Fundamentals of Engineering Exam Sample Math Questions
Directions: Select the best answer.
1. The partial derivative of is:
a.
b.
c.
d.
2. If the functional form of a curve is known, differentiation can be used to determine all of the following EXCEPT the
a. concavity of the curve.
b. location of the inflection points on the curve.
c. number of inflection points on the curve.
d. area under the curve between certain bounds.
3. Which of the following choices is the general solution to this differential equation: ?
a. b. c. d.
4. If D is the differential operator, then the general solution to
a.
b.
c.
d.
5. A particle traveled in a straight line in such a way that its distance S
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1.9 b. 2.05 c. 2.1 d. 2.09
25. The diagram shown below shows two intersecting curves: y = x, and.
Which of the following expressions gives the distance from the y-axis to the centroid of the area bounded by the two curves shown in the diagram?
a.
b.
c.
d.
26. Find the value of the limit:
a. 0 b. ½ c. 1 d. 2 27. The following equation describes a 2nd order system: . The system may be described as:
a. non-linear b. over-damped c. critically damped d. under-damped
28. Find the solution as , for
a. y = 0 b. c. d. y = 5
29. It takes a pigeon X, 2 hours to fly straight home averaging 20 km/h. It takes pigeon Y, 2 hours and 20 minutes to fly straight home averaging 30 km/h. If both pigeons start from the same spot but fly at an angle to each other, about how far apart do they live?
a. 96 km b. 87 km c. 80 km d. 73 km
30. A matrix B has Eigen-values (characteristic values) found from which of the following equations?
a.
b.
c.
d.
31. The divergence of the vector function at the point (0, 1, 1) is
a. -4 b. -1 c. 0 d. 4
32. A right circular cone cut parallel with the axis of symmetry could reveal a
a. circle b. hyperbola c. ellipse
41. On a map with a scale of 1:50,000, the distance between point A and B is 18 centimeters. What is the actual ground distance in meters?
A 18. D Read the Diagram 1. E 2. C 3.
d. It should appear in the tail signifying a negative relationship, with .05 in that tail.
ii) Find an initial value problem (IVP) satisfied by y. Please see over . . .
2) Compute the boundaries bm such that am lies in the centroid of two adjacent boundaries. (1)
The movement that makes this object is a uniformly varied movement, because it is subject to the acceleration of gravity. In these types of movement, the position of the body with respect to time, is described by a quadratic function of the form:
c) Explain how the location of each curve graphed in question 7b would be altered if (1) total fixed cost had been $100 rather than $60 and (2) total variable cost had been $10
*Hint* Read and study the explanations within the lab for assistance. (1 point) This is the administrative distance and states that the floating static route.
This, along with the philosophical statements in agreements with the earlier assumptions, such as those of Plato, and a harmonic opinion with them, there is then substantial evidence of your standpoint on calculus, and how the subject should be presented. In this, I observe that you see a greater potential for calculus outside its present insinuations of monotony, and a respect for the long history in developing
It would be depicted into a diagram of triangle as follows: Diagram
The form of a quadratic function is f(x)=ax^2+bx+c (Quadratic Functions). The U shape formed by the graph is called a parabola (Quadratic Functions). A quadratic function can be graphed to open either up or down (Stewart, Ingrid). The coefficient is “a” (Stewart, Ingrid). If the coefficient is negative the graph will open down (Stewart, Ingrid). If it is positive the graph will open up (Stewart, Ingrid). If the graph opens up “a” is greater than 0 and if the graph opens down “a” is less than 0.
19. Graph in the plane above, over the window [-1, 8] X [-25, 25]. 20.
Then P(x0,f0) is a point on the curve . Draw the tangent to the curve at P the point
An ODE is an equation that contains ordinary derivatives of a mathematical function. Solutions to ODEs involve determining a function or functions that satisfy the given equation. This can entail performing an anti-derivative i.e. integrating the equation to find the function that best satisfies the differential equation. There are several techniques developed to solve ODEs so as to find the most satisfactory function. This discussion seeks to explore some of these techniques by providing worked out examples.
2-12. For the graph of figure, classify as planar or nonplanar, and determine the quantities specified in equations 2-13 & 2-14.