FE Mechanical Practice
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 - correct answer 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?
(A) 12 and 16
(B) 13 and 17
,(C) 16 and 12
(D) 18 and 13 - correct answer 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 - correct answer 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 - correct answer 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
(B) (x + 3)^2 + (y+2)^2 = sqrt(74)
(C) (x - 3)^2 + (y-2)^2 = 74
(D) (x-2)^2 + (y-3)^2 = 74
, 1-1 PP - correct answer 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 - correct answer 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 - correct answer D
What is the area of the shaded portion of the circle shown?
(SEE 1-2 PP FOR IMAGE)
(A) (5pi/6) - 1
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 - correct answer 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?
(A) 12 and 16
(B) 13 and 17
,(C) 16 and 12
(D) 18 and 13 - correct answer 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 - correct answer 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 - correct answer 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
(B) (x + 3)^2 + (y+2)^2 = sqrt(74)
(C) (x - 3)^2 + (y-2)^2 = 74
(D) (x-2)^2 + (y-3)^2 = 74
, 1-1 PP - correct answer 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 - correct answer 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 - correct answer D
What is the area of the shaded portion of the circle shown?
(SEE 1-2 PP FOR IMAGE)
(A) (5pi/6) - 1
