FE Mechanical Practice Problems EXAM
2025 QUESTIONS AND ANSWERS
To find the width of a river, a surveyor sets up a transit at point C on one river bank and sights
directly across to point B on the other bank. The surveyor then walks along the bank for a
distance of 275 m to point A. The CAB angle is 57 degrees 28'.
(SEE 1-1 PP FOR IMAGE)
What is the approximate width of the river?
(A) 150 m
(B) 230 m
(C) 330 m
(D) 430 m - ANS D
In the following illustration, angles 2 and 5 are 90 degrees, AD = 15, DC = 20, and AC = 25.
(SEE 1-1 PP FOR IMAGE)
What are the lengths BC and BD, respectively?
1
(A) 12 and 16
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, (B) 13 and 17
(C) 16 and 12
(D) 18 and 13 - ANS C
What is the length of the line segment with slope 4/3 that extends from the point (6, 4) to the
y-axis?
(A) 10
(B) 25
(C) 50
(D) 75
1-1 PP - ANS A
Which of the following expressions is equivalent to sin (2 theta)?
(A) 2sin(theta)cos(theta)
(B) (cos(theta))^2 - (sin(theta))^2
(C) sin(theta)cos(theta)
(D) (1-cos(2 theta))/2
1-1 PP - ANS A
Which of the following equations describes a circle with center at (2, 3) and passing through the
point (-3, -4)?
(A) (x + 3)^2 + (y+4)^2 = 85
2
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(B) (x + 3)^2 + (y+2)^2 = sqrt(74)
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, (C) (x - 3)^2 + (y-2)^2 = 74
(D) (x-2)^2 + (y-3)^2 = 74
1-1 PP - ANS D
The equation for a circle is x^2 + 4x + y^2 + 8y = 0. What are the coordinates of the circle's
center?
(A) (-4,-8)
(B) (-4, -2)
(C) (-2, -4)
(D) (2, -4)
1-1 PP - ANS C
Which of the following statements is FALSE for all noncircular ellipses?
(A) The eccentricity, e, is less than one.
(B) The ellipse has two foci
(C) The sum of the two distances from the two foci to any point on the ellipse is 2a (i.e., twice
the semimajor distance).
(D) The coefficients A and C preceding the x^2 and y^2 terms in general form of the equation
are equal.
1-1 PP - ANS D
What is the area of the shaded portion of the circle shown?
3
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2025 QUESTIONS AND ANSWERS
To find the width of a river, a surveyor sets up a transit at point C on one river bank and sights
directly across to point B on the other bank. The surveyor then walks along the bank for a
distance of 275 m to point A. The CAB angle is 57 degrees 28'.
(SEE 1-1 PP FOR IMAGE)
What is the approximate width of the river?
(A) 150 m
(B) 230 m
(C) 330 m
(D) 430 m - ANS D
In the following illustration, angles 2 and 5 are 90 degrees, AD = 15, DC = 20, and AC = 25.
(SEE 1-1 PP FOR IMAGE)
What are the lengths BC and BD, respectively?
1
(A) 12 and 16
Page
@COPYRIGHT BRAINBARTER 2025/2026
, (B) 13 and 17
(C) 16 and 12
(D) 18 and 13 - ANS C
What is the length of the line segment with slope 4/3 that extends from the point (6, 4) to the
y-axis?
(A) 10
(B) 25
(C) 50
(D) 75
1-1 PP - ANS A
Which of the following expressions is equivalent to sin (2 theta)?
(A) 2sin(theta)cos(theta)
(B) (cos(theta))^2 - (sin(theta))^2
(C) sin(theta)cos(theta)
(D) (1-cos(2 theta))/2
1-1 PP - ANS A
Which of the following equations describes a circle with center at (2, 3) and passing through the
point (-3, -4)?
(A) (x + 3)^2 + (y+4)^2 = 85
2
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(B) (x + 3)^2 + (y+2)^2 = sqrt(74)
@COPYRIGHT BRAINBARTER 2025/2026
, (C) (x - 3)^2 + (y-2)^2 = 74
(D) (x-2)^2 + (y-3)^2 = 74
1-1 PP - ANS D
The equation for a circle is x^2 + 4x + y^2 + 8y = 0. What are the coordinates of the circle's
center?
(A) (-4,-8)
(B) (-4, -2)
(C) (-2, -4)
(D) (2, -4)
1-1 PP - ANS C
Which of the following statements is FALSE for all noncircular ellipses?
(A) The eccentricity, e, is less than one.
(B) The ellipse has two foci
(C) The sum of the two distances from the two foci to any point on the ellipse is 2a (i.e., twice
the semimajor distance).
(D) The coefficients A and C preceding the x^2 and y^2 terms in general form of the equation
are equal.
1-1 PP - ANS D
What is the area of the shaded portion of the circle shown?
3
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