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SEKOLAH MENENGAH KEBANGSAAN TINGGI BUKIT MERTAJAM(HIGH SCHOOL BUKIT MERTAJAM)

PEPERIKSAAN PERCUBAAN STPM BAHARU PENGGAL 3 TAHUN 2015

SIJIL TINGGI PERSEKOLAHAN MALAYSIA(MALAYSIA HIGHER SCHOOL CERTIFICATE TRIAL EXAM)

Instructions to candidates:

DO NOT OPEN THIS QUESTION PAPER UNTIL YOU ARE TOLD TO DO SO .Answer all questions in Section A and any one question in Section B.

All necessary working should be shown clearly.

Scientific calculators may be used. Programmable and graphic display calculators are prohibited.

Kertas soalan ini terdiri daripada 5 halaman bercetak © Hak Cipta Unit Peperiksaan dan Penilaian HSBM 2015

Disediakan oleh Disemak oleh Disahkan oleh

………………….. ….…………………… ……….……………………..( Tan Gaik Choo ) ( Pn Normah Bt Ismail ) ( Pn Che Noora Bt Md Said ) Guru Subjek MM Ketua Panitia Matematik Tambahan PK Tingkatan 6 HSBM

950/3 PEPERIKSAANPERCUBAAN TAHUN 2015

PRAUNIVERSITI ATAS2011 MATHEMATICS M

KERTAS 3 Satu Jam Setengah

MATHEMATICAL FORMULAE

Interest and annuity:

Effective interest rate, reff = (1 + i )n – 1

Future value of an annuity,

Present value of an annuity,

Inventory models:

For basic EOQ model,

For basic EOQ model with planned shortages,

Section A [45 marks]Answer ALL questions in this section.

1. A computer was bought for RM 3600 and has a useful life of 3 years. If the rate of depreciation is 40%. Using reducing balance depreciation,

(a) obtain an equation which gives the book value of the computer after t years. [2]

(b) construct a table showing the book value at year start and year end, and the accumulated depreciation. [4]

2. (a) The management of a cell phone company realizes the revenue and cost (in RM) as follows:

R( x )=450 x and C ( x )=10000+3 x2

(i) Determine the number of units of cell phones that has to be produced in order to maximize the profits. [3] (ii) Find the total profit at this production level. [1]

(b) The demand function D(p), and the supply function S(p) of Bo Huat Coffee are given by: D (p) = 23 — 4p and S (p) = 5 + 2p , where p is the unit price in RM. (i) Find the equilibrium price and the equilibrium quantity. [2]

(ii) Sketch the demand and supply curves on the same axes. Label the equilibrium point. [3]

3. The following tableau represents a specific simplex iteration for a maximization linear programming problem. All variables are non-negative.

Basic z x1 x2 x3 x4 x5 solutionz 1 0 -1 5 0 1 15

x30 0 2 9 5 -1 15

x50 5 3 6 0 1 15

Determine the entering variable and the leaving variable, and complete the simplex computation until you obtain the optimal solution. State the maximum value of z. [5]

4. The diagram below shows the activity on- node network of a certain project.

Indicator

(a) Copy and complete the above activity on-node network. [2]

(b) State the critical path of the project and the minimum time required to complete the project. [2]

(c) Draw a Gantt chart. [3]

5. A loan for RM 100000 is taken to buy a machinery. If the annual interest rate on this loan is 7.5 % per annum, compounded monthly, over 25 years.

(a) what is the monthly payment? [3](b) what is the total interest paid? [2] (c) what is the outstanding balance after 20 years. [3] (d) complete the amortization schedule of payments for the first 6 months. [4]

Paymen

t number

Payment amount

(RM)

Interest charged

(RM)

Repayment of principal

(RM)

Outstanding balance

(RM)

0123456

6. The pay-off matrix for a two-person zero sum game is given below:

Player II

Player I

( 3 1 4 0 ¿ )¿¿

¿¿

(a) Find the play-safe strategies for the players. [2]

Start

A 2C 3 E 1

B 3D 2 F 1

Activity DurationEST LST

(b) Use graphical method to determine the optimal solution and the value of the game. [4]

Section B [15 marks] Answer any ONE question in this section

7. A company sells air filters at a rate of 800 per year. It cost RM 10 to place an order and the unit cost is RM 25 per filter. The inventory carrying cost is RM 2 / unit per year. It takes 20 working days for the new stock to arrive and the backorder cost is RM 5 / unit per year. The company operates 250 days per year

(a) Determine the optimal order quantity. [3]

(b) Calculate the maximum shortages allowed. [2]

(c) How many orders would be made each year and what is the time between orders? [3]

(d) Determine the total annual inventory cost. [3]

(e) What is the reorder point? [2]

(f) Draw a graph to illustrate. [2]

8. The following table lists six activities in a project with its duration, preceding activity, and the number of workers required for each activity.

ActivityPreceding

Activity

Duration

(days)

Number of workers required

U 4 2V - 3 4W U,V 2 6X V 6 5Y W 5 3Z X,Y 6 2

(a) Draw an AOA network diagram and determine the critical path and the minimum completion time.[6]

(b) Draw the Gantt chart, and draw the resource histogram for the project if all activities start as early as possible. [6] (c) Determine the minimum number of workers required at any given time in order to complete the project in the shortest time. [3]

END OF QUESTION PAPER