FE Electrical – Math_medium_difficulty

#1. Solve for x: 9x + 4 = 77.

9.896

10.301

8.111

9.571

#2. Compute sin(60°)cos(60°).

0.585

0.433

0.398

0.355

#3. Find the magnitude of the complex number z = 5 + j6.

7.81

6.092

8.435

10.544

#4. How many permutations of 4 items can be selected from 8 distinct items?

1672

1688

70

1680

#5. Find the distance between points (-1, -2) and (8, 14).

16.155

18.358

23.314

20.56

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

15.34

16.51

8.45

13

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

52.65

59.13

90.72

81

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

8.544

9.569

6.664

10.424

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

0.364

0.323

0.245

0.299

#10. Solve the linear system: 4x + 5y = 17, 5x + 2y = 18. Find x.

2.899

4.019

3.294

2.701

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

20

13

25

22

#12. Find the largest eigenvalue of matrix [[4,0],[0,3]].

3.52

5.4

3.12

4

#13. Solve for x: 2x + 12 = 42.

20.25

15

9.75

16.2

#14. Find the magnitude of the complex number z = 5 + j4.

6.403

4.994

5.635

5.891

#15. How many permutations of 5 items can be selected from 10 distinct items?

30250

252

30230

30240

#16. Find the distance between points (6, 2) and (16, 12).

19.092

14.142

16.688

11.031

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

19.5

27

25

28

#18. Evaluate the definite integral ∫_0^4 5x dx.

40

54

26

50.8

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

8.944

8.229

10.554

9.66

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

0.062

0.055

0.067

0.051

#21. Solve the linear system: 3x + 1y = 43, 7x + 4y = 39. Find x.

28.728

26.6

19.418

33.782

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

20

16

10

16 (alt 3)

#23. Find the largest eigenvalue of matrix [[7,0],[0,6]].

6.16

7

8.26

8.89

#24. Solve for x: 2x + 4 = 47.

24.08

21.5

25.37

17.63

#25. Compute sin(30°)cos(30°).

0.433

0.316

0.485

0.355

#26. Find the magnitude of the complex number z = 11 + j9.

14.213

17.339

10.375

9.238

#27. How many permutations of 4 items can be selected from 9 distinct items?

3033

3024

126

3015

#28. Find the distance between points (-2, 1) and (13, 8).

16.553

15.229

20.195

18.539

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

12.15

7.02

10.62

9

#30. Evaluate the definite integral ∫_0^3 1x dx.

4.5

4.14

6.075

2.925

#31. For f(x,y) = 5x^2 + 6y, find |∇f| at (3,2).

41.302

26.923

25.087

30.594

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

2.031

2.207

1.435

2.472

#33. Solve the linear system: 5x + 3y = 22, 8x + 2y = 18. Find x.

0.964

0.464

0.557

0.714

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

13

25

19

23

#35. Solve for x: 5x + 4 = 29.

4.4

4.6

3.65

5

#36. Compute sin(75°)cos(75°).

0.162

0.28

0.25

0.205

#37. Find the magnitude of the complex number z = 8 + j11.

12.513

16.05

13.601

11.153

#38. How many permutations of 5 items can be selected from 6 distinct items?

6

720

714

726

#39. Find the distance between points (-5, -4) and (10, 13).

22.672

20.858

19.951

14.737

#40. For f(x) = 5x^2 + 1x, compute f'(x) at x = 4.

48.38

41

50.02

31.98

#41. Evaluate the definite integral ∫_0^6 5x dx.

109.8

65.7

90

58.5

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

19.914

21.758

13.461

18.439

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

0.182

0.149

0.131

0.122

#44. Solve the linear system: 3x + 4y = 44, 5x + 2y = 26. Find x.

1.349

1.28

1.143

0.743

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

21

10

14

15

#46. Find the largest eigenvalue of matrix [[3,0],[0,2]].

4.05

3.24

3.66

3

#47. Solve for x: 7x + 4 = 38.

3.789

4.274

5.926

4.857

#48. Find the magnitude of the complex number z = 12 + j10.

14.371

11.403

19.057

15.62

#49. Find the distance between points (1, 2) and (10, 16).

12.15

21.137

16.643

15.312

#50. For f(x) = 5x^2 + 5x, compute f'(x) at x = 3.

44.45

28.7

42.7

35

#51. Evaluate the definite integral ∫_0^4 1x dx.

7.04

5.84

8.96

8

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

5.701

9.919

7.81

10.544

#53. Solve y’ + y = 0 with y(0) = 2. What is y(4)?

0.024

0.041

0.037

0.029

#54. Solve the linear system: 5x + 5y = 33, 5x + 3y = 29. Find x.

4.6

3.358

5.152

2.99

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

43

52

36

34

#56. Solve for x: 6x + 8 = 25.

2.493

2.833

3.343

2.21

#57. Find the magnitude of the complex number z = 6 + j4.

5.264

7.211

4.687

6.346

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

120

1

115

125

#59. Find the distance between points (-6, -1) and (16, 14).

29.822

28.757

26.627

20.769

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

20.24

26.84

22

16.06

#61. Evaluate the definite integral ∫_0^5 4x dx.

36.5

46

50

56

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

33.768

24.723

36.783

30.15

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

0.119

0.106

0.135

0.16

#64. Solve the linear system: 6x + 1y = 21, 3x + 5y = 21. Find x.

3.484

3.951

2.862

3.111

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

46

54

55

51

#66. Find the largest eigenvalue of matrix [[6,0],[0,5]].

7.62

6

4.38

7.32

#67. Solve for x: 2x + 1 = 56.

30.8

24.2

32.45

27.5

#68. Find the magnitude of the complex number z = 2 + j10.

7.445

6.629

10.198

11.422

#69. How many permutations of 2 items can be selected from 6 distinct items?

36

15

24

30

#70. Find the distance between points (-6, -3) and (11, 16).

25.495

19.886

30.084

22.436

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

41.04

34.96

38

48.26

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

11.662

13.061

9.096

10.262

#73. Solve y’ + y = 0 with y(0) = 4. What is y(2)?

0.688

0.541

0.444

0.66

#74. Solve the linear system: 5x + 1y = 41, 7x + 2y = 37. Find x.

15

19.05

18.3

9.75

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

60

54

67

60 (alt 3)

#76. Find the largest eigenvalue of matrix [[2,0],[0,1]].

2

1.3

1.56

2.54

#77. Solve for x: 6x + 3 = 73.

9.1

13.067

11.667

13.767

#78. Compute sin(15°)cos(15°).

0.28

0.295

0.25

0.305

#79. Find the magnitude of the complex number z = 5 + j8.

10.189

8.302

9.434

8.679

#80. How many permutations of 3 items can be selected from 7 distinct items?

210

203

217

35

#81. Find the distance between points (-4, 2) and (13, 9).

16.914

18.385

14.34

13.421

#82. For f(x) = 6x^2 + 5x, compute f'(x) at x = 3.

48.38

41

55.35

45.92

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

7.445

12.442

11.014

10.198

#84. Solve the linear system: 7x + 1y = 21, 3x + 4y = 10. Find x.

2.96

2.427

2.309

1.924

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

43

35

38

34

#86. Solve for x: 7x + 7 = 102.

13.571

11.943

10.586

14.657

#87. Find the magnitude of the complex number z = 3 + j2.

3.606

3.894

3.173

4.038

#88. How many permutations of 2 items can be selected from 10 distinct items?

45

90

100

80

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

17.029

13.964

13.283

21.627

#90. For f(x) = 2x^2 + 5x, compute f'(x) at x = 1.

10.08

9

10.98

11.43

#91. Evaluate the definite integral ∫_0^5 2x dx.

27

22

28

25

#92. For f(x,y) = 4x^2 + 6y, find |∇f| at (2,4).

12.474

14.012

19.139

17.088

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

0.092

0.071

0.103