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Mth 277
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Question Form_labelMessages **
TestQuest
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You stated in an email that you would post a practice test for Mth 277. I was just curious when that would be done and where it would be posted. Would it just be for test one or the other four tests for the class would also be posted. Also, I wanted to thank you for your help on a practice test I submitted for Phys 232. You were very helpful with the short time period given.
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I've emailed the practice test ... no, that was for Mth 279. My error.
Here's a copy, which I'll also email:
Chapter 9 Test
Signed by Proctor or Attendant, with Current Date and Time: ______________________
If picture ID has been matched with student and name as given above, Attendant please sign here: _________
Instructions:
Test is to be taken without reference to text or outside notes.
No calculator is necessary for this test.
Test is to be taken on blank paper or testing center paper.
No time limit but test is to be taken in one sitting.
Please place completed test in Dave Smith's folder, OR mail to Dave Smith, Science and Engineering, Va. Highlands CC, Abingdon, Va., 24212-0828 OR email copy of document to dsmith@vhcc.edu, OR fax to 276-739-2590. Test must be returned by individual or agency supervising test. Test is not to be returned to student after it has been taken.
Directions for Student:
Completely document your work. Show all steps and explain all reasoning.
Unless test is to be faxed or sent as PDF or other electronic means, please write on one side of paper only, and if possible staple test pages together.
1. What is the equation of a sphere with center (3, -4, 8) if the vector 2 i - 4 j + k coincides with a radius of the sphere?
2. Find the scalar and vector projections ofu = 3 i- 7 j + 3 k onv = - j+ 3 k, as well the component of u in the direction of v.
3. Find the volume of the parallelepiped determined by u =-2 i+ 5 k, v = 3 i - 4 j, and w = 5 k + i.
4. Identify the quadric surface given by the equation x / 64- (y^2)/4 + (z^2)/9 = 16. Describe the traces of this surface in planes parallel to the coordinate planes, sketch the graph of the surface, and give the name the surface (e.g., an ellipsoid, an elliptical paraboloid, etc..)
5. Determine if u = i + 4j + 3k is parallel to v = <-2, -8, -5>.
6. Find the area of the triangle with vertices P(2,2,0), Q(1,-1,-1), R(-3,1,2).
Chapter 10 Test
Signed by Proctor or Attendant, with Current Date and Time: ______________________
If picture ID has been matched with student and name as given above, Attendant please sign here: _________
Instructions:
Test is to be taken without reference to text or outside notes.
No calculator is necessary for this test.
Test is to be taken on blank paper or testing center paper.
No time limit but test is to be taken in one sitting.
Please place completed test in Dave Smith's folder, OR mail to Dave Smith, Science and Engineering, Va. Highlands CC, Abingdon, Va., 24212-0828 OR email copy of document to dsmith@vhcc.edu, OR fax to 276-739-2590. Test must be returned by individual or agency supervising test. Test is not to be returned to student after it has been taken.
Directions for Student:
Completely document your work. Show all steps and explain all reasoning.
Unless test is to be faxed or sent as PDF or other electronic means, please write on one side of paper only, and if possible staple test pages together.
1. Describe and sketch the graph of the function R ( t ) = -3 sin(t) i - 4 cos(t) j + 1 / (t + 1) k, t >= 0.
For this function find R ' ( t ) and R '' ( t ),
What is the equation of the plane parallel to R ' (t) and R (t), at the t = 0 point of the graph?
2. For the function R ( t ) = 7 cos(pi t) i - 4 sin ( pi t) j + sin(2 pi t) k, t > 0, calculate the unit tangent and unit normal vectors.
3. Find the first and second derivatives of the function R(t) = r(t) u_r, where r(t) = 3 and theta(t) = t^2.
4. Find the expression for the curvature of the curve defined by R(t) = 2 cos(pi t) i + t^2 j + 2 sin( pi t) k and find the equation of the osculating circle at the t = 1 point of this curve.
5. Find the tangential and normal components of an object's acceleration given its position vectorR(t) = sin(t) i + 2 cos(t) j + 3 k
6. If a(t) = 3 j with v(0) = 3 i -j and r(0) = -5 i, then what is r(t) when the y component of its velocity reaches 8?
Chapter 11 Test
Signed by Proctor or Attendant, with Current Date and Time: ______________________
If picture ID has been matched with student and name as given above, Attendant please sign here: _________
Instructions:
Test is to be taken without reference to text or outside notes.
No calculator is necessary for this test.
Test is to be taken on blank paper or testing center paper.
No time limit but test is to be taken in one sitting.
Please place completed test in Dave Smith's folder, OR mail to Dave Smith, Science and Engineering, Va. Highlands CC, Abingdon, Va., 24212-0828 OR email copy of document to dsmith@vhcc.edu, OR fax to 276-739-2590. Test must be returned by individual or agency supervising test. Test is not to be returned to student after it has been taken.
Directions for Student:
Completely document your work. Show all steps and explain all reasoning.
Unless test is to be faxed or sent as PDF or other electronic means, please write on one side of paper only, and if possible staple test pages together.
1. Find the critical points of f(x,y) = 3 x^2 + 4 y^2 - 8 x y + 9. Classify each as either a relative maximum, relative minimum, or saddle point.
2. Give the standard form equation for the tangent plane to the surface z(x,y) = x^2 + sqrt(y) at the point (1, 2, 3).
3. The ideal gas law states that P V = n k T, where k is a constant. Suppose V is also held constant, so that V / k can be regarded as constant. Then n becomes a function of P and T, with n ( P, T) = ( V / k) * P / T, with (V / k) being constant. In the P vs. T plane, sketch a representative series of level curves of n ( P , T ).
4. Find grad(f) when f(x,y,z) = e^(x^2+y^2+z^2).
5. Find f_x, f_y, f_xy, f_xx and f_yy for f(x, y) = sqrt(x^2 y - x y^2). What equation(s) would you solve to determine where f_x and f_y are both zero?
6. Find three positive numbers such that the sum of the first, double the second and triple the third is 50, and the sum of whose squares is as large as possible.
7. Find the equation of all horizontal tangent planes to the surface z + 4 x ^2 + 4 y^2 + 36 x = 1.
8. Sketch and describe the traces of the quadric surface z = x^2 / 4 - y^2 / 9
Chapter 12 Test
Signed by Proctor or Attendant, with Current Date and Time: ______________________
If picture ID has been matched with student and name as given above, Attendant please sign here: _________
Instructions:
Test is to be taken without reference to text or outside notes.
No calculator is necessary for this test.
Test is to be taken on blank paper or testing center paper.
No time limit but test is to be taken in one sitting.
Please place completed test in Dave Smith's folder, OR mail to Dave Smith, Science and Engineering, Va. Highlands CC, Abingdon, Va., 24212-0828 OR email copy of document to dsmith@vhcc.edu, OR fax to 276-739-2590. Test must be returned by individual or agency supervising test. Test is not to be returned to student after it has been taken.
Directions for Student:
Completely document your work. Show all steps and explain all reasoning.
Unless test is to be faxed or sent as PDF or other electronic means, please write on one side of paper only, and if possible staple test pages together.
1. Find the volume of the solid bounded above by the graph of z = f(x,y) and below by the xy-plane when f(x,y) = x sin(xy) and R: 0 <= x <= pi/2, 0 <= y <= 1.
2. Integrate 1/( x + 1)^2 over D with respect to A using a double integral where D is the region of the first quadrant bounded by the curve y = 9 – x^2. Sketch this region, estimate its area and based on your estimate determine the approximate average value of the function on the region.
3. Use a double integral to find the area of the region described by 0 <= r <= 1 + sin(theta), 0 <= theta <= 2 pi. Sketch and describe the region over which this integral is taken.
4. Compute the magnitude of the fundamental cross product for the surface parametrically described by R(r, theta) =(2 r cos(theta))i + (3 r sin(theta))j + (1 + sqrt(r)))k.
5. Use a triple integral to find the volume of the solid bounded by x^2 + 4 y^2 + z^2 = 25 and z = 3.
6. Use double integration to find the center of mass when delta(x,y) = y over the region below the curve y = e^-(k x) in the first quadrant, for x < 1.
7. Convert the equation 2x^2 + 2y^2 + 2z^2 = 1 to spherical coordinates.
Chapter 13 Test
Signed by Proctor or Attendant, with Current Date and Time: ______________________
If picture ID has been matched with student and name as given above, Attendant please sign here: _________
Instructions:
Test is to be taken without reference to text or outside notes.
No calculator is necessary for this test.
Test is to be taken on blank paper or testing center paper.
No time limit but test is to be taken in one sitting.
Please place completed test in Dave Smith's folder, OR mail to Dave Smith, Science and Engineering, Va. Highlands CC, Abingdon, Va., 24212-0828 OR email copy of document to dsmith@vhcc.edu, OR fax to 276-739-2590. Test must be returned by individual or agency supervising test. Test is not to be returned to student after it has been taken.
Directions for Student:
Completely document your work. Show all steps and explain all reasoning.
Unless test is to be faxed or sent as PDF or other electronic means, please write on one side of paper only, and if possible staple test pages together.
1. Use the divergence theorem to evaluate the surface integral Int[Int[ F dot N dS, S]] where F = i, S is and N is the outward unit normal vector field.
2. Using Stokes' Theorem, evaluate Int[ F dot ds, C] where F = (x + z) i + (y + x) j + (z + y) k and C is the boundary of the triangular region with vertices (6,0,0), (0,4,0), (0,0,3) traversed counterclockwise as viewed from above.3. Evaluate Int[xe^(yz) ds, C], where C is the line segment from (0,0,0) to (1, 3, 2).
3. Evaluate Int[Int[ F dot N dS, S]], where F = 3 xi - y j + 2z k, S is the surface of the cube bounded by the planes x = 0, x = 1, y = 0, y = 2, z = 0, z = 3. N is the outward directed normal field.
4. Using a line integral, find the area enclosed in the semicircle y = sqrt(a^2 - x^2), where a is a constant. You can easily find the area of the region without using Green's Theorem, and you should compare your result with that expression, but you need to find the result using an appropriate line integral.
5. Show that the vector field F = < y^2 sqrt(z), 2 x y sqrt(z), x y^2 / (2 sqrt(z) ) > is conservative and evaluate Int[ F dot dR, C], where C is any smooth path connecting (1,1,-1) to (-1,-1,1).
6. Evaluate Int[ x y / z^3 ds, C], where C is the straight line segment from (1, 1, 1) to (3, 4, 2).
7. Find div F, given that F = grad(f), where f(x,y,z) = x e^(x^2 + y^2).
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