# Fundamentals of Engineering Exam Sample Math Questions

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Fundamentals of Engineering Exam Sample Math Questions

1. The partial derivative [pic 1] of [pic 2] is:
1. [pic 3]
2. [pic 4]
3. [pic 5]
4. [pic 6]

1. If the functional form of a curve is known, differentiation can be used to determine all of the following EXCEPT the
1. concavity of the curve.
2. location of the inflection points on the curve.
3. number of inflection points on the curve.
4. area under the curve between certain bounds.

1. Which of the following choices is the general solution to this differential equation:  [pic 7] [pic 8]?
1. [pic 9]             b.  [pic 10]             c.  [pic 11]              d.  [pic 12]
1. If D is the differential operator, then the general solution to [pic 13]
1. [pic 14]
2. [pic 15]
3. [pic 16]
4. [pic 17]
1. A particle traveled in a straight line in such a way that its distance S from a given point on that line after time t was [pic 18]. The rate of change of acceleration at time t=2 is:
1. 72                 b.  144                   c.  192                   d.  208
1. Which of the following is a unit vector perpendicular to the plane determined by the vectors  A=2i + 4j and B=i + j - k?
1. -2i + j - k
2. [pic 19](i + 2j)
3. [pic 20](-2i + j - k)
4. [pic 21](-2i - j - k)
1. If [pic 22], then [pic 23]using implicit differentiation would be
1. [pic 24]        b.     [pic 25]     c.   [pic 26]        d.  [pic 27]

(Questions 8-10) Under certain conditions, the motion of an oscillating spring and mass is described by the differential equation [pic 28]where x is displacement in meters and t is time in seconds.  At t=0, the displacement is .08 m and the velocity is 0 m per second; that is [pic 29]and [pic 30]

1. The solution that fits the initial conditions is:
1. [pic 31]
2. [pic 32]
3. [pic 33]
4. [pic 34]

1. The maximum amplitude of the motions is:
1.  0.02 m             b.   0.08 m              c.   0.16 m             d.   0.32 m
1. The period of motion is
1. [pic 35]sec           b. [pic 36]sec             c. [pic 37]sec              d. [pic 38]sec
1. The equation of the line normal to the curve defined by the function [pic 39]at the point (1,6) is:
1. [pic 40]
2. [pic 41]
3. [pic 42]
4. [pic 43]
1. The Laplace transform of the step function of magnitude a is:
1. [pic 44]           b. [pic 45]            c. [pic 46]            d. [pic 47]          e.  s + a
1. The only point of inflection on the curve representing the equation [pic 48]is at x equal to:
1. [pic 49]        b.  [pic 50]           c.  0           d.  [pic 51]          e.  [pic 52]

1. The indefinite integral of [pic 53] is
1. [pic 54]
2. [pic 55]
3. [pic 56]
4. [pic 57]
1. Consider a function of x equal to the determinant shown here: [pic 58]. The first derivative [pic 59]of this function with respect to x is equal to
1. [pic 60]
2. [pic 61]
3. [pic 62]
4. [pic 63]

Questions 16-18, relate to the three vectors A, B, and C in Cartesian coordinates; the unit vectors i, j, and k are parallel to the x, y, and z axes, respectively.

A = 2i+3j+k                B = 4i-2j-2k                C = i-k

1. The angle between the vectors A and B is:
1. [pic 64]         b. [pic 65]         c. [pic 66]         d. [pic 67]        e. [pic 68]

1. The scalar projection of A on C is:
1. [pic 69]         b. [pic 70]          c. [pic 71]         d. [pic 72]        e. [pic 73]
1. The area of the parallelogram formed by vectors B and C is:
1. [pic 74]           b. 12             c. [pic 75]             d. 17              e. 24
1. A paraboloid  4 units high is formed by rotating [pic 76]about the y-axis. Compute the volume for this paraboloid.
1. 4π               b.  6π               c.  8π               d.  10π

Questions 20-21. The position x in kilometers of a train traveling on a straight track is given as a function of time t in hours by the following equation, [pic 77]. The train moves from point P to point Q and back to point P according to the equation above. The direction from P to Q is positive; P is the position at time t = 0 hours.

1. What is the train’s velocity at time t = 4hours?
1. -16 km/h        b. -8 km/h          c. 0 km/h          d. 32 km/h           e. 64 km/h

1. What is the train’s acceleration at time t = 4 hours?
1. -16 km/h[pic 78]     b. 0 km/h[pic 79]        c. 12 km/h[pic 80]     d. 16 km/h[pic 81]       e. 32 km/h[pic 82]

1. Let [pic 83]be a continuous function on the interval from x=a to x=b. The average value of the curve between a and b is:
1. [pic 84]                                c. [pic 85]
2. [pic 86]                                d. [pic 87]
1. Let [pic 88], and [pic 89]. The (2,1) entry of [pic 90]is:
1. 29          b. 53           c. 33           d. 64
1. The general equation of second degree is [pic 91]

[pic 92]

The values of the coefficients in the general equation for the parabola shown in the diagram could be

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