1. The distance of a point in the 3-D system from the origin
a. is defined by the absolute value of the vector from the origin to this point.
b. is the square root of the square of the sums of the x-, y- and z-values.
c. is the square root of the sum of the squares of x-, y- and z-values.
d. can either be negative or positive.
e. None of the above.
2. In parametrizing lines connected by two points in 3-D plane,
a. there is only one correct parametrization.
b. symmetry equations may not exist.
c. a, b, and c must not be equal to 0.
d. the vector that connects the two points is a scalar multiple of the vector containing the direction numbers.
e. None of the above.
3. A plane in 3D-space system
a. is generated by at least three points.
b. can lie in more than one octant.
c. must have a z-dimension.
d. must have a point other than the origin.
e. None of the above.
4. A quadric surface
a. must have either x2, y2, or z2
or a combination of those, on its general expression.
b. must have a trace on any of the combination of two axes.
c. has only a polynomial degree of 2.
d. has only six types.
e. None of the above.
5. An elliptic cone with an ellipse trace parallel to yz-plane,
a. Has a hyperbola trace in both xz- and xy-planes.
b. Has a negative coefficient at y2.
c. Has a negative coefficient at z2.
d. Has a negative coefficient at x2.
e. None of the above.
6. The integral equation for a normal distribution curve’s probability
a. is an example of a non-elementary integral.
b. is an example of a logarithmic integral.
c. is an example of an exponential integral.
d. is an example of Gaussian integral.
e. None of the above.
7. When a non-elementary integral
a. is definite and continuous, it cannot be solved by any mathematical method.
b. is indefinite and continuous, it cannot be solved by any elementary operations.
c. is discontinuous and definite, no approximation method is applicable.
d. is discontinuous and definite, there is still a possibility of solving its integral.
e. None of the above.
8. The order of differentiation in multiple integration of continuous integrand
a. has six possibilities.
b. has two possibilities.
c. can be interchanged for real-valued limits.
d. may or may not be interchanged depending on the limits of integration.
e. None of the above.
9. In changing the differentiating variable to a polar coordinate system,
a. dx and dy becomes dr and dθ, respectively.
b. dx and dy becomes rdr and dθ, respectively.
c. dy and dx becomes rdr and dθ, respectively.
d. dy and dx becomes dr and dθ, respectively.
e. None of the above.
10. Why does in some cases, the arc length is changed to its parametric form to determine the line integral?
a. Because the arc length exists in the 3-D plane.
b. To avoid double integration.
c. Because the limits of integration are given based on the parameter value.
d. Because the arc length is a piecewise smooth curve.
e. None of the above.