http://interval.louisiana.edu/courses/109/fall-1999-math-109_exam_hints.html

### Math. 109-10, Fall, 1999 Hints for the Exams

Instructor: R. Baker Kearfott, Department of Mathematics, University of Louisiana at Lafayette
Office hours and telephone, Email: rbk@louisiana.edu.

/ First Exam / Second Exam / Third Exam / Fourth Exam / Final Exam /

Note:  Previously given exams are available below in Postscript format, that can be printed with a Postscript printer.  The files can also be viewed and printed with Ghostscript and GSview.

The first exam:

The second exam:
• You will be required to find the equation of a line through two points, or through a point and with a given slope.  You should be able to put an equation in slope-intercept form, find the slope and the intercept, and graph the equation.  Also, you should review composition of functions, as you may need to compose linear functions.
• You will be required to compute a linear least squares fit to some data, and to interpret the results.  You will need to know how to interpolate and extrapolate, and you will need to know the difference between interpolation and extrapolation.
• You should be able to find equations of parabolas, given points on the parabola or the vertex and another point on the parabola.

• You will need to know how to set up and work word problems for maximizing or minimizing a quantity, where the quantity obeys a quadratic relationship.

The third exam:
The exam will have three problems, from the following four kinds of problems.

1. Design a polynomial function  that has specified simple x-intercepts, that has specified multiple x-intercepts, and whose graph passes through a specified point.
2. Given a table of (x,y) data, compute the first and second-order differences.
1. Assuming the data represents exactly either a linear or a quadratic relationship, determine which kind of relationship it is from the differences you computed.  Use the differences to explicitly write down either the appropriate degree-1 or appropriate degree-2 polynomial.
2. Evaluate your polynomial at various points.  State, for each of these evaluations, whether it represents an interpolation or an extrapolation.
3. Given a large table of data,
1. determine linear, quadratic, cubic, and quartic fits to the data.
2. Graph the linear, quadratic, cubic, and quartic fits, and sketch the graphs on your paper.
3. Based on the graphs, decide which fit best represents the data.
4. Given a rational function f(x),
1. sketch the graph the function on your paper, labeling x-intercepts, the y-intercept, vertical asymptotes, and horizontal asymptotes with numbers.
2. Write down various limits, both infinite and non-infinite.  (You need to be very familiar with the limit notation from §3.5.)

The fourth exam:
The exam will have five problems, to test the following skills.

• Computation of logarithms from the definition, such as log24 or log5(512345) or 10log(3210).
• Understanding problems involving compound interest, where the compounding is a specific number of times per year, or else continuous.
• Understanding solution of equations in which the variable occurs in an exponent.
• Understanding solution of equations in which the variable occurs in an argument to a logarithm function.
• Sketching the graph of a function that involves logarithms, labeling with numbers the asymptotes and intercepts.