STUDENT IDENTIFICATION NO MULTIMEDIA COLLEGE JALAN GURNEY KIRI 54100 KUALA LUMPUR FIRST & EIGHTH SEMESTER FINAL EXAMINATION, 2013 SESSION MTH2143 BUSINESS MATHEMATICS DIAW-E-F-1/13, DMGW-E-F-1/13, DMGT-E-F-1/13, DMGS-E-F-1/13, DIAA-E-F-1/13, DMGA-E-F-1/13, DMGQ-E-F-1/13, DMGT-E-F-2/12, DIAW-E-F-1/12, DMGQ-E-F-3/12, DIAW-E-F-1/11, DMGW-E-F-1/11, DMGQ-E-F-1/11, DMGW-E-F-3/10, DMBW-E-F-3/10 20 SEPTEMBER 2013 9.00 a.m 12.00 p.m (3 Hours) INSTRUCTION TO STUDENT 1. This Examination paper has TWENTY (20) printed pages. 2. This question paper consists of ONE (1) section. Section A : Answer TEN (10) questions only. 3. Please write all your answers in the Answer Booklet provided.
SECTION A : PROBLEM SOLVING QUESTIONS - (100 Marks) BAHAGIAN A : SOALAN PENYELESAIAN MASALAH - (100 Markah) INSTRUCTION : ANSWER TEN (10) QUESTIONS ONLY. ARAHAN : JAWAB SEPULUH (10) SOALAN SAHAJA. Question / Soalan 1 a) Ahmad invests RM 9,660 at 6% simple interest in a bank. Find the amount in the account after ten(10) months. Ahmad melabur RM 9,660 pada 6% faedah ringkas di sebuah bank. Cari jumlah dalam akaun selepas sepuluh(10) bulan. (5 Marks / Markah) b) Donald saves RM 15,000 on 20 March 2013 in an account that offer r % simple interest per year. If the exact simple interest earned on 8 June 2013 is RM 80.00, find: Donald menyimpan RM 15,000 pada 20 Mac 2013 dalam akaun yang menawarkan r % faedah ringkas setahun. Jika faedah ringkas tepat diperolehi pada 8 Jun 2013 ialah RM 80.00, cari: i. the exact time of the investment / masa tepat bagi pelaburan tersebut ii. the value of r using exact time / nilai r mengunakan masa tepat (5 Marks / Markah) NFAA/KNA/NFCM/HI/UI Page 2 of 20
Question / Soalan 2 a) Augustine invested RM 2,000 in an account that offered interest rate 8% compounded quarterly. Find the value of this investment after five(5) years. Augustine melabur RM 2,000 di dalam akaun yang menawarkan kadar bunga yang dikompoun 8% suku tahun. Cari nilai pelaburan ini selepas lima(5) tahun. b) Given two interest rates: / Diberi dua kadar faedah: (5 Marks / Markah) i. 8% compounded monthly / 8% dikompaun setiap bulan ii. 9% compounded every four (4) months / 9% dikompaun setiap empat(4) bulan Which of the two interest rates provides a better return? Manakah antara kedua-dua kadar faedah memberikan pulangan yang lebih baik? (5 Marks / Markah) NFAA/KNA/NFCM/HI/UI Page 3 of 20
Question / Soalan 3 a) Cook and Daughters Farm Equipment accepts a RM5,800 simple interest note at 12% for 100 days, for a small tractor. The note is dated May 12. On June 17, the firm discounts the note at the bank, at a 13% discount rate. Find the proceeds. Cook dan Daughters Farm Equipment menerima sekeping nota janji RM5,800 faedah mudah pada 12% selama 100 hari, untuk sebuah traktor kecil. Nota bertarikh 12 Mei. Pada 17 Jun, firma memberi diskaun nota di bank dengan 13% kadar diskaun. Cari hasilnya. (5 Marks / Markah) b) A contractor receives proceeds of RM4,713.54 on a 12.5% simple discount note with a face value of RM5,000. Find the time of the note in days. Seorang kontraktor menerima hasil sebanyak RM4,713.54 terhadap 12.5% diskaun mudah nota dengan suatu nilai muka RM5,000. Cari tempoh masa nota dalam hari. (5 Marks / Markah) NFAA/KNA/NFCM/HI/UI Page 4 of 20
Question / Soalan 4 A tuition centre purchased the following items at the given list prices and trade discounts. Calculate: Sebuah pusat tuisyen membeli barangan berikut pada senarai harga dan diskaun niaga yang telah diberikan. Kirakan: Item / Barang Number of items purchased / Bilangan barangan yang dibeli Price per unit / Harga seunit (RM) Trade discount / Diskaun niaga Calculators / Kalkulator 30 42.00 10% Files / Fail 3 dozen 1.10 10% Notepads / Buku Nota 20 2.50 20% a) the net price of the calculators / harga bersih untuk semua kalkulator (3 Marks / Markah) b) the net price of the files / harga bersih untuk semua fail (3 Marks /Markah) c) the net price of the notepads / harga bersih untuk semua buku nota (3 Marks / Markah) d) the total net price of the items purchased jumlah harga bersih untuk semua barangan yang dibeli (1 Mark / Markah) NFAA/KNA/NFCM/HI/UI Page 5 of 20
Question / Soalan 5 a) A television set with a catalogue price of RM 3,500 is offered a chain discount of 30%, 10% and 5%. Calculate the net price. Sebuah set televisyen dengan katalog harga RM 3,500 telah ditawarkan diskaun rantaian sebanyak 30%, 10% dan 5%. Kira harga bersih. (3 Marks / Markah) b) Sam s Department Store sells a shirt with discounts of 12% and 20%, while Anand s Department Store sells the same type of shirt with discounts of 10%, 10% and 12%. Gedung Serbaneka Sam menjual baju dengan diskaun sebanyak 12% dan 20%, manakala Gedung Serbaneka Anand menjual baju yang sama dengan diskaun sebanyak 10%, 10% dan 12%. i. Which store offers a higher discount? Gedung mana yang menawarkan diskaun yang lebih tinggi? (4 Marks / Markah) ii. If the list price of the shirt is RM90, calculate the net price of that shirt in Sam s Department Store. Jika harga baju ialah RM90, kira harga bersih baju tersebut di Gedung Serbaneka Sam. (3 Marks / Markah) NFAA/KNA/NFCM/HI/UI Page 6 of 20
Question / Soalan 6 Farid, a furniture shop owner, buys a new set of furniture worth RM 9,250. She receives an invoice dated 26 October 2009 with trade discounts of 9%, 2% and is offered cash discount terms 3/15, 2/30, n/60. Farid, seorang pemilik kedai perabot, membeli satu set baru perabot bernilai RM 9,250. Beliau menerima invois bertarikh 26 Oktober 2009 dengan diskaun niaga sebanyak 9%, 2% dan ditawarkan diskaun tunai 3/15, 2/30, n/60. a) Calculate the single discount equivalent to the trade discounts given. Kirakan persamaan diskaun tunggal yang bersamaan dengan diskaun niaga diberikan. b) Calculate the last day to receive the 2% cash discount. Kira hari terakhir untuk menerima diskaun tunai 2%. c) Determine the total amount due if Farid pays the invoice on 17 November 2009. Tentukan jumlah akhir jika Farid membayar invois pada 17 November 2009. d) If Farid pays RM 5,437 on 3 November 2009, how much is the balance due before the credit term ends? Jika Farid membayar RM 5,437 pada 3 November 2009, berapa banyak baki yang terhutang sebelum tempoh kredit tamat? (10 Marks / Markah) NFAA/KNA/NFCM/HI/UI Page 7 of 20
Question / Soalan 7 A retailer bought a computer table for RM 250. The retailer wants to make 12% net profit based on the cost and the operating expenses incurred in selling the computer table is 25% of the cost. Find: Seorang peruncit membeli meja komputer pada harga RM 250. Peruncit ingin membuat keuntungan bersih 12% dari harga kos dan perbelanjaan operasi dalam menjual meja komputer ialah 25% dari harga kos. Cari: a) the retail price / harga jualan b) the gross profit / untung kasar c) the breakeven price / harga pulang modal (2 Marks / Markah) (2 Marks / Markah) (2 Marks / Markah) d) the maximum markdown percent that can be offered without making any loss. peratus penurunan harga paling maksimum yang dapat ditawarkan tanpa membuat sebarang kerugian (2 Marks / Markah) e) Assume that the customer walks in and offers to buy the computer table at RM 300. Find the net profit or loss if the retailer sells the computer table at this price. Andaikan seorang pelanggan masuk dan menawarkan untuk membeli meja komputer pada harga RM 300. Cari untung bersih atau kerugian jika peruncit menjual pada harga tersebut. (2 Marks / Markah) NFAA/KNA/NFCM/HI/UI Page 8 of 20
Question / Soalan 8 Abby bought a computer listed at RM950 cash through an instalment plan. She paid RM50 as a down payment. The balance was settled by making ten(10) monthly instalments. If the interest rate charged was 6.5% per annum on the original balance, find: Abby membeli sebuah komputer pada harga RM950 tunai melalui pelan ansuran. Dia membayar RM50 sebagai pendahuluan. Baki diselesaikan dengan membuat sepuluh(10) bulan ansuran. Jika kadar faedah dikenakan ialah 6.5% setahun pada baki asal, cari: a) the total interest charged / jumlah faedah yang dikenakan b) the installment price / harga ansuran c) the monthly payment / bayaran bulanan (4 Marks / Markah) (3 Marks / Markah) (3 Marks / Markah) Question / Soalan 9 A netbook was purchased by making a down payment of RM2,000 and 24 monthly payments of RM120 each. If the interest rate was 8% per annum on the reducing balance, calculate: Sebuah netbook telah dibeli dengan membuat pendahuluan RM2,000 dan 24 bayaran bulanan RM120 setiap bulan. Jika kadar faedah ialah 8% setahun menggunakan kaedah baki berkurangan, kira: a) the instalment price / harga ansuran b) cash price / harga tunai (4 Marks / Markah) (6 Marks / Markah) NFAA/KNA/NFCM/HI/UI Page 9 of 20
Question / Soalan 10 A hire purchase loan of RM15,000 at a flat rate of 9% per annum was repaid with 18 monthly instalments. Find: Satu pinjaman sewa beli RM15,000 pada kadar rata 9% setahun telah dibayar balik dengan 18 ansuran bulanan. Cari: a) the total finance charged. / jumlah faedah yang dikenakan (3 Marks / Markah) b) the monthly payment. / bayaran bulanan (3 Marks / Markah) c) the outstanding balance just after the sixth payment using the Rule of 78. baki yang belum dijelas selepas sahaja pembayaran ke-enam menggunakan Rule 78. (4 Marks/ Markah) Question / Soalan 11 The fourth term of an arithmetic progression is 15 and the sum of the first five (5) terms is 55. Sebutan ke-empat bagi janjang aritmetik ialah 15 dan hasil tambah lima(5) sebutan pertama ialah 55. a) Find the first term and the common difference. Cari sebutan pertama dan beza sepunya. b) Find the sum of the first eleven terms. Cari hasil tambah sebelas sebutan pertama. (6 Marks/ Markah) (4 Marks/ Markah) NFAA/KNA/NFCM/HI/UI Page 10 of 20
Question / Soalan 12 Mrs. Gan estimates that the monthly expenses of a baby will increase by 4% every month. If the expenses for the first month are estimated to be RM50, determine: Pn. Gan menganggarkan bahawa perbelanjaan bulanan seorang bayi akan meningkat oleh 4% setiap bulan. Jika belanja untuk bulan pertama dianggarkan sebanyak RM50, tentukan: a) the expenses for the 25 th month / perbelanjaan pada bulan ke-25 (5 Marks/ Markah) b) the total expenses for the first 12 months / jumlah perbelanjaan bagi 12 bulan pertama. (5 Marks/ Markah) Question / Soalan 13 Evergreen Farms Berhad need a new tractor in three(3) years and has been told to deposit RM3,000 at the end of each quarter for three(3) years to accumulate the needed funds. What lump sum deposited today will generate the same future value at 8% interest compounded quarterly? Evergreen Farms Berhad memerlukan sebuah traktor baru dalam masa tiga(3) tahun dan telah diberitahu untuk mendeposit RM3,000 dipenghujung setiap suku selama tiga(3) tahun bagi mengumpulkan dana yang diperlukan. Berapakah jumlah sekaligus yang perlu didepositkan hari ini yang akan menjana nilai masa depan sama pada kadar 8% kepentingan dikompaun suku tahunan? (10 Marks/ Markah) NFAA/KNA/NFCM/HI/UI Page 11 of 20
Question / Soalan 14 a) Evaluate for each of the following functions at the given point: Nilaikan bagi setiap fungsi berikut pada titik yang diberi: (i) at/pada (2 Marks / Markah) (ii) f ( x) 5x 2 3x x 4 at/pada (3 Marks / Markah) b) Find: / Cari: (i) (2 Marks / Markah) (ii) 0 3 x 5 3x 2 2x 5 dx 1 (3 Marks / Markah) NFAA/KNA/NFCM/HI/UI Page 12 of 20
Question / Soalan 15 A firm produces x units of a product per month and the total cost per month in ringgit is given C(x)=300 + 0.05x 2. Find: Sebuah firma menghasilkan x unit produk sebulan dan jumlah kos sebulan dalam ringgit ialah C(x)=300 + 0.05x 2. Dapatkan: a) the total cost when 50 units are produced. / jumlah kos bila 50 unit dihasilkan. (2 Marks / Markah) b) the average cost function. / fungsi kos purata. (2 Marks / Markah) c) the average cost when 50 units are produced. / kos purata bila 50 unit dihasilkan. (2 Marks / Markah) d) the marginal cost function. / fungsi kos margin. (4 Marks / Markah) NFAA/KNA/NFCM/HI/UI Page 13 of 20
CH 1: SIMPLE INTEREST LIST OF FORMULAE I = Prt S = P + I S = P (1 + rt) P = S (1 +rt) -1 CH 2: COMPOUND INTEREST S = P (1 + j/m) n P = S (1 + j/m) -n (1 + j/m) m = (1 + j/m) m CH 3: PROMISSORY NOTES D = Sdt P = S D P = S (1 dt) r = d/ (1 dt) d = r/ (1 + rt) NFAA/KNA/NFCM/HI/UI Page 14 of 20
CH 4: MATHEMATICS OF BUYING TD = LP NP Amount TD = LP (r) NP = LP (1 r) NP = LP (1 r 1 ) (1 r 2 ) (1 r 3 ) r = 1 - (1 r 1 ) (1 r 2 ) (1 r 3 ) Amount paid = Credit given (1 d) Amount outstanding = LP TD CD NFAA/KNA/NFCM/HI/UI Page 15 of 20
CH 5: MATHEMATICS OF RETAILING R = C + M Markup % based on retail price = M / R (100%) Markup % based on retail price = [% markup on cost price / (100% + % markup on cost price) ] (100%) Markup % based on cost price = M / C (100%) Markup % based on cost price = [% markup on retail price / (100% - % markup on retail price)] (100%) MD = OR NR % MD = MD / OR (100%) NR = (100% - % MD) (OR) R = C + OE + NP BEP = C + OE GP = R C or NP + OE Maximum % MD without getting loss = [(R BEP) / R ] (100%) NFAA/KNA/NFCM/HI/UI Page 16 of 20
CH 6: INSTALMENT PURCHASES B = CP DP Total monthly instalment = B + I R = Total monthly instalment / n Unearned Interest = I [ N (N + 1) / n (n + 1) ] Rule of 78; B = RN I [ N (N + 1) / n (n + 1) ] Annuity Method: A = R [ {1 (1 + i) -n } / i ] S = R [ {(1 + i) n 1} / i ] R = Ai / 1 (1+ i) -n Constant Ratio Formula; I = rb (n + 1) / 2m r = 2mI / B (n + 1) NFAA/KNA/NFCM/HI/UI Page 17 of 20
CH 7: SEQUENCES Arithmetic Sequence; T n = a + (n 1) d S n = n/2 [2a + (n 1) d] Geometric Sequence; T n = ar n-1 S n = a (1- r n ) / 1 - r if r < 1 S n = a (r n - 1) / r - 1 if r > 1 CH 8: ANNUITY Present value of annuity; A = R [ {1 (1 + i) -n } / i ] Future value of annuity; S = R [ {(1 + i) n 1} / i ] For Forborne annuity, S = R [ {(1 + i) n 1} / i ] (1 + i) N-n Periodic Payment; R = Ai / 1 (1+ i) -n if A is known R = Si / (1+ i) n - 1 if S is known NFAA/KNA/NFCM/HI/UI Page 18 of 20
CH 9 : DIFFERENTIATION d/dx (c) = 0 d/dx (mx + b) = m d/dx (x n ) = nx n-1 d/dx [f(x) + g(x)] = d/dx f(x) + d/dx g(x) d/dx [cf(x)] = c d/dx f(x) d/dx [f(x)g(x)] = [d/dx f(x)] g(x) + f(x) [d/dx g(x)] Product Rule d/dx [f(x)/g(x)] = g(x) [d/dx f(x)] - f(x) [d/dx g(x)] / [g(x)] 2 Quotient Rule d/dx [u(x) n ] = n. u(x) n-1 u (x) Power Rule d/dx g[u(x)] = g [u(x)]u (x) Chain Rule Applications of the derivatives; C(x) = total cost; MC(x) = marginal cost = C (x) R(x) = total revenue; MR(x) = marginal revenue = R (x) P(x) = total profit; MP(x) = marginal profit = P (x) MP(x) = MR(x) - MC(x) NFAA/KNA/NFCM/HI/UI Page 19 of 20
CH 10: INTEGRATION x n dx = [x n+1 / n +1] + c b f(x) dx = F(b) F(a) a Applications of the integral; Total cost = MC(x)dx = C(x) + A A is a constant Total revenue = MR(x)dx = R(x) End of Page. NFAA/KNA/NFCM/HI/UI Page 20 of 20