Sample Major Quiz

This is a sample of the first (and only) Major Quiz.  It is strongly recommended that you ignore this quiz for the time being and prepare for it by thoroughly studying

• the class notes and video links as relevant to your course, and
• the text and other materials for your course, with close attention to the assigned problems and to the instructor's feedback on the problems you have submitted.

If you submit this sample test you will receive a response indicated the grade you would have made, as well as a constructive critique on your work and an indication of how to improve your score.

1. Sketch a graph of the basic exponential function y = 2 ^ x. Sketch the graph of this function stretched vertically by factor 2 then shifted +3 units vertically.
2. At clock times t = 100, 110, 120 and 130 seconds, the depth of water in a uniform cylinder was observed to be 90, 60, 35 and 15 cm. At what average rate was the depth changing during each of the four time intervals? Look at the rates you have calculated and predict what the next average rate would be. If your prediction is correct, then what will be the depth at t = 140 seconds?
3. What function do we get if we vertically stretch the basic y = x ^ 2 parabola vertically by a factor of -.5, then shift it -3 units vertically? Sketch a graph showing what happens to selected points and to the graph in general during the vertical stretch, then during the vertical shift.
4. For the function y = f(t) = .02 t^2 - 12 t + 70, what are the values of the following: f(-2) and f( 2a + b )? What equation would you solve to determine the value of t for which f(t) = 50? (You need not actually evaluate the equation). What is the value of the function for clock time t = 40?
5. Find the zeros of the quadratic function y = 4 t ^ 2 - 7 t - 2. Find the vertex and the points 1 unit to the right and the left of the vertex, and sketch the graph of the function.
6. The quadratic depth vs. clock time model corresponding to depths of 42.5, 30 and 23.5 cm at clock times t = 5, 10 and 15 seconds is depth(t) = .1 t^2 - 4 t + 60. Use the model to determine whether the depth will ever reach zero.