Precalculus I

Time and Date Stamps (logged): 12:39:21 05-21-2012 ｰｱ浚ｸ浤ｰｯｴ浤ｰ浤ｯｰｱ Precalculus I

Precalculus I Major Quiz

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Instructions:

Test is to be taken without reference to text or outside notes.
Graphing Calculator is allowed, as is 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. Student may, if proctor deems it feasible, make and retain a copy of the test..

Directions for Student:

Completely document your work.
Numerical answers should be correct to 3 significant figures. You may round off given numerical information to a precision consistent with this standard.
Undocumented and unjustified answers may be counted wrong, and in the case of two-choice or limited-choice answers (e.g., true-false or yes-no) will be counted wrong. Undocumented and unjustified answers, if wrong, never get partial credit. So show your work and explain your reasoning.
Due to a scanner malfunction and other errors some test items may be hard to read, incomplete or even illegible. If this is judged by the instructor to be the case you will not be penalized for these items, but if you complete them and if they help your grade they will be counted. Therefore it is to your advantage to attempt to complete them, if necessary sensibly filling in any questionable parts.
Please write on one side of paper only, and staple test pages together.

Test Problems:

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Problem Number 1

Problem: Obtain a quadratic depth vs. clock time model if depths of 42.40351 cm, 32.5878 cm and 27.55286 cm are observed clock times t = 13.06683, 26.13366 and 39.20049 seconds.

Problem: The quadratic depth vs. clock time model corresponding to depths of 42.40351 cm, 32.5878 cm and 27.55286 cm at clock times t = 13.06683, 26.13366 and 39.20049 seconds is depth(t) = .014 t² + -1.3 t + 57. Use the model to determine whether the depth will ever reach zero.

Problem Number 2

Problem: Evaluate f( 41.97753) and f( 2a + b ) for the function y = f(t) = .014 t^2 + -2.2 t + 96. What is the value of the function for clock time t = 62.96629? What equation would you solve to determine the value of t for which f(t) = 34.4806? (You need not actually evaluate the equation).

Problem: Sketch a graph representing the linear function family y = m x + b for m = .46, with b varying over all positive real numbers.

Problem Number 3

Find the vertex and the zeros of y = .024 t² + -1.7 t + 89.

Problem Number 4

Make tables and sketch graphs of y = x, y = x² , y = x^-1 and y = 2^x , for x = -3 to x = 3.

Show what happens to each graph if it is vertically stretched by factor 4.

Problem Number 5

At clock time t = 13 sec the depth of water in a container is 64 cm, while at clock time t = 35 sec the depth is 26 cm. Plot the corresponding points on a graph of depth vs. clock time and determine the slope of the straight line segment connecting these points. Explain why this slope represents the average rate at which the water depth changes over this time interval.

For the quadratic function y = f(t) = .02 t² + -2.69 t + 96, determine the average rate of change of y with respect to t, between clock times t = 35 and t = 40.