Fields marked with * are required! Your Name:* E-Mail Address:* Please answer all of the following questions. When you are finished, press the Send Mail button at the bottom of the form. Note: All angles are in radians, where 2 &pi radians = 360 degrees. 1. The displacement vectors A and B have magnitudes a and b respectively. In general, the magnitude of vector C = A + B is a) smaller than |a-b| b) larger than |a+b| c) smaller than |a+b| d) equal to (a2 + b2)1/2 2) The displacement (in meters) of a vertically mounted spring is given by y = 3 cos(4 &pi t + b) where b is a constant. The displacement at t =1.25 (sec) is y=1.5 meters and the velocity is upward (toward more positive y). How many seconds will pass before the displacement is 1.5 meters again? a) 1/4 b) 1/6 c) 1/3 d) 1/2 3) Two right triangles, one solid and one dashed, appear in the figure below. In terms of h, the hypotenuse for the dashed triangle, and angle &theta, what is the length of the dashed leg marked b (Note: b is the full length of the dashed leg)? a) h/(tan &theta) b) h sin &theta c) h cos &theta d) h tan &theta 4) The horizontal displacement of an object in meters with respect to time (in seconds) is given by x= 5t2-3t + 4 What is the velocity of the object (the rate of change of displacement with time) at t = 3 sec? a) 40/3 m/s b) 10 m/s c) 36 m/s d) 27 m/s 5) Vector A = (3,6,1) vector B = (6,2,13). The unit vector which points along the direction of B-A is given by a) (9,8,4)/(92 + 82 + 122 ) (1/2) b) (6,2,13)/(237)(1/2) c) (3,4,12)/(19)(1/2) d) (3,-4,12)/(169)(1/2) 6) The speed of water flow (v) along a pipe of variable circular cross section A = &pi r2 is given by vr2=constant At some place where the pipe's radius is 2 cm, the water's speed is 8 m/sec. What is the water's speed at a place where the pipe necks down to a 1 cm radius? a) 8 m/sec b) 16 m/sec c) 4 m/sec d) 32 m/sec 7) Consider two non-zero, non-parallel vectors A and B of magnitudes a and b. In general, the magnitude of Vector C = (A+B)x(A+B) is a) a2 + 2ab + b2 b) 2ab c) a2+ b2 d) 0 8) Consider two non-zero, non-parallel vectors A and B and their dot product d = A · B. If we rotate vectors A and B by 180 degrees about the z axis a) Their dot product changes sign. b) Their dot product is still 0. c) Their dot product remains the same. d) Only the z-component of the dot product changes sign. 9) The y-displacement vs. time of an object is pictured in the graph below. Which of the following equations best describes the graph? a) y = e-t(cos(20t)) b) y = 0.1 + e-t(cos(t)) c) y = 0.1 + e-t(1+(0.5)*cos(20t)) d) y = -0.25 + e-t(1+cos(5t)) 10) Which curve which best represents xe-x for 0 < x < 5 a) upper left b) upper right c) lower left d) lower right 11) Simplify (xi) (2y)j (4z)k )/( (6x)(i+1)(2y)(k-j)z(-k) ) a) x y(-k) z (2/3) b) x-1y(2j-k)z(2k) 2(2j - k - i - 1))/(3(i+1)) c) x-1y(2j - k)z(2k) 2(2j + k - i - 1)/(3(i+1)) d) x y(k)z(2k) 2(j + 2k - i - 1)/(3(i+1)) 12) ln [(xi) (2y)(-j)/(3y)j] = a) ln(xi) - ln(2jy)-ln(3yj) b) i lnx - 2j lny + 3j lny c) i lnx - j ln2 - 2j lny - j ln3 13) The limit as n-> infinity of the nth real root of 2 is a) 0 b) 1 c) a little larger than 1.414 d) 2 14) As x goes to infinity, (1+3x +6x2)/(7-6x+4x2) goes to a) 1/7 b) 9/4 c) 3/2 d) 0 15) The set of points (x,y) which satisfy the equation ((x-2)/4)2 - ((y+3)/3)2 = 0 is best described as a) a circle of radius 5 b) an ellipse with axis lengths of 6 and 8 c) a pair of straight lines d) the null set 16) (3/x)-(2/y) = a) 1/(x-y) b) 6/(xy) c) (3y-2x)/(xy) d) 6/(x-y) 17) (6.67 x 10-11 x 4 x 1031 x 6.2 x 1025)/(9.7x1011)2 is approximately equal to a) 2 x 1023 b) 2 x 1036 c) 8 x 1025 d) 2 x 1026 18) The derivative of (2x2 + 18x+40)/(5+x) is a) (4x + 18)/5 b) (4x + 18) c) 2 d) (4x+18)/(5+x)2 19) Seven vectors of equal length are shown below. Along which direction does their vector sum point? (The dashed vectors are included only to show the cardinal directions (1,0) and (0,1) ). a) (1,1) b) (1,0) c) (-1,1) d) (1,-1) 20) A mountain climber's vertical progress ( in meters) for t>0 is given by y(t) = -t2+ 100t + 20 where t is in hours. The air temperature (Kelvin) on the mountain as a function of y (meters) is given by T(y) = 273-y/100. The temperature at any place on the mountain does not depend on time. How quickly is the temperature experienced by the climber changing with time at t = 25 hours, in degrees Kelvin per hour? a) 2 b) -0.02 c) 0.75 d) -0.5 21) The polar equation r = a sin(&theta) describes a) A straight line with Cartesian equation y=a b) A spiral centered at the origin c) A circle centered at the origin d) A circle NOT centered at the origin 22) Vector n is perpendicular to plane p. A pair of vectors r,s whose tails are at the origin and whose heads lie in the plane can be described by a) (r-s) = cn for some constant c b) (r+s) · n = 0 c) (r-s) · n = 0 d) (r-s) x n = 0 23) e0.01 is approximately equal to a) 0.01 b) 2.71801 c) 1.01 d) 1.005 24) Two lines are given by the expressions kx + 3y = 5 mx - 4y = 2 with positive constants k and m. In terms of k and m, the x coordinate of the intersection point of the two lines is a) 12k + 5m b) 3/(4k-3m) c) 20/(6k+5m) d) 26/(4k+3m) 25) Suppose that vector V is the cross product of two non-zero, non-parallel vectors A and B: A x B = V. If we rotate vectors A and B about the z axis by 90 degrees we find that the cross product of A and B a) is unchanged b) is 0 c) has been rotated by 180 degrees about the z-axis d) has been rotated by 90 degrees about the z-axis 26) the integral of x e-x from 0 -> infinity is equal to a) 0 b) 1 c) -1 d) 2 27) The derivative of sin2(2x) with respect to x = a) 4 sin(x) b) 2 cos2(2x) c) 4 sin(2x) d) 2 sin(4x) 28) The derivative of 7x2 + 3 x + 1 with respect to x evaluated at x = 1 is a) 14 b) 17 c) 11 d) undefined 29) The graph of y = 4x2 -20x + 16 is best described as a) An ellipse NOT centered at the origin b) A hyperbola centered at the origin c) A parabola which lies entirely in the upper half plane d) A parabola which is concave up and has two real roots 30) The derivative of ln(cos(x)) with respect to x is given by a) esin(x) b) 1/(sin(x)) c) -tan(x) d) ln(sin(x)) 31) Two sides of a triangle meet at an angle &theta which is between 90 and 180 degrees. If a and b denote the lengths of those two sides, the length of the remaining side is given by a) (a2 + b2)1/2 b) a + b c) (a2 + b2 + 2ab cos(&theta))1/2 d) (a2 + b2 - 2ab cos(&theta))1/2 32) In the figure below the length of segnment b = 2, the length of segment a (the segment of the hypotenuse to the left of the altitude) = 1. What is the length of segment d (the rest of the hypotenuse)? a) 3 b) 4 c) 5 d) 2