1. FE Math Exam Tutorial http://fe.eng.usf.edu

2. If you were not attending today’s evening FE session, your plan was to 1.Binge on Netflix 2.Spend with your loved one 3.Spend it with the cat 4.Spend it with your imaginary lover 5.Get bad service at any local restaurant

3. 1. Vectors

4. What can you say about two vectors whose dot product is negative? 1.The vectors are orthogonal 2.Angle between vectors is <90 o 3.Angle between vectors is >90 o

5. If two vectors u and v are orthogonal to each other, then u.v= A.-1 B.0 C.1

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7. 2. Analytic Geometry

8. Two straight lines are perpendicular to each other. The product of the slope of the two lines is A.-1 B.0 C.1 D.Cannot be determined

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10. 3. Roots of Equations

11. The value of x that satisfies f (x)=0 is called the 1.root of equation f (x)=0 2.root of function f (x) 3.zero of equation f (x)=0 4.none of the above

12. A quadratic equation has ______ root(s) 1.one 2. two 3. three 4. cannot be determined

13. For a certain cubic equation, at least one of the roots is known to be a complex root. The total number of complex roots the cubic equation has is 1.one 2. two 3. three 4.cannot be determined

14. Equation such as tan (x)=x has __ root(s) 1.zero 2. one 3. two 4. infinite

15. A polynomial of order n has zeros 1.n -1 2. n 3. n +1 4. n +2

16. The velocity of a body is given by v (t)=5e -t +4, where t is in seconds and v is in m/s. The velocity of the body is 6 m/s at t = 1. 0.1823 s 2. 0.3979 s 3. 0.9162 s 4. 1.609 s

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18. 4. Numerical Methods

19. The number of significant digits in 2.30500 is A.3 B.4 C.5 D.6

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21. 5. Ordinary Differential Equations

22. In the differential equation the variable x is the variable A.Independent B.Dependent

23. In the differential equation the variable y is the variable A.Independent B.Dependent

24. Ordinary differential equations can have these many dependent variables. A.one B.two C.any positive integer

25. Ordinary differential equations can have these many independent variables. A.one B.two C.any positive integer

26. A differential equation is considered to be ordinary if it has A.one dependent variable B.more than one dependent variable C.one independent variable D.more than one independent variable

27. Classify the differential equation A.linear B.nonlinear C.undeterminable to be linear or nonlinear

28. Classify the differential equation A.linear B.nonlinear C.linear with fixed constants D.undeterminable to be linear or nonlinear

29. Classify the differential equation A.linear B.nonlinear C.linear with fixed constants D.undeterminable to be linear or nonlinear

30. The velocity of a body is given by Then the distance covered by the body from t=0 to t=10 can be calculated by solving the differential equation for x(10) for A.) B.) C.) D.)

31. The form of the exact solution to is A. B. C. D.

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33. 6. Matrices

34. The size of matrix 1. 2. 3. 4. is

35. The c 32 entity of the matrix 1. 2 2. 3 3. 6.3 4. does not exist

36. Given then if [C]=[A]+[B], c 12 = 1. 0 2.6 3. 12

37. Given then if [C]=[A]-[B], c 23 = 1. -3 2. 3 3. 9

38. A square matrix [A] is lower triangular if 1. 2. 3. 4.

39. A square matrix [A] is upper triangular if 1. 2. 3. 4.

40. An identity matrix [I] needs to satisfy the following 1. 2. 3. 4. all of the above matrix is square

41. Given then if [C]=[A][B], then c 31 =. 1.-57 2.-45 3.57 4.Does not exist

42. The following system of equations x + y=2 6x + 6y=12 has solution(s). 1.no 2.one 3.more than one but finite number of 4.infinite

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44. 7. Differential Calculus

45. To find velocity from the location vs time data of the body, the mathematical procedure used is A.Differentiation B.Integration

46. The definition of the derivative of a function f (x) is 1.(A ): 2.(B ): 3.( C ): 4.( D ): 5.

47. The exact derivative of f (x)=x 3 at x=5 is most nearly 1.25.00 2.75.00 3.106.25 4.125.00

48. Given y=sin (2x), dy/dx at x=3 1.0.9600 2.0.9945 3.1.920 4.1.989

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50. 8. Integral Calculus

51. To find the velocity from acceleration vs time data, the mathematical procedure used is A.Differentiation B.Integration

52. Physically, integrating means finding the A.Area under the curve from a to b B.Area to the left of point a C.Area to the right of point b D.Area above the curve from a to b

53. The value of the integral A.x 3 B.x 3 +C C.x 3 /3 D.x 3 /3 +C E.2x

54. Given the f(x) vs x curve, and the magnitude of the areas as shown, the value of y x a 5 7 2 b c A.5 B.12 C.14 D.Cannot be determined

55. Given the f(x) vs x curve, and the magnitude of the areas as shown, the value of y x a 5 7 2 b c A.-7 B.-2 C.7 D.12

56. Given the f(x) vs x curve, and the magnitude of the areas as shown, the value of y x a 5 7 2 b c A.-7 B.-2 C.12 D.Cannot be determined

57. 9. Partial Differential Equations

58. The number of independent variable(s) for partial differential equations is more than or equal to _____. A.one B.two C.three D.four

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