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FE_Ques_NCB10303_SET_A_Jan 2015_1 - CONFIDENTIAL UNIVERSITI...

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CONFIDENTIAL UNIVERSITI KUALA LUMPUR British Malaysian Institute FINAL EXAMINATION JANUARY 2015 SESSION SUBJECT CODE : NCB 10303 SUBJECT TITLE : MATHEMATICS FOR ENGINEERS 2 LEVEL : BACHELOR TIME / DURATION DATE : : (3 HOURS) 2015 INSTRUCTIONS TO CANDIDATES 1. Please read the instructions given in the question paper CAREFULLY. 2. This question paper is printed on both sides of the paper. 3. This question paper consists of TWO (2) sections. 4. Answer ALL questions in Section A and ONLY ONE (1) question out of two questions in Section B. 5. If you answer more questions than specified, ONLY the first answer (up to the specified number) will be marked. 6. Please write your answers on the answer booklet provided. 7. Appendix is appended. THERE ARE 10 PRINTED PAGES IN THIS QUESTION PAPER
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CONFIDENTIAL 2 Group L01 L02 Total No of Student Tutor Verification Subject Leader Head of Section IEB Signature Name NAS Date
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CONFIDENTIAL 3 SECTION A (Total: 80 marks) INSTRUCTION: Answer ALL questions. Please use the answer booklet provided. Question 1 (a) Under ideal laboratory conditions, the rate of growth of streptococcus bacteria in a culture is proportional to the size of the culture at any time t . The first order ODE equation is given by, ?? ?? = 𝑘? where ? = the number of streptococcus bacteria at time t 𝑘 = the constant of proportionality (i) Show that the solution of the given first order ODE equation is ?(?) = ? 𝑘? . ? ? using the separation of variables method. (2 marks) (ii) Suppose there are 35,000 bacteria present initially in a culture and 105,000 are present after 2 hours. Compute the number of bacteria in the culture after 4 hours. (6 marks) (b) Determine the general solution of the following second order non-homogeneous differential equation, ? 2 ? ?? 2 ?? ?? − 6? = 4? ? + 3? + 5 (12 marks)
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CONFIDENTIAL 4 Question 2 (a) Classify the given partial differential equation as elliptic, hyperbolic or parabolic.
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