FE Mathematics Review

1. FE Mathematics Review Dr. Omar Meza Assistant Professor Department of Mechanical Engineering

2. Topics covered • Analytic geometry • Equations of lines and curves • Distance, area and volume • Trigonometric identities • Algebra • Complex numbers • Matrix arithmetic and determinants • Vector arithmetic and applications • Progressions and series • Numerical methods for finding solutions of nonlinear equations • Differential calculus • Derivatives and applications • Limits and L’Hopital’s rule • Integral calculus • Integrals and applications • Numerical methods • Differential equations • Solution and applications • Laplace transforms

3. Tips for taking exam • Use the reference handbook • Know what it contains • Know what types of problems you can use it for • Know how to use it to solve problems • Refer to it frequently • Work backwards when possible • FE exam is multiple choice with single correct answer • Plug answers into problem when it is convenient to do so • Try to work backwards to confirm your solution as often as possible • Progress from easiest to hardest problem • Same number of points per problem • Calculator tips • Check the NCEES website to confirm your model is allowed • Avoid using it to save time! • Many answers do not require a calculator (fractions vs. decimals)

4. Equations of lines Handbook page:

5. Equations of lines

6. Equations of lines

7. Equations of lines 1 2 3 4 5 -0- -1- -2- -3- -4- -5- -6- • 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

8. 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 Try using standard form Handbook pg 3: y = mx + b Given (x1, y1) = (4, 0) Given (x2, y2) = (0, -6) Equations of lines Answer is (C)

9. 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 Work backwards Substitute (x1, y1) = (4, 0) Substitute (x2, y2) = (0, -6) See what works Equations of lines Alternative Solution Answer is (C)

10. Equations of lines

11. Equations of lines

12. Equations of lines

13. Quadratic Equation Handbook page:

14. Quadratic Equation A) 1, 2; B) 3, 2; C) 0.5,-3; D) -0.5, -3 Answer is (C) Handbook page:

15. Quadratic Equation

16. Equations of curves

17. Equations of curves

18. Equations of curves

19. Equations of curves

20. Equations of curves

21. Equations of curves

22. Equations of curves

23. Equations of curves

24. Equations of curves

25. Equations of curves

26. Equations of curves

27. Equations of curves

28. Equations of curves

29. Equations of curves

30. Equations of curves

31. Equations of curves

32. Logarithms

33. Logarithms Answer is (D)

34. Logarithms Answer is (D)

35. Trigonometry

36. Trigonometry

37. Trigonometry

38. Trigonometry

39. For some angle q, cscq = -8/5. What is cos 2q? Use trigonometric identities on handbook. Confirm with calculator First find q = csc-1(-8/5) Then find cos 2q Trigonometry (A) 7/32 (B) 1/4 (C) 3/8 (D) 5/8 Answer is (A)

40. Trigonometry Answer is (C)

41. Trigonometry

42. Complex Numbers

43. Complex Numbers

44. Complex Numbers

45. Complex Numbers

46. Polar coordinates

47. What is rectangular form of the polar equation r2 = 1 – tan2q? (A) –x2 + x4y2 + y2 = 0 (B) x2 + x2y2 - y2 - y4 = 0 (C) –x4 + y2 = 0 (D) x4 – x2 + x2y2 + y2 = 0 Polar coordinate identities on handbook Polar coordinates Answer is (D)

48. Polar coordinates

49. Matrices

50. Matrices