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Unformatted text preview: Math 114 Fall 2009 Practice Exam 1 with Solutions Contents 1 Problems 2 2 Solution key 8 3 Solutions 9 1 1 Problems Question 1: Let L be the line tangent to the curve r ( t ) = (big t 2 + 3 t + 2 , e t cos t, ln( t + 1) )big at t = 0. Find the coordinates of the point of intersection of L and the plane x + y + z = 8. (A) (2 , 1 , 0) (B) (6 , e 2 cos 2 , ln(2)) (C) (2 , , 1) (D) (5 , 2 , 1) (E) (8 , 3 , 2) (F) (0 , 4 , 4) Solution Key: 2.1 Solution: 3.1 Question 2: Find the distance from the point (1 , 1 , 3) to the the plane 3 x + 2 y + 6 z = 6. (A) 17 7 (B) 3 (C) 12 5 (D) 5 8 (E) 0 (F) 1 Solution Key: 2.2 Solution: 3.2 2 Question 3: Which of these expressions is always equal to the box (triple) product of A , B and C ? (A) ((2 A + B ) C ) A (B) (( A B ) C ) (C) C ( B A ) (D) the area of the parallelogram with sides A and B , times the length of C (E)  A   B   C  sin , where is the angle between A and B . (F) none of the above Solution Key: 2.3 Solution: 3.3 Question 4: Which of the following points lies on the same plane with (1 , 2 , 0), (2 , 2 , 1), (0 , 1 , 1)? (A) (1 , 1 , 1) (B) (4 , 1 , 1) (C) (4 , 1 , 1) (D) (1 , 1 , 1) (E) (2 , 1 , 3) (F) (2 , 1 , 3) Solution Key: 2.4 Solution: 3.4 3 Question 5: A particle starts at the origin with initial velocity hatwide + hatwide hatwide k . Its acceleration is a ( t ) = t hatwide + hatwide + t hatwide k . Find the position of the particle at t = 1. (A) 1 6 hatwide + 1 2 hatwide + 1 3 hatwide k (B) 7 6 hatwide + 1 2 hatwide 5 6 hatwide k (C) hatwide + hatwide + hatwide k (D) 7 6 hatwide + 3 2 hatwide 5 6 hatwide k (E) 5 6 hatwide + 2 3 hatwide 5 6 hatwide k (F) hatwide + 2 hatwide hatwide k Solution Key: 2.5 Solution: 3.5 Question 6: Find the equation of the surface consisting of all points P whose distance to the zaxis is equal to three times the distance from P to the xyplane. (A) x 2 + y 2 = z 2 (B) x 2 y 2 = 3 z 2 (C) 3 x 2 + 3 y 2 = z 2 (D) x 2 + y 2 = 9 z 2 (E) x 2 + y 2 = 3  z  (F) none of the above Solution Key: 2.6 Solution: 3.6 4 Question 7: The set of points P such that QP B = 2 is (A) a line though Q parallel to B (B) a plane through Q parallel to B (C) a plane through Q perpendicular to B (D) a line parallel to B but not passing through Q (E) a plane perpendicular to B but not passing through Q (F) a line through Q and perpendicular to B Solution Key: 2.7 Solution: 3.7 5 Question 8: Match the equations to their graphs. Enter your answers in the table at the bottom of the page and show your reasoning on the next page....
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This note was uploaded on 10/19/2009 for the course MATH 114 taught by Professor Temkin during the Spring '07 term at UPenn.
 Spring '07
 Temkin
 Math, Calculus

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