FE Review-Math - Purdue University College of Engineering

1 FE Review-Math 1. FE Review-Math 2. FE Review-Math 3. FE Review-Math 4. FE Review-Math Problem 01. What is the length of a line segment with a slope of 4/3, measured from the y-axis to a point (6,4)? A. 10. B. 25. C. 50. D. 75. 5. FE Review-Math Problem 02. What is the general form of the equation for a line whose x-intercept is 4 and y-intercept is -6? A. 2x - 3y - 18 = 0. B. 2x + 3y + 18 = 0. C. 3x - 2y - 12 = 0. D. 3x + 2y + 12 = 0. 6. FE Review-Math Problem 03. Simplify and eva luate the following expression. log3 ( %)+ log (12)- log (2).

2 3 3. A. B. C. D. 7. FE Review-Math Problem 04. For some angle 8, csc(8) = -8/5. What is cos(28)? A. 7/32. B. 1/4. C. 3/8. D. 5/8. 8. FE Review-Math Problem 05. The expression .. csc(x ) cos 3 (x) tan ( x).. is equivalent to which of the following? A. sin(x). B. cos(x). C . 1 - sin 2 (x).. D. 1 + sin 2 (x). 9. FE Review-Math Problem 06. What is the value of x (less than 360 ). that will satisfy the following equation? 2. sin (x)+ 4sin(x)+3 = 0. A. 45 . B. 90 . C. 180 . D. 270 . 10. FE Review-Math Problem 07. If the rectangu lar coordinates of a point are (-3, ), what are its polar coordinates?

3 A. (-6, -120 ). B. (6, -120 ). C. (6, 120 ). D. (6, -150 ). 11. FE Review-Math Problem 08. Determine the {x, y) coordinates of the center of the ci rcle defined by the following equation? x 2 - 8x + l - IOy + 25 = 0. A. (3, 2). B. (3, 4). C. (4, 5). D. (5, 4).. 12. FE Review-Math Problem 09. What is the slope of the following curve when it crosses the positive part of the x-axis? y = I Ox 2 - 3x - I. A. 3/20. B. 1/5. c. 1/3. D. 7. 13. FE Review-Math Problem 10. What is the maximum value of the following function on the interval x < O?}

4 3 2. f (x) = 2x + 12x - 30x+ 10. A. -210. B. -36. C. -5. D. 210. 14. FE Review-Math Problem 11. What is the value of the followi ng limit? lim[ (5__,_x)]. <- >0 X. A. 0. B. C. 1. D. 5. 15. FE Review-Math Problem 12. What is the partial derivative with respect to "x" of the following function? f(x)= x2/ +x/ + sin(x) +cos 2 (x)+sin3 (y). A. (2x+ y )/ +3 sin 2 (y) cos(y). B. (4x-3/)xy2 + 3sin 2 (y)cos (y). C. ( 3x + 4/ ).ry+3sin 2 (y )cos (y). D. (2x+ y )y3 +[t-2sin(x)]cos (x). 16. FE Review-Math Problem 13. What is the result of the following indefinite integral?

5 F( 15x -8xJ + ~ + 7 )dx 4. 4. A. 3x5 - 2x + In l,~+7x+ C. B. 60x3 - 24x2 - x -2 + C. C. 60x4 -24x3 -x-2 + 7x + C. D. (15/ 4)x5 - (8/ 3)x4 - x-2 + 7x +C.. 17. FE Review-Math Problem 14. What is the result of the following indefinite integral? fcos (x)sin(x) dx 2. A. -2/3[sin3(x)] +c B. - 1/3 [COS3(X)] + C. C. l/3[sin3(x)] +c D. l/2[sin 2 (x )cos2 (x)] +C. 18. FE Review-Math Problem 15. What is the total area of the region bounded by the x-axis and the curve y = sin (x) on the interval between x = n/2 and x = 2n? A. 1.

6 B. 2. C. 3. D. 4. 19. FE Review-Math Problem 16. What is the general solution to the following differential eq uation? y"-8y' + l6y=0. A. y= C,e4x B. y=(C1 +C2x)e4.. Y -- Ce-4x+Ce 4. C. I 2. ". D. y = C1e2 x + C2 e4x 20. FE Review-Math Problem 17. For the three vectors what is the value of the following product? A (B x C). - A = 6i + 8j + 1Ok - B = i + 2j + 3k - C = 3i + 4j + 5k A. 0. B. 64. C. 80. D. 216. 21. FE Review-Math Problem 18. What is the ang le between the two given vectors? - A = 4i + 12j + 6k - B = 24i - 8j + 6k A.

7 B.. C. 101 .20 . D.. 22. FE Review-Math Problem 19. What is the determinant of the following matrix? 2 3 4]. A; 5 6 7. [7 8 9. A. -8. B. -4. C. 0. D. 4. 23. FE Review-Math Problem 20. The second and sixth terms of a geometric progression are 3/10 and 243/160, respectively. What is the first term of this sequence? A. 1/10. B. 1/5. C. 3/5. D. 3/2. 24. FE Review-Math 1. To find the width of a river, a surveyor sets up a transit at point C on one river bank and sights directly across to point B on the other bank. The surveyor then walks along the bank for a distance of 275 m to point A.

8 The angle CAB is 57 28'. B. - - 57 28'. 275 m What is the approximate width of the river? (A) 150 m (B) 230 m (C) 330 m (D) 430 m 25. FE Review-Math 2. In the following illustration, angles 2 and 5 are 90 , AD = 15, DC = 20, and AC= 25. D. What are the lengths BC and BD, respectively? (A) 12 and 16. (B) 13 and 17. (C) 16 and 12. (D) 18 and 13. 26. FE Review-Math 3. What is the length of the line segment with slope 4/3. that extends from the point (6, 4) to the y-axis? (A) 10. (B) 25. (C) 50. (D) 75. 4. Which of the following expressions is equivalent to sin 20?

9 (A) 2 sin 0 cos 0. (B) cos2 0 - sin2 0. (C) sin 0 cos 0. (D) 1 - cos 20. 2. 27. FE Review-Math 5. Which of the following equations describes a circle with center at (2, 3) and passing through the point (-3 , - 4)? (A) (x+ 3) 2 + (y+ 4) 2 = 85. (B) (X + 3) 2 + ( y + 2) 2 = J74. (C) (x-3)2+(y-2)2=74. (D) (x - 2)2 + (y - 3) 2 = 74. 6. The equation for a circle is x2 + 4x+ y2 + 8y = 0. What are the coordinates of the circle's center? (A) (-4, - 8). (B) (-4, - 2). (C) (-2, -4). (D) (2 , - 4). 28. FE Review-Math 7. Which of the following statements is FALSE for all noncircular ellipses?

10 (A) The eccentricity, e, is less than one. (B) The ellipse has two foci. ( C) The sum of the two distances from the two foci to any point on the ellipse is 2 a ( , twice the semimajor distance). (D) The coefficients A and C preceding the x2 and i/. terms in the general form of the equation are equal. 8. What is the area of the shaded portion of the circle shown? (A) 5n - 1. 6. (B) (~~) (5n - 3). (C) 50n 3. (D) 49n - v'3. 29. FE Review-Math 9 . A pipe with a 20 cm inner diameter is filled to a depth equal to one-third of its diameter.