midterm sample 1

midterm sample 1 - HKUST MATH 152 Applied Linear Algebra...

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Unformatted text preview: HKUST MATH 152 Applied Linear Algebra and Differential Equations Mid-Term Examination Name: 22nd October 2005 Student ID: 10:00–12:30 Tutorial Section: Directions: • Do NOT open the exam until instructed to do so. • All mobile phones and pagers should be switched off during the examination. • Please write your Name, ID number, and Section in the space provided above. • Answer ALL questions. You are advised to try the problems you feel more comfortable with first. • This is a closed book examination. • No graphical calculators are allowed. • You may write on both sides of the examination papers. • Once you are allowed to open the exam, please check that you have 10 pages in addition to this cover page. • For answering Part II, you must show all your working steps in order to receive full marks. • Cheating is a serious offense. Students who commit this offense may receive zero mark in the examination. However, more serious penalty may be imposed. Question No. Marks Out of Q. 1-15 30 Q. 16 6 Q. 17 8 Q. 18 8 Q. 19 8 Q. 20 8 Q. 21 8 Q. 22 8 Q. 23 8 Q. 24 8 Total Marks 100 1 Part I: Answer each of the following 15 multiple choice questions. Each correct answer is worth 2 marks. Question 1 2 3 4 5 6 7 8 9 10 Answer Question 11 12 13 14 15 Total Answer 1. Which one of the following equations is solvable by the method of integrating factor? (a) dy dt + ty = y 2 (b) dy dt = 2 ty t 2 + 2 y (c) y = t 2 + 1 y (d) dy dt- 2 y + 1 2 t = 2 t + 1 2 y (e) y 00 + 4 y- 5 y = 0 2. Consider the initial value problem y 00- y + 1 4 y = 0 , y (0) = 1 , y (0) = b. Find the critical value of b that distinguishes y ( t ) grows positively and negatively, as t → ∞ . (a) 1 4 (b) 1 2 (c) 1 (d) 2 (e) 4 3. The velocity v ( t ) of a falling object satisfies the initial value problem dv dt + 0 . 2 v = 9 . 8 , v (0) = 0 . Find the time that must elapse for the object to reach 98% of its limiting velocity. (a) 5ln50 (b) 25ln10 (c) 50ln5 (d) 25 (e) 50 4. Determine the value of b which makes the following differential equation exact. ( x + ye 2 xy ) dx + bxe 2 xy dy = 0 . (a) 1 (b) 2 (c) 3 (d) 4 (e) 5 2 5. The third-order differential equation x 000 + 3 x 00 + 2 x- 5 x = sin2 t can be converted to a system of three first-order equations. They are (a) x 1 = x 2 + x 3 , x 2 = x 1- x 3 , x 3 = x 1- x 2- 3 x 3 + sin2 t (b) x 1 =- x 2 , x 2 = 2 x 3 , x 3 = x 1- 3 x 2 + sin2 t (c) x 1 = x 2- x 3 , x 2 = x 3- x 1 , x 3 =- 3 x...
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midterm sample 1 - HKUST MATH 152 Applied Linear Algebra...

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