Some students have requested some sample problems for the upcoming test. The problems that follow are not necessarily typical of test problems, and they don't include every possible topic (for example I don't ask you to show the picture and give the explanation for the slope = slope equation, or specifically for any of the stuff you are supposed to have memorized; and there are many other topics I don't have time to cover here), but they should provide useful material for a study session.
Of course, the assigned problems and the last couple of sets of problems, suggested problems and examples provide important material for review.
1. If we can get 1 hour of video on a 5-inch CD, how much could we get on a 10-inch CD?
2. If a 50-foot sperm whale weighs 35 tons, how much would a geometrically similar 60-foot sperm whale weigh?
3. Suppose you can hold a half-gallon container of water at arm's length for 150 seconds, a gallon for 120 seconds and a gallon and a half for 80 seconds. Obtain a linear model and a quadratic model for this data. Use both models to predict the length of time you could hold a 2-gallon container, the amount you could hold for 10 seconds, and the maximum amount you could raise. (For study you should find the equations in every possible way, including DERIVE; except that you probably don't need anymore practice on fitting a quadratic using simultaneous equations).
Using DERIVE be sure to author the appropriate data set, fit your linear and quadratic functions, plot the graph, author and solve the appropriate equations. And be sure you know the syntax and the procedure for each operation.
4. Sketch the family of linear functions for b = 5, and the family for m = 3.
5. Determine the first six numbers in the sequence defined by a(n+1) = a(n) + 2 n^2, a(0) = 3. Fit a cubic polynomial (using DERIVE) to your first four points and show that the resulting function gives a perfect fit for the remaining points. Emulate the analysis of the first example on the last handout. See what is similar and what is different.
6. For a quadratic function y = f(x) = a x^2 + bx + c, write and simplify the expression for the slope between point x = x1 and x = x1 + h. (I'm not going to ask a problem like this using a quadratic, but it will provide excellent practice in doing and simplifying a symbolic substitution).