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DIPLOMA IN

ACCOUNTING / BUSINESS ADMINISTRATION / MARKETING

DECEMBER 2007 EXAMINATION

BUSINESS MATHEMATICS

Paper No : 3MSC0104

TIME ALLOWED : 3 HOURS

INSTRUCTIONS TO CANDIDATE:

1. Answer all questions in SECTION A.

2. Answer any FOUR (4) questions out of FIVE (5) questions inSECTION B.

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SECTION A

(Answer all multiple choice questions)

A1. Miss Tan deposited RM5,000 in a bank and obtained RM80 simple interest after three

months. Find the simple interest rate offered.

(a) 0.4%

(b) 0.64%

(c) 6.4%(d) 8.4%

A2. Ernie and Roni want to accumulate RM25,000, 17 years from now, as a college fund for

their baby son. How much must they invest now, at an interest rate of 3% per annum

compounded semiannually, to have RM25,000 in 17 years.

(a) RM9,151.12(b) RM12,517.92(c) RM15,069.35

(d) RM16,527.95

A3. Albert invested RM4,500 at 4.2% per annum interest compounded quarterly for 5 years.

Calculate the compound amount of Alberts investment.

(a) RM4,741.26

(b) RM5,527.78

(c) RM5,545.48(d) RM10,246.30

A4. By referring to question A3, what is the annual percentage rate of 4.2% per annumcompounded quarterly?

(a) 1.05%(b) 4.27%

(c) 10.58%

(d) 17.89%

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A5. RM200 is deposited at the end of each month for 3 years 4 months at an interest rate of 6%

per annum. What is the future value of this annuity at the end of the investment period?

(a) RM8,000.00

(b) RM8,831.77

(c) RM21,381.23(d) RM30,952.39

A6. By referring to question 5, how much interest is earned?

(a) RM831.77

(b) RM6,743.21(c) RM13,381.23

(d) RM22,952.39

A7. Evaluate the following

yx

yx

9

3 2

(a) yx2

9

1

(b) yx9

1

(c) yx31

(d) yx2

3

1

A8. What is the marginal cost function if 232 ++= xxC

(a) xx +23(b) xx +26

(c) 13 +x(d) 16 +x

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A9. Evaluate the following:

+

52

413

12

13

(a)

168

136

(b)

168

139

(c)

156

123

(d)

12

13

A10. =+ dxx 5

(a) xx 52 +

(b) cx +

2

1

21

(c) xx 53

22

3

+

(d) cxx ++ 53

22

3

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SECTION B

(Answer any FOUR (4) questions out of FIVE (5) questions)

Question 2

(a) Rohan invests RM2,000 in an investment fund for 4 years. At the end of the investmentperiod, his investment will be worth RM2,800. Find the simple interest rate that is offered.

(3 marks)

(b) RM15,000 is invested for 2 years 8 months. If the investment is offered 5% per annum

compounded semiannually for the first 2 years, 6% per annum compounded monthly for

the rest of the period, find the future value of this investment.

(3 marks)

(c) Leena invested a certain sum of money in an account that pays 4% per annum compoundedquarterly. The account will amount to RM8,800 in 6 years. Calculate the original principal

that was invested (to the nearest RM).(4 marks)

(d) A family undertakes a mortgage of RM80,000 from a bank in order to buy their new home.

They repay the loan by making monthly payments for 20 years. Calculate the monthly

repayment if the interest rate is 1% per month. (The payments are made at the end of eachmonth).

(10 marks)

(Total : 20 marks)

Question 3

(a) If

=

310

211

120

A ,

=

113

132

121

B and

=

231

142

024

C , evaluate the followings:

(i) 2A + B

(3 marks)

(ii) C A

(2 marks)

(iii) AB

(3 marks)

(iv) C2

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(3 marks)

(v) A + B C

(3 marks)

(b) Solve the simultaneous equations below by using the method of matrix.

2x + y = 9

3x y = 1

(6 marks)

(Total : 20 marks)

Question 4

(a) EER Ltd. Produces a variety of high-quality garden furniture and associated items, mostly

in wood and wrought iron.

The wood factory is divided into four departments. The Store receives wood direct from atimber merchant. This wood is machined and cut to size in the Machining Department.

Individual pieces are then fitted together in the Assembly Department. Finally, each item

goes to the Finishing Department for engraving, weather treatment, and hand finishing etc.

Two types of wooden garden seat produced are standard and De Luxe. The unit variable

costs are RM50 and RM60 respectively. The time (in hours) required for each process are

as follows:

Department Standard De LuxeTotal available

hours per week

Machining 1 2 200

Assembly 2.5 2.5 400

Finishing 1 4 360

At present, these garden seats are sold only to the trade because the company does not have

the capacity to make more. The prices are:Standard RM80, De Luxe RM100.

On the basis of the production and pricing data, use a graphical technique to determine the

maximum contribution per week from making an optimal combination of Standard and DeLuxe garden seats.

Notes: Contribution = sale value variable costsProfit = sale value variable cost fixed cost

(Total : 20 marks)

Question 5

(a) Differentiate the functions below:

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(i) xxxy 74223 += (2 marks)

(ii) xxxy= 2

3 3

2

(3 marks)

(iii) x + dxx

x2

2 13 + (4 marks)

(iv) 52 x + dx

xx 10

5

3

13

2 ++ (4 marks)

(b) Find the turning point for the equation 2322 += xxy .

(7 marks)(Total : 20 marks)

Question 6

The demand for an item produced by BBE is given by p + 0.2x = 100 where p is the price per unitand x is the quantity demanded. The total cost, C(x) of producing x units of the item is given by

C(x) = 800 + 30x where x is the level of output. Find

(a) the total revenue function, (3 marks)

(b) the total profit function, (3 marks)

(c) the total profit when 100 units are sold, (2 marks)

(d) the marginal profit function, (2 marks)

(e) the marginal profit when:

(i) 90 units are sold

(ii) 300 units are sold

(4 marks)

(f) the average cost when 200 units are produced, (4 marks)

(g) sketch the graph of demand function. (2 marks)

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(Total : 20 marks)

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