MULTIMEDIA COLLEGE JALAN GURNEY KIRI KUALA LUMPUR
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1 MULTIMEDIA COLLEGE JALAN GURNEY KIRI KUALA LUMPUR FOURTH & FIFTH SEMESTER EXAMINATION, 011 SESSION DDMWW-E-F-/10, DTEW-E-F-/10, DMWW-E-F-1/10, DTEW-E-F-1/10, DTEA-E-F-/10, DTEA-E-F-1/10, DTEQ-E-F-/10, DTEQ-E-F-1/10, DTEA-E-F-/10, DTET-E-F-/10, DTET-E-F-1/10 MTH073 ENGINEERING MATHEMATICS 3 IRA SHAKIRA ROSTI / MUHAMMAD FAIZUL DIRIS / AHMAD KAMAL ABDUL AZIZ/ ISAABDULLAH / NUR FATIHA CHE MOHD 3 NOVEMBER PM 5.30 PM (3 Hours) INSTRUCTION TO STUDENT 1. This Examination paper has TEN (10) printed pages.. This question paper consists of ONE (1) section. Answer ALL questions. 3. Please write all your answers in the Answer Booklet provided.
2 MTH073 ENGINEERING MATHEMATICS III 3 NOVEMBER 011 PERATURAN PEPERIKSAAN KOLEJ MULTIMEDIA PENYELEWENGAN AKADEMIK 1. Pelajar tidak boleh melakukan mana-mana penyelewengan di bidang akademik seperti berikut atau sebarang arahan peperiksaan yang dikeluarkan oleh Ketua Pengawas Peperiksaan. HUKUMAN 1.1 Pelajar yang meniru hasil kerja orang lain atau tidak mengiktiraf kerja orang lain (plagiat) untuk tujuan tugasan atau ujian akan dikenakan tindakan tatatertib. 1. Pelajar juga tidak dibenarkan bersubahat dalam peniruan atau penipuan yang dinyatakan dalam para Pelajar perlu juga mematuhi peraturan lain mengenai penilaian yang dinyatakan secara lisan atau bertulis. 1. Sekiranya pelajar didapati telah melakukan pelanggaran mana-mana daripada peraturan peperiksaan ini, setelah dibicara dan sabit kesalahannya, maka Jawatankuasa Disiplin Pelajar boleh mengambil tindakan dari mana-mana satu, atau apa-apa kombinasi yang sesuai dari dua atau lebih hukuman-hukuman berikut:- (a) amaran (b) denda tidak melebihi RM 500 (c) (d) (e) memberi markah '0' kepada peperiksaan akhir bagi mata pelajaran berkenaan atau memberi markah sifar '0' bagi keseluruhan keputusan peperiksaan mata pelajaran yang berkenaan (termasuk kerja kursus) menggantung pengajian pelajar selama tempoh yang difikirkan patut oleh Jawatankuasa Disiplin lain-lain hukuman yang akan ditetapkan oleh Jawatankuasa Disiplin Pelajar Kolej. Pelajar yang melanggar peraturan juga boleh diambil tindakan tatatertib mengikut peruntukan yang terdapat dalam Peraturan & Tatatertib Pelajar, Kolej Multimedia, 000. Dikeluarkan oleh Unit Peperiksaan & Rekod Pelajar, Kolej Multimedia Kuala Lumpur, Julai 001 ISR/MFI/AKAA/IA/NFCM Page of 10
3 MTH073 ENGINEERING MATHEMATICS III 3 NOVEMBER 011 ARAHAN : KERTAS INI MENGANDUNGI LIMA (5) SOALAN. JAWAB EMPAT (4) SOALAN SAHAJA. INSTRUCTION : THIS PAPER CONTAINS FIVE (5) QUESTIONS. ANSWER FOUR (4) QUESTIONS ONLY. Soalan/Question 1 a) Diberi dan. Given and. Carikan: Find: (i) (iii) (iv) (v) (15 markah/marks) b) Sebutan pertama bagi suatu janjang aritmetik ialah 13 dan hasil tambah bagi 5 sebutan pertama ialah 875. Hitungkan: The first term of an arithmetic progression is 13 and the sum of the first 5th terms is 875. Calculate: (i) Beza sepunya / the common difference Sebutan ke-1 / the 1st term (iii) Hasil tambah bagi 1 sebutan pertama / the sum of the twelve terms (6 markah/ marks) ISR/MFI/AKAA/IA/NFCM Page 3 of 10
4 MTH073 ENGINEERING MATHEMATICS III 3 NOVEMBER 011 c) Dapatkan jelmaan Laplace songsang bagi setiap ungkapan berikut : Get the inverse Laplace for every equation : (i) s 16s 9 3 9s 4 (4 markah/marks) Soalan/Question a) Selesaikan persamaan terbitan boleh pisah berikut: Solve the following separable differential equation: dy x (i) 1 y dy y x( x 1) (10 markah/ marks) b) Dapatkan penyelesaian persamaan pembezaan homogen berikut dengan syarat awal y ( 0) dy x xy y Find the solution differentiation homogen equation dy with initial-value condition y ( 0) x xy y (10 markah/marks) ISR/MFI/AKAA/IA/NFCM Page 4 of 10
5 MTH073 ENGINEERING MATHEMATICS III 3 NOVEMBER 011 c) Dapatkan jelmaan Laplace bagi Compute the Laplace transform for t (i) f ( t) e sinh(t ) 1 f ( t) sinh( t) kosh(3t ) (5 markah/marks) ISR/MFI/AKAA/IA/NFCM Page 5 of 10
6 MTH073 ENGINEERING MATHEMATICS III 3 NOVEMBER 011 Soalan/Question 3 a) Carikan scalar produk a b, kemudian kirakan sudut di antara vektor a dan b untuk setiap kes berikut: Find the scalar product b for each of the following cases: (i) a 5i j dan b 4i j a b, then calculate the angle between the vectors a and (iii) (iv) a 4i j k dan b 3 i k a 3i k dan b 3 i j k a i 5 j 6k dan b 7 i j k (1 markah/marks) b) Gerakan pada suatu zarah mematuhi persamaan d x 169x 0 dt dt dengan memenuhi syarat awal t = 0, x = 0 dan 8. dt Movement on one particle comply with equation d x 169x 0 dt dt with initial condition t = 0, x = 0 and 8. dt i) Cari nilai supaya persamaan cirian mempunyai punca berulang dan tentukan dalam sebutan t. Find the value of so that the characteristic equation has repeated root and define in terms of t. ISR/MFI/AKAA/IA/NFCM Page 6 of 10
7 MTH073 ENGINEERING MATHEMATICS III 3 NOVEMBER 011 ii) Jika = 1, cari x dalam sebutan t. If = 1, find x in terms of t. iii) Jika = 14, cari x dalam sebutan t. If = 14, find x in terms of t. (10 markah/marks) c) Sebutan pertama suatu janjang aritmetik adalah 4, dan sebutan ke sembilan belasnya ialah 15. Dapatkan beza sepunya dan sebutan keenam. The first term of an arithmetic progression is 4, and the nineteenth term is 15. Find the common difference and the sixth term. (3 markah/marks) ISR/MFI/AKAA/IA/NFCM Page 7 of 10
8 MTH073 ENGINEERING MATHEMATICS III 3 NOVEMBER 011 Soalan/Question 4 a) Tulis ungkapan berikut dalam bentuk pecahan separa dan seterusnya dapatkan jelmaan Laplace songsang. Write the functions in partial fraction and then get the inverse Laplace transform. (i) 5s 3s 6 G ( s) ( s )( s )( s 3) s 1 G ( s) ( s )( s s 10) (6 markah/marks) b) Nilaikan kamiran gandadua: Evaluate the double integral: R y cosx dy dengan R ialah rantau yang diberi oleh 0 y 1, 0 x, where R is a region given by 0 y 1, 0 x. (8 markah / marks) ISR/MFI/AKAA/IA/NFCM Page 8 of 10
9 MTH073 ENGINEERING MATHEMATICS III 3 NOVEMBER 011 c) d y dy 6x 5 y e Dengan menggunakan persamaan berikut, dapatkan i. Persamaan fungsi pelengkap, y h complimentary solution equation, y h ii. Persamaan kamiran khusus, y k specific integration equation, y k iii. Persamaan penyelesaian am, y the general solution, y dy iv. Penyelesaian am yang memenuhi syarat y = 1 dan apabila x=0 dy the general solution that fulfill condition when y = 1 and when x = 0 (11 markah/marks) ISR/MFI/AKAA/IA/NFCM Page 9 of 10
10 MTH073 ENGINEERING MATHEMATICS III 3 NOVEMBER 011 Soalan/Question 5 a) Dapatkan penyelesaian persamaan terbitan berikut: Solve the following differential equation: (i) (10 markah/ marks) b) Nilaikan kamiran ganda dua berikut: Evaluate the following double integral: (7 markah/ marks) c) Diberi titik P(1,, 3), Q(, -1, 1) dan R(-1, -3, ), gunakan scalar product untuk membuktikan cos <PQR = - (1/14). Given the points P(1,, 3), Q(, -1, 1) and R(-1, -3, ), use scalar product of vectors to prove that cos <PQR = - (1/14). (8 markah/marks) End of Pages ISR/MFI/AKAA/IA/NFCM Page 10 of 10
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