FE Electrical – Math _high_difficulty

#1. Solve for x: 8x + 7 = 95.

12.32

11

13.97

9.68

#2. Compute sin(15°)cos(15°).

0.25

0.28

0.22

0.205

#3. Find the magnitude of the complex number z = 5 + j5.

8.344

5.798

7.071

5.162

#4. How many permutations of 4 items can be selected from 12 distinct items?

495

11868

11880

11892

#5. Find the distance between points (-1, 5) and (9, 13).

16.264

9.989

15.111

12.806

#6. For f(x) = 2x^2 + 4x, compute f'(x) at x = 2.

10.56

14.16

9.84

12

#7. Evaluate the definite integral ∫_0^9 2x dx.

81

71.28

98.82

102.87

#8. For f(x,y) = 3x^2 + 4y, find |∇f| at (2,2).

10.372

12.649

14.926

9.234

#9. Solve y’ + y = 0 with y(0) = 1. What is y(2)?

0.125

0.106

0.135

0.099

#10. Solve the linear system: 5x + 5y = 39, 2x + 6y = 20. Find x.

6.7

7.236

8.509

5.896

#11. Compute the dot product of vectors A= and B=.

7

0

5

5 (alt 3)

#12. Given A=[[5,1],[0,4]], determine the dominant eigenvalue of A.

5

3.9

4.4

6.1

#13. Solve for x: 3x + 3 = 119.

25.133

52.2

38.667

30.16

#14. Compute sin(30°)cos(30°).

0.398

0.485

0.55

0.433

#15. Find the magnitude of the complex number z = 11 + j4.

11.705

10.3

13.812

9.13

#16. Find the distance between points (-2, 6) and (9, 9).

11.402

8.323

13.454

15.392

#17. For f(x) = 6x^2 + 3x, compute f'(x) at x = 4.

51

62.22

46.92

39.78

#18. Evaluate the definite integral ∫_0^6 4x dx.

72

59.04

46.8

52.56

#19. For f(x,y) = 2x^2 + 5y, find |∇f| at (1,2).

7.812

6.403

5.635

4.162

#20. Solve y’ + y = 0 with y(0) = 2. What is y(2)?

0.238

0.271

0.249

0.33

#21. Solve the linear system: 2x + 4y = 37, 8x + 1y = 32. Find x.

3.033

3.397

2.791

3.852

#22. Compute the dot product of vectors A= and B=.

28

36

41

35

#23. Given A=[[3,1],[0,2]], determine the dominant eigenvalue of A.

2.64

3

3.54

2.34

#24. Solve for x: 8x + 6 = 72.

7.26

8.25

9.24

9.735

#25. Compute sin(60°)cos(60°).

0.281

0.528

0.355

0.433

#26. Find the magnitude of the complex number z = 12 + j2.

11.192

12.166

14.842

9.489

#27. How many permutations of 4 items can be selected from 6 distinct items?

354

360

15

366

#28. Find the distance between points (-3, -2) and (9, 16).

21.633

17.739

24.229

19.037

#29. For f(x) = 3x^2 + 1x, compute f'(x) at x = 3.

23.18

17.48

13.87

19

#30. Evaluate the definite integral ∫_0^4 3x dx.

24

19.68

29.28

25.92

#31. For f(x,y) = 5x^2 + 5y, find |∇f| at (1,4).

11.18

8.721

12.075

9.168

#32. Solve y’ + y = 0 with y(0) = 3. What is y(1)?

1.302

1.104

0.905

1.015

#33. Solve the linear system: 2x + 5y = 30, 8x + 3y = 20. Find x.

0.259

0.347

0.271

0.294

#34. Compute the dot product of vectors A= and B=.

26

30

35

23

#35. Solve for x: 4x + 1 = 42.

7.482

6.663

10.25

12.505

#36. Find the magnitude of the complex number z = 2 + j4.

3.488

4.83

4.472

6.037

#37. How many permutations of 3 items can be selected from 12 distinct items?

1308

220

1320

1332

#38. Find the distance between points (-4, 3) and (16, 9).

26.518

19.21

15.243

20.881

#39. For f(x) = 2x^2 + 4x, compute f'(x) at x = 4.

14.6

25.4

23.6

20

#40. Evaluate the definite integral ∫_0^7 2x dx.

40.18

35.77

59.78

49

#41. For f(x,y) = 2x^2 + 5y, find |∇f| at (3,1).

10.14

10.66

13

11.44

#42. Solve y’ + y = 0 with y(0) = 6. What is y(3)?

0.299

0.364

0.194

0.335

#43. Solve the linear system: 7x + 4y = 34, 7x + 5y = 33. Find x.

4.777

5.863

5.429

6.08

#44. Compute the dot product of vectors A= and B=.

47

50

38

43

#45. Given A=[[7,1],[0,6]], determine the dominant eigenvalue of A.

5.11

5.46

7

8.54

#46. Solve for x: 8x + 8 = 53.

6.637

5.625

4.613

6.3

#47. Compute sin(45°)cos(45°).

0.59

0.54

0.41

0.5

#48. Find the magnitude of the complex number z = 6 + j2.

7.084

6.325

7.716

8.032

#49. How many permutations of 2 items can be selected from 9 distinct items?

81

36

72

63

#50. Find the distance between points (-3, -1) and (8, 10).

16.801

12.134

15.556

17.423

#51. For f(x) = 5x^2 + 2x, compute f'(x) at x = 4.

32.76

53.34

42

27.3

#52. Evaluate the definite integral ∫_0^7 3x dx.

73.5

47.775

60.27

86.73

#53. For f(x,y) = 3x^2 + 4y, find |∇f| at (4,1).

30.9

24.331

22.385

27.251

#54. Solve y’ + y = 0 with y(0) = 3. What is y(4)?

0.065

0.055

0.043

0.074

#55. Solve the linear system: 7x + 4y = 42, 2x + 6y = 12. Find x.

6.72

4.92

4.38

6

#56. Compute the dot product of vectors A= and B=.

32

30

41

36

#57. Given A=[[2,1],[0,1]], determine the dominant eigenvalue of A.

2.24

2

2.54

1.76

#58. Solve for x: 7x + 10 = 26.

2.286

1.486

2.103

3.086

#59. How many permutations of 4 items can be selected from 10 distinct items?

5030

5040

5050

210

#60. Find the distance between points (3, -5) and (16, 15).

32.203

18.606

23.854

25.762

#61. For f(x) = 4x^2 + 6x, compute f'(x) at x = 1.

18.9

16.52

15.12

14

#62. Evaluate the definite integral ∫_0^3 4x dx.

16.56

19.44

11.7

18

#63. For f(x,y) = 4x^2 + 5y, find |∇f| at (2,3).

21.289

14.751

16.763

18.104

#64. Solve y’ + y = 0 with y(0) = 6. What is y(1)?

2.605

2.693

2.207

1.722

#65. Solve the linear system: 5x + 4y = 26, 2x + 6y = 12. Find x.

3.584

4.909

5.302

5.989

#66. Compute the dot product of vectors A= and B=.

43

46

38

34

#67. Solve for x: 4x + 9 = 87.

17.16

26.325

21.84

19.5

#68. Find the magnitude of the complex number z = 2 + j5.

4.739

4.954

6.354

5.385

#69. How many permutations of 5 items can be selected from 12 distinct items?

95052

95040

95028

792

#70. Find the distance between points (0, -6) and (14, 7).

19.105

13.947

15.666

17.577

#71. For f(x) = 3x^2 + 6x, compute f'(x) at x = 4.

19.5

21.9

30

33.6

#72. Evaluate the definite integral ∫_0^9 1x dx.

54.675

40.5

31.59

29.565

#73. For f(x,y) = 5x^2 + 6y, find |∇f| at (2,1).

28.189

25.474

15.243

20.881

#74. Solve y’ + y = 0 with y(0) = 5. What is y(4)?

0.081

0.075

0.092

0.06

#75. Solve the linear system: 2x + 5y = 39, 2x + 6y = 26. Find x.

70.2

66.04

52

47.84

#76. Compute the dot product of vectors A= and B=.

21

22

26

29

#77. Solve for x: 5x + 8 = 36.

4.368

5.6

3.64

6.272

#78. Compute sin(75°)cos(75°).

0.28

0.25

0.22

0.205

#79. How many permutations of 2 items can be selected from 7 distinct items?

42

49

21

35

#80. Find the distance between points (4, 2) and (10, 15).

9.307

14.318

10.452

15.463

#81. For f(x) = 5x^2 + 5x, compute f'(x) at x = 4.

50.4

45

36.9

29.25

#82. Evaluate the definite integral ∫_0^10 4x dx.

156

200

236

176

#83. For f(x,y) = 4x^2 + 4y, find |∇f| at (4,2).

26.444

38.054

32.249

29.669

#84. Solve y’ + y = 0 with y(0) = 2. What is y(3)?

0.1

0.126

0.065

0.112

#85. Solve the linear system: 2x + 4y = 25, 2x + 1y = 10. Find x.

2.7

2.05

2.3

2.5

#86. Compute the dot product of vectors A= and B=.

58

54

50

53

#87. Solve for x: 9x + 7 = 94.

8.893

9.667

11.793

12.277

#88. Find the magnitude of the complex number z = 9 + j7.

11.402

9.349

12.314

8.323

#89. Find the distance between points (-3, 1) and (8, 10).

14.213

17.339

11.086

9.238

#90. For f(x) = 6x^2 + 5x, compute f'(x) at x = 2.

29

34.22

35.38

22.62

#91. Evaluate the definite integral ∫_0^3 5x dx.

24.3

25.2

22.5

19.8

#92. For f(x,y) = 2x^2 + 4y, find |∇f| at (2,3).

10.018

10.554

10.912

8.944

#93. Solve y’ + y = 0 with y(0) = 6. What is y(2)?

0.991