Precalculus II

Time and Date Stamps (logged): 17:12:20 06-10-2020 ｰｶ涓ｱ浤ｯｯｵ涓ｯ浤ｯｱｯ Precalculus II

Precalculus I Test 1

Completely document your work and your reasoning.

You will be graded on your documentation, your reasoning, and the correctness of your conclusions.

Test should be printed using Internet Explorer. If printed from different browser check to be sure test items have not been cut off. If items are cut off then print in Landscape Mode (choose File, Print, click on Properties and check the box next to Landscape, etc.).

Write on ONE SIDE of paper only
If a distance student be sure to email instructor after taking the test in order to request results.

Name and Signature of Student _____________________________

Signed by 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.
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

At clock time t = 10 sec the temperature of an object is 69 Celsius, while at clock time t = 29 sec the temperature is 42 Celsius. Plot the corresponding points on a graph of temperature 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 temperature changes over this time interval.

For the exponential function y = f(t) = .021 * 1.015^t, determine the average rate of change of y with respect to t, between clock times t = 29 and t = 31.

Problem Number 2

If water depths of 58.1, 44.7, 35.6 and 30.8 cm are observed at clock times 19.4, 29.1, 38.8 and 48.5 sec, then at what average rate does the depth change during each time interval?

Sketch a graph of this data set and use a sketch to explain why the slope of this graph between 29.1 and 38.8 sec represents the average rate at which depth changes during this time interval.

If f(x) = x², give the vertex and the three basic points of the graphs of f(x--.25), f(x) - -1.65, .5 f(x) and .5 f(x--.25) + -1.65. Quickly sketch each graph.

Problem Number 3

Using a completely labeled graph with points (x1,y1), (x2,y2) and (x,y) lying on a common straight line, explain how to obtain the equation for the straight line through two known points. Get an equation for the line and solve it for x.

Problem Number 4

Problem: Sketch a graph representing the linear function family y = m x + b for b = 2.49, with m varying over all positive real numbers.

Problem: Find f( 12.11114) and f( t - 1 ) for the function y = f(t) = .025 t^2 + -1.1 t + 78. What equation would you solve to determine the value of t for which f(t) = 70.91286? (You need not actually evaluate the equation). What is the value of the function for clock time t = 6.055572?

Problem Number 5

Approximate e using n = 1, 1000 and 1,000,000. Knowing that to n decimal places e = 2.718281828, how does the number of accurate digits in the approximation change when n increases by a factor of 1000?

Problem Number 6

Find the equation of the straight line through the t = 5 sec and the t = 13 sec points of the quadratic function depth(t) = .1 t^2 + -2 t + 44, where depth is in centimeters when time is in seconds.

What does the slope of your line tell you about the depth function?

Evaluate both the linear function and the quadratic depth function at four equally spaced points between t = 5 sec and t = 13 sec. How closely does the linear function approximate the quadratic function at each of these times?

Problem Number 7

Find the first 4 terms of the sequence defined by a(n) = a(n-1) + 2 n, a(0) = 3.

Problem Number 8

Solve using ratios instead of functional proportionalities:

If a sand pile 2 meters high has a mass of 4320 kg, then what would we expect to be the mass of a geometrically similar sand pile 6.3 meters high?
If there are 1.56 billion grains of sand exposed on the surface of the first sand pile, how many grains of sand we expect to be exposed on the surface of the second?