FE Civil – Math_medium_difficulty

#1. In a site plan using Cartesian coordinates, point A is at (-1, 6) and point B is at (10, 15). What is the straight-line distance AB in m?

20 m

14.21 m

12.21 m

17.06 m

#2. A roadway centerline segment connects (-7, -3) and (-3, -8). What are the midpoint coordinates?

(-2, 2.5)

(-5, -5.5)

(-10, -11)

(-5.5, -5)

#3. A line passing through (4, -14) has slope -2. Which equation is correct?

y = 2x + -6

y = -2x – -6

x = -2y + -6

y = -2x + -6

#4. The center of a circular tank is at (-2, 4) and radius is 4 ft. Which equation represents the circle?

(x – -2)^2 + (y – 4)^2 = 16

(x + -2)^2 + (y + 4)^2 = 16

(x – -2)^2 – (y – 4)^2 = 16

x^2 + y^2 = 4

#5. For quality control, a measured point P(-3, -5) is compared to line 1x + 1y + -7 = 0. What is the perpendicular distance in ft?

15 ft

6.36 ft

10.61 ft

12.11 ft

#6. In a site plan using Cartesian coordinates, point A is at (6, -8) and point B is at (14, -5). What is the straight-line distance AB in ft?

11 ft

6.54 ft

8.54 ft

10.25 ft

#7. A roadway centerline segment connects (6, -3) and (-2, 5). What are the midpoint coordinates?

(2, 1)

(4, -4)

(4, 2)

(1, 2)

#8. A line passing through (-2, -1) has slope 1.5. Which equation is correct?

y = -1.5x + 2

y = 1.5x – 2

y = 1.5x + 2

x = 1.5y + 2

#9. The center of a circular tank is at (4, 4) and radius is 6 ft. Which equation represents the circle?

(x – 4)^2 + (y – 4)^2 = 36

(x + 4)^2 + (y + 4)^2 = 36

(x – 4)^2 – (y – 4)^2 = 36

x^2 + y^2 = 6

#10. For quality control, a measured point P(-3, -5) is compared to line 2x + 4y + 5 = 0. What is the perpendicular distance in m?

21 m

2.82 m

6.2 m

4.7 m

#11. In a site plan using Cartesian coordinates, point A is at (-7, 2) and point B is at (2, 9). What is the straight-line distance AB in m?

16 m

9.4 m

11.4 m

13.68 m

#12. A roadway centerline segment connects (3, 3) and (4, -9). What are the midpoint coordinates?

(3.5, -3)

(-0.5, 6)

(7, -6)

(-3, 3.5)

#13. A line passing through (2, -5) has slope 0.5. Which equation is correct?

y = -0.5x + -6

y = 0.5x – -6

y = 0.5x + -6

x = 0.5y + -6

#14. The center of a circular tank is at (0, -4) and radius is 4 ft. Which equation represents the circle?

(x + 0)^2 + (y + -4)^2 = 16

(x – 0)^2 – (y – -4)^2 = 16

(x – 0)^2 + (y – -4)^2 = 16

x^2 + y^2 = 4

#15. For quality control, a measured point P(-4, 0) is compared to line 2x + 2y + 6 = 0. What is the perpendicular distance in ft?

2 ft

0.42 ft

0.71 ft

2.21 ft

#16. In a site plan using Cartesian coordinates, point A is at (-6, -4) and point B is at (4, 1). What is the straight-line distance AB in ft?

15 ft

11.18 ft

9.18 ft

13.42 ft

#17. A roadway centerline segment connects (-8, 4) and (7, -7). What are the midpoint coordinates?

(-7.5, 5.5)

(-0.5, -1.5)

(-1, -3)

(-1.5, -0.5)

#18. A line passing through (4, 6) has slope 0.5. Which equation is correct?

y = -0.5x + 4

y = 0.5x – 4

x = 0.5y + 4

y = 0.5x + 4

#19. The center of a circular tank is at (-5, -4) and radius is 4 ft. Which equation represents the circle?

(x + -5)^2 + (y + -4)^2 = 16

(x – -5)^2 – (y – -4)^2 = 16

x^2 + y^2 = 4

(x – -5)^2 + (y – -4)^2 = 16

#20. For quality control, a measured point P(1, -3) is compared to line 2x + 4y + 7 = 0. What is the perpendicular distance in m?

3 m

0.67 m

0.4 m

2.17 m

#21. In a site plan using Cartesian coordinates, point A is at (5, -2) and point B is at (8, 2). What is the straight-line distance AB in m?

7 m

5 m

3 m

6 m

#22. A roadway centerline segment connects (2, -10) and (2, -2). What are the midpoint coordinates?

(2, -6)

(0, -4)

(4, -12)

(-6, 2)

#23. A line passing through (2, 3) has slope 2.5. Which equation is correct?

y = -2.5x + -2

y = 2.5x + -2

y = 2.5x – -2

x = 2.5y + -2

#24. The center of a circular tank is at (3, 5) and radius is 8 ft. Which equation represents the circle?

(x + 3)^2 + (y + 5)^2 = 64

(x – 3)^2 – (y – 5)^2 = 64

x^2 + y^2 = 8

(x – 3)^2 + (y – 5)^2 = 64

#25. For quality control, a measured point P(-2, -3) is compared to line 4x + 2y + -2 = 0. What is the perpendicular distance in ft?

16 ft

2.15 ft

5.08 ft

3.58 ft

#26. If f(x) = 1x^3 + 6x^2 + 5, what is f'(x) at x = 1?

12

15

21

Insufficient information

#27. Compute the definite integral ∫[0 to 2] (3x^2 + 0) dx.

10

4

12

8

#28. Find lim_(x→6) (x^2 – 36)/(x – 6).

6

12

0

36

#29. A rectangular lot uses 50 m of fencing on three sides, with one side along a river. Maximum area occurs at width = 25 m. What is the maximum area?

1250 m^2

312.5 m^2

937.5 m^2

625 m^2

#30. What is the average value of f(x) = 6x^2 + 2x on [0, 4]?

40

36

104

18

#31. If f(x) = 1x^3 + 6x^2 + -5, what is f'(x) at x = 2?

36

27

18

42

#32. Compute the definite integral ∫[0 to 2] (1x^2 + 4) dx.

12.67

10.67

5.33

12

#33. Find lim_(x→7) (x^2 – 49)/(x – 7).

7

0

14

49

#34. A rectangular lot uses 35 m of fencing on three sides, with one side along a river. Maximum area occurs at width = 17.5 m. What is the maximum area?

612.5 m^2

153.12 m^2

306.25 m^2

459.38 m^2

#35. What is the average value of f(x) = 5x^2 + 2x on [0, 3]?

21

51

18

9

#36. If f(x) = 5x^3 + 3x^2 + 3, what is f'(x) at x = 1?

11

21

24

Insufficient information

#37. Compute the definite integral ∫[0 to 5] (5x^2 + 0) dx.

213.33

104.17

125

208.33

#38. Find lim_(x→7) (x^2 – 49)/(x – 7).

7

0

14

49

#39. A rectangular lot uses 57 m of fencing on three sides, with one side along a river. Maximum area occurs at width = 28.5 m. What is the maximum area?

1624.5 m^2

406.12 m^2

1218.38 m^2

812.25 m^2

#40. What is the average value of f(x) = 6x^2 + 2x on [0, 7]?

105

112

308

52.5

#41. If f(x) = 3x^3 + 3x^2 + 4, what is f'(x) at x = 3?

112

99

33

102

#42. Compute the definite integral ∫[0 to 5] (2x^2 + 2) dx.

93.33

98.33

46.67

60

#43. Find lim_(x→3) (x^2 – 9)/(x – 3).

3

6

0

9

#44. A rectangular lot uses 39 m of fencing on three sides, with one side along a river. Maximum area occurs at width = 19.5 m. What is the maximum area?

760.5 m^2

380.25 m^2

190.12 m^2

570.38 m^2

#45. What is the average value of f(x) = 5x^2 + 2x on [0, 7]?

88.67

95.67

259

44.33

#46. If f(x) = 1x^3 + 2x^2 + 1, what is f'(x) at x = 1?

4

9

7

Insufficient information

#47. Compute the definite integral ∫[0 to 3] (1x^2 + 4) dx.

24

10.5

21

Insufficient information

#48. Find lim_(x→6) (x^2 – 36)/(x – 6).

6

0

12

36

#49. A rectangular lot uses 36 m of fencing on three sides, with one side along a river. Maximum area occurs at width = 18 m. What is the maximum area?

324 m^2

648 m^2

162 m^2

486 m^2

#50. What is the average value of f(x) = 3x^2 + 2x on [0, 7]?

63

56

161

28

#51. Given vector v = , what is |v|?

11

153

14.37

12.37

#52. For vectors a = and b = , compute a·b.

8

5

Insufficient information

Cannot be determined

#53. Two force vectors are F1 = kN and F2 = kN. What is the resultant magnitude?

13 kN

13.03 kN

7 kN

16 kN

#54. Compute a × b for a = and b = .

#55. Find the scalar projection of a = onto b = .

4.22

34

4.69

Insufficient information

#56. Given vector v = , what is |v|?

0

5.1

26

7.1

#57. For vectors a = and b = , compute a·b.

34

5

2

Insufficient information

#58. Two force vectors are F1 = lb and F2 = lb. What is the resultant magnitude?

14.87 lb

1 lb

13.45 lb

16.45 lb

#59. Compute a × b for a = and b = .

#60. Find the scalar projection of a = onto b = .

77

Insufficient information

8.77

Cannot be determined

#61. Given vector v = , what is |v|?

9.27

16

86

11.27

#62. For vectors a = and b = , compute a·b.

2

34

5

Insufficient information

#63. Two force vectors are F1 = kN and F2 = kN. What is the resultant magnitude?

12.81 kN

13.42 kN

2 kN

15.81 kN

#64. Compute a × b for a = and b = .

#65. Find the scalar projection of a = onto b = .

40

6.4

Insufficient information

5.66

#66. Given vector v = , what is |v|?

7.07

4

50

9.07

#67. For vectors a = and b = , compute a·b.

2

13

Insufficient information

10

#68. Two force vectors are F1 = lb and F2 = lb. What is the resultant magnitude?

2 lb

18.44 lb

21.44 lb

Insufficient information

#69. Compute a × b for a = and b = .

#70. Find the scalar projection of a = onto b = .

4.26

20

4.9

Insufficient information

#71. Given vector v = , what is |v|?

7.81

5

61

9.81

#72. For vectors a = and b = , compute a·b.

6

-3

Insufficient information

-6

#73. Two force vectors are F1 = kN and F2 = kN. What is the resultant magnitude?

17.91 kN

4 kN

17.2 kN

20.2 kN

#74. Compute a × b for a = and b = .

#75. Find the scalar projection of a = onto b = .

45

6.48

6.12

Insufficient information

#76. A sample of slump values (mm) is [47, 58, 52, 27, 44]. What is the sample mean?

47 mm

31 mm

50.6 mm

45.6 mm

#77. Concrete strength has known σ = 10 MPa. For n = 49 and a 95% confidence interval, what is the margin of error?

±5.6 MPa

±2.8 MPa

±0.2 MPa

±1.43 MPa

#78. If defect probability per beam is p = 0.1, what is P(exactly 2 defects in 8 beams) using a binomial model?

0.2

0.4305

0.1488

0.2488

#79. For sample mean x̄ = 60, population mean μ = 83, σ = 12, and n = 36, what is the z-score?

-1.92

11.5

Insufficient information

-11.5

#80. Given data points x=[1, 2, 3, 4] and y=[13, 16, 19, 22], estimate the least-squares regression slope.

7

4

2

3

#81. A sample of slump values (mm) is [24, 80, 62, 78, 41]. What is the sample mean?

62 mm

56 mm

57 mm

Insufficient information

#82. Concrete strength has known σ = 12 MPa. For n = 64 and a 95% confidence interval, what is the margin of error?

±5.88 MPa

±2.94 MPa

±0.19 MPa

±1.5 MPa

#83. If defect probability per beam is p = 0.1, what is P(exactly 2 defects in 8 beams) using a binomial model?

0.2

0.1488

0.4305

0.2488

#84. For sample mean x̄ = 92, population mean μ = 69, σ = 12, and n = 25, what is the z-score?

1.92

-9.58

Insufficient information

9.58

#85. Given data points x=[1, 2, 3, 4] and y=[15, 19, 23, 28], estimate the least-squares regression slope.

8.5

5.3

3.3

4.3

#86. A sample of slump values (mm) is [38, 55, 28, 32, 46]. What is the sample mean?

39.8 mm

38 mm

27 mm

44.8 mm

#87. Concrete strength has known σ = 12 MPa. For n = 100 and a 95% confidence interval, what is the margin of error?

±4.7 MPa

±0.12 MPa

±2.35 MPa

±1.2 MPa

#88. If defect probability per beam is p = 0.2, what is P(exactly 2 defects in 8 beams) using a binomial model?

0.4

0.1678

0.3936

0.2936

#89. For sample mean x̄ = 85, population mean μ = 85, σ = 8, and n = 25, what is the z-score?

0

Insufficient information

Cannot be determined

1

#90. Given data points x=[1, 2, 3, 4] and y=[12, 16, 20, 24], estimate the least-squares regression slope.

7.2

5

4

3

#91. A sample of slump values (mm) is [70, 57, 58, 61, 40]. What is the sample mean?

58 mm

30 mm

62.2 mm

57.2 mm

#92. Concrete strength has known σ = 10 MPa. For n = 100 and a 95% confidence interval, what is the margin of error?

±1.96 MPa

±3.92 MPa

±0.1 MPa

±1 MPa

#93. If defect probability per beam is p = 0.4, what is P(exactly 1 defects in 8 beams) using a binomial model?

0.0896

0.4

0.0168

0.1896

#94. For sample mean x̄ = 92, population mean μ = 80, σ = 12, and n = 16, what is the z-score?

1

4

-4

Insufficient information

#95. Given data points x=[1, 2, 3, 4] and y=[11, 13, 15, 18], estimate the least-squares regression slope.

5.7

2.3

3.3

1.3

#96. A sample of slump values (mm) is [62, 60, 59, 41, 25]. What is the sample mean?

59 mm

49.4 mm

37 mm

54.4 mm

#97. Concrete strength has known σ = 12 MPa. For n = 49 and a 95% confidence interval, what is the margin of error?

±6.72 MPa

±0.24 MPa

±1.71 MPa

±3.36 MPa

#98. If defect probability per beam is p = 0.3, what is P(exactly 1 defects in 5 beams) using a binomial model?

0.3601

0.3

0.1681

0.4601

#99. For sample mean x̄ = 69, population mean μ = 51, σ = 8, and n = 16, what is the z-score?

9

2.25

-9

Insufficient information

#100. Given data points x=[1, 2, 3, 4] and y=[11, 16, 21, 26], estimate the least-squares regression slope.

7.4

6

4

5

Math – Medium Difficulty

Results

#1. In a site plan using Cartesian coordinates, point A is at (-1, 6) and point B is at (10, 15). What is the straight-line distance AB in m?

#2. A roadway centerline segment connects (-7, -3) and (-3, -8). What are the midpoint coordinates?

#3. A line passing through (4, -14) has slope -2. Which equation is correct?

#4. The center of a circular tank is at (-2, 4) and radius is 4 ft. Which equation represents the circle?

#5. For quality control, a measured point P(-3, -5) is compared to line 1x + 1y + -7 = 0. What is the perpendicular distance in ft?

#6. In a site plan using Cartesian coordinates, point A is at (6, -8) and point B is at (14, -5). What is the straight-line distance AB in ft?

#7. A roadway centerline segment connects (6, -3) and (-2, 5). What are the midpoint coordinates?

#8. A line passing through (-2, -1) has slope 1.5. Which equation is correct?

#9. The center of a circular tank is at (4, 4) and radius is 6 ft. Which equation represents the circle?

#10. For quality control, a measured point P(-3, -5) is compared to line 2x + 4y + 5 = 0. What is the perpendicular distance in m?

#11. In a site plan using Cartesian coordinates, point A is at (-7, 2) and point B is at (2, 9). What is the straight-line distance AB in m?

#12. A roadway centerline segment connects (3, 3) and (4, -9). What are the midpoint coordinates?

#13. A line passing through (2, -5) has slope 0.5. Which equation is correct?

#14. The center of a circular tank is at (0, -4) and radius is 4 ft. Which equation represents the circle?

#15. For quality control, a measured point P(-4, 0) is compared to line 2x + 2y + 6 = 0. What is the perpendicular distance in ft?

#16. In a site plan using Cartesian coordinates, point A is at (-6, -4) and point B is at (4, 1). What is the straight-line distance AB in ft?

#17. A roadway centerline segment connects (-8, 4) and (7, -7). What are the midpoint coordinates?

#18. A line passing through (4, 6) has slope 0.5. Which equation is correct?

#19. The center of a circular tank is at (-5, -4) and radius is 4 ft. Which equation represents the circle?

#20. For quality control, a measured point P(1, -3) is compared to line 2x + 4y + 7 = 0. What is the perpendicular distance in m?

#21. In a site plan using Cartesian coordinates, point A is at (5, -2) and point B is at (8, 2). What is the straight-line distance AB in m?

#22. A roadway centerline segment connects (2, -10) and (2, -2). What are the midpoint coordinates?

#23. A line passing through (2, 3) has slope 2.5. Which equation is correct?

#24. The center of a circular tank is at (3, 5) and radius is 8 ft. Which equation represents the circle?

#25. For quality control, a measured point P(-2, -3) is compared to line 4x + 2y + -2 = 0. What is the perpendicular distance in ft?

#26. If f(x) = 1x^3 + 6x^2 + 5, what is f'(x) at x = 1?

#27. Compute the definite integral ∫[0 to 2] (3x^2 + 0) dx.

#28. Find lim_(x→6) (x^2 – 36)/(x – 6).

#29. A rectangular lot uses 50 m of fencing on three sides, with one side along a river. Maximum area occurs at width = 25 m. What is the maximum area?

#30. What is the average value of f(x) = 6x^2 + 2x on [0, 4]?

#31. If f(x) = 1x^3 + 6x^2 + -5, what is f'(x) at x = 2?

#32. Compute the definite integral ∫[0 to 2] (1x^2 + 4) dx.

#33. Find lim_(x→7) (x^2 – 49)/(x – 7).

#34. A rectangular lot uses 35 m of fencing on three sides, with one side along a river. Maximum area occurs at width = 17.5 m. What is the maximum area?

#35. What is the average value of f(x) = 5x^2 + 2x on [0, 3]?

#36. If f(x) = 5x^3 + 3x^2 + 3, what is f'(x) at x = 1?

#37. Compute the definite integral ∫[0 to 5] (5x^2 + 0) dx.

#38. Find lim_(x→7) (x^2 – 49)/(x – 7).

#39. A rectangular lot uses 57 m of fencing on three sides, with one side along a river. Maximum area occurs at width = 28.5 m. What is the maximum area?

#40. What is the average value of f(x) = 6x^2 + 2x on [0, 7]?

#41. If f(x) = 3x^3 + 3x^2 + 4, what is f'(x) at x = 3?

#42. Compute the definite integral ∫[0 to 5] (2x^2 + 2) dx.

#43. Find lim_(x→3) (x^2 – 9)/(x – 3).

#44. A rectangular lot uses 39 m of fencing on three sides, with one side along a river. Maximum area occurs at width = 19.5 m. What is the maximum area?

#45. What is the average value of f(x) = 5x^2 + 2x on [0, 7]?

#46. If f(x) = 1x^3 + 2x^2 + 1, what is f'(x) at x = 1?

#47. Compute the definite integral ∫[0 to 3] (1x^2 + 4) dx.

#48. Find lim_(x→6) (x^2 – 36)/(x – 6).

#49. A rectangular lot uses 36 m of fencing on three sides, with one side along a river. Maximum area occurs at width = 18 m. What is the maximum area?

#50. What is the average value of f(x) = 3x^2 + 2x on [0, 7]?

#51. Given vector v = , what is |v|?

#52. For vectors a = and b = , compute a·b.

#53. Two force vectors are F1 = kN and F2 = kN. What is the resultant magnitude?

#54. Compute a × b for a = and b = .

#55. Find the scalar projection of a = onto b = .

#56. Given vector v = , what is |v|?

#57. For vectors a = and b = , compute a·b.

#58. Two force vectors are F1 = lb and F2 = lb. What is the resultant magnitude?

#59. Compute a × b for a = and b = .

#60. Find the scalar projection of a = onto b = .

#61. Given vector v = , what is |v|?

#62. For vectors a = and b = , compute a·b.

#63. Two force vectors are F1 = kN and F2 = kN. What is the resultant magnitude?

#64. Compute a × b for a = and b = .

#65. Find the scalar projection of a = onto b = .

#66. Given vector v = , what is |v|?

#67. For vectors a = and b = , compute a·b.

#68. Two force vectors are F1 = lb and F2 = lb. What is the resultant magnitude?

#69. Compute a × b for a = and b = .

#70. Find the scalar projection of a = onto b = .

#71. Given vector v = , what is |v|?

#72. For vectors a = and b = , compute a·b.

#73. Two force vectors are F1 = kN and F2 = kN. What is the resultant magnitude?

#74. Compute a × b for a = and b = .

#75. Find the scalar projection of a = onto b = .

#76. A sample of slump values (mm) is [47, 58, 52, 27, 44]. What is the sample mean?

#77. Concrete strength has known σ = 10 MPa. For n = 49 and a 95% confidence interval, what is the margin of error?

#78. If defect probability per beam is p = 0.1, what is P(exactly 2 defects in 8 beams) using a binomial model?

Math –
Medium Difficulty