FE Exam Tutorial

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

2. Math syllabus

3. 1. Vectors

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

5. If two vectors u and v are orthogonal to each other, then u.v= • -1 • 0 • 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 • -1 • 0 • 1 • 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 • root of equation f (x)=0 • root of function f (x) • zero of equation f (x)=0 • none of the above

12. A quadratic equation has ______ root(s) • one • two • three • 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 • one • two • three • cannot be determined

14. Equation such as tan (x)=x has __ root(s) • zero • one • two • infinite

15. A polynomial of order n has zeros • n -1 • n • n +1 • 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 6m/s at t = • 0.1823 s • 0.3979 s • 0.9162 s • 1.609 s

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18. 4. Numerical Methods

19. The number of significant digits in 2.30500 is • 3 • 4 • 5 • 6

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21. 5. Ordinary Differential Equations

22. In the differential equation the variable x is the variable • Independent • Dependent

23. In the differential equation the variable yis the variable • Independent • Dependent

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

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

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

27. Classify the differential equation • linear • nonlinear • undeterminable to be linear or nonlinear

28. Classify the differential equation • linear • nonlinear • linear with fixed constants • undeterminable to be linear or nonlinear

29. Classify the differential equation • linear • nonlinear • linear with fixed constants • 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

31. The form of the exact solution to is

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33. 6. Matrices

34. The size of matrix is

35. The c32 entity of the matrix • 2 • 3 • 6.3 • does not exist

36. Given • 0 • 6 • 12 then if [C]=[A]+[B], c12=

37. Given • -3 • 3 • 9 then if [C]=[A]-[B], c23=

38. A square matrix [A] is lower triangular if

39. A square matrix [A] is upper triangular if

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

41. Given • -57 • -45 • 57 • Does not exist then if [C]=[A][B], then c31=.

42. The following system of equations x + y=26x + 6y=12has solution(s). • no • one • more than one but finite number of • 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 • Differentiation • Integration

46. The definition of the derivative of a function f (x) is

47. The exact derivative of f (x)=x 3 at x=5 is most nearly • 25.00 • 75.00 • 106.25 • 125.00

48. Given y=sin (2x), dy/dx at x=3 • 0.9600 • 0.9945 • 1.920 • 1.989

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50. 8. Integral Calculus