal places
	57
(iii)	0.7825 as a percentage correct to 3 decimal places
(iv)	2,973,490 correct to 3 significant figures
(v)	76% as a decimal
(vi)	65% as a fraction in its simplest form	(9 marks)

2. 
   Without the use of a calculator, find the value of the following, showing all steps in your calculations:
   

(i)		(		1		2	1
				2 – + 1—				× 4–
				6		12^)	5
				1	7	3
(ii)3 – + – – —
				2	8	16

(4 marks)

3. 
   The profits of a food retailing company are shared between its three partners,
   

Mr Wright, Mr Prakash and Mr Young, in the ratio 1:2:4 respectively. If Mr Prakash’s share of the profits is £1,600, calculate:

1. 
   the share of the profits received by Mr Wright
   

2. 
   the difference between the share of the profits received by Mr Wright and Mr Young
   

3. 
   the ratio of Mr Prakash’s share of the profits in terms of Mr Young’s share of the
   

profits, expressing your answer in the form 1:n (6 marks)

4. 
   Use a calculator to calculate the following correct to 2 decimal places (note that the value of e is 2.7182818):
   

1. 
   (√450 ÷ (0.58²)) × ^–5.68^—–
   

(ii) (6.7)^1.2 ÷ (e^2.67) (6 marks)
(Total 25 marks)

IQM0608 2

Q2 (a) A van driver took 4 hours and 15 minutes to deliver a pallet of Belgian chocolate from Brussels to Paris, which is a distance of 261 kilometres (km).

1. 
   Calculate the van driver’s average speed in kilometres per hour (km/hr).
   

2. 
   Given that 1 kilometre is approximately equal to 0.62 miles, calculate the average
   

speed in miles per hour (m/hr). (5 marks)

2. 
   A hotel uses 1,500 units of electricity and 800 units of heating oil over a six-month period. The tariffs for each service are:
   

	Electricity	Heating oil
Fixed charge	8 pence per day	£10 per month
Variable charge	1.5 pence per unit	8 pence per unit

Given that the six-month period consists of 182 days and £1 is equivalent to 100 pence, find the total cost of electricity and heating oil over the six-month period.

(Give your answer in £, correct to 2 decimal places.) (7 marks)

3. 
   The following table gives the exchange rates to convert £1 sterling into a number of foreign currencies.
   

Country	Exchange rate
India	82.5879	Rupees
France	1.43477	Euro
United States	2.10948	US Dollars
Japan	237.635	Yen
Hong Kong	16.4029	HK Dollars
Malaysia	7.02169	Ringgits

Using these £1 sterling exchange rates, calculate the exchange rates to convert the following three transactions directly from the first currency to the second currency. Use these new exchange rates to calculate how much currency a trader would receive if she were to carry out the following three currency transactions. For each transaction, assume that a commission of 2% is charged on the final currency amount. (Give your answer correct to 2 decimal places.)

1. 
   10,000 Indian Rupees are converted to Malaysian Ringgits
   

2. 
   500 US Dollars are converted to Hong Kong Dollars
   

(iii) 150 Euros are converted to Japanese Yen (9 marks)

4. 
   The average yield of a crop of wheat used to produce flour for bread-making is
   

6 tonnes per hectare and this wheat sells for £170 per tonne. If a farmer were to grow lower quality wheat for use as animal feed, which sells at £152 per tonne, what yield per hectare would the farmer need to achieve to receive the same monetary return per

hectare? (Give your answer correct to 2 decimal places.) (4 marks)


(Total 25 marks)


[Turn over

3 IQM0608

Q3 (a) A food wholesaler purchased some fresh vegetables for £1,700 and sold them for £2,000.

1. 
   Calculate the percentage profit received.
   

2. 
   If the wholesaler offered a 17.65% discount on the selling price, what would be
   

the new selling price of the fresh vegetables? (2 marks)

2. 
   An office manager purchased a computer desk at a 15% discounted price for £57.80.
   

What was the original price of the desk? (2 marks)

3. 
   A business entrepreneur is considering investing £1,000 for 8 years and has the choice of three different investments, each having different interest rates and terms:
   

–9% simple interest per annum

–8.2% compound interest per annum

–0.683% compound interest per month

1. 
   Calculate the total interest that would be received after 8 years for each of these investments.
   

2. 
   Calculate the difference in interest payments received between the investment that has the best return and the investment that has the worst return. (9 marks)
   

3. 
   What annual rate of compound interest would be necessary in order for £750 to grow
   

to £1,264 by the end of 5 years? (4 marks)

5. 
   A new car is purchased at a price of £17,250. It loses 25% of its value immediately and 8% per year thereafter.
   

1. 
   How much is the car worth at the end of 5 years? (Give your answer to the nearest £.)
   

2. 
   What is the overall percentage loss of the car’s value over the 5 years? (Give your answer correct to 1 decimal place.)
   

3. 
   If depreciation on the car is calculated using the straight-line method, what annual depreciation rate (%) will be necessary if the car has the same value at the end of year 5 as calculated using the declining balance method? Assume that the car still loses 25% of its value immediately. (Give your answer correct to 2 decimal places.)
   

(8 marks)


(Total 25 marks)

IQM0608 4

(10 marks) (Total 25 marks)

[Turn over IQM0608
Q4 (a) The demand curve for a product has the equation (expressing quantity as a function of price):


q = 175 – 6 p

where q is the quantity demanded (units)

p is the price of the product (£)

1. 
   Find the quantity demanded if the price of the product is £12
   

2. 
   Rewrite the equation expressing price as a function of quantity
   

(iii) Find the price of the product if the quantity demanded is 40 units (6 marks)

2. 
   Solve the following equations:
   

1. 
   2(4x – 9) = 42
   

2. 
   x² – 8x + 15 = 0, using factorisation
   

3. 
   4x² + 9x – 8 = 0, using the quadratic formula correct to 2 decimal places
   

(9 marks)

3. 
   Solve the following pair of simultaneous equations:
   

5x – 3y = 2

6x + 7y = 13

Plot each equation on a fully labelled graph. Use the graph to find the co-ordinates:

9. 
   of their points of intersection with the x and y axes
   

(ii) where the two lines intersect

5

Q5 (a) The manager of a bakery employs a total of 7 staff: two male and five female. At the end of the working day, the manager counts how many loaves of bread each member of staff has baked. Draw a tree diagram to calculate the probability that the most productive three employees will:

1. 
   be all female
   

2. 
   include both his male employees
   

(iii) include at least one male and one female employee (13 marks)

2. 
   The weight of a particular type of chocolate bar is found to be normally distributed with a mean of 100g and a standard deviation of 8g.
   

1. 
   Find the probability that a randomly selected chocolate bar weighs:
   

• 
  more than 112g;
  

• 
  less than 90g;
  

• 
  between 80g and 90g.
  

2. 
   If 100 chocolate bars were selected at random, how many would weigh less than
   

90g? Give your answer to the nearest whole number. (12 marks)