Ganguli | Math 1375 | Fall 2020

Author: Suman Ganguli (Page 2 of 16)

Guide to the Practice Final Exam

A set of Practice Final Exam exercises is available in WebWork. Submit written solutions to your exercises on Blackboard by Monday night (Dec 14). Your written solutions will be graded and counted as a quiz.

Note: This WebWork set is set up as a test with a 2h time limit, but you can ignore the time limit and the corresponding “recorded score.” You can still use WebWork to check your answers, but you should focus on understanding the exercises and writing up complete solutions.

The final exam will be Wed Dec 16-Fri Dec 18, and will be very similar in format to this Practice Final Exam.

Here is a guide to the exercises, with notes on examples to review from the WebWork, from the various quizzes and exams, from examples I have posted on OpenLab, and from the textbook:

  1. Inequalities:
    • absolute value inequality – show algebra leading to solution set (see WebWork “Absolute Value Inequalities”; Quiz #1; Exam #1)
    • polynomial inequality – show algebra solving for x-intercepts, then sketch graph to show solution set of inequality or use “test points” in each subinterval to find solution set (see WebWork “Polynomial Inequalities”; Exam #2; textbook Example 12.2)
    • rational function inequality- show algebra solving for x-intercepts and vertical asymptotes, then sketch graph or use “test points” in each subinterval to find solution set of inequality (see see WebWork “Rational Inequalities”; Exam #2; textbook Example 12.4)
  2. Rational function (show all algebra for finding domain, asymptotes, roots/intercepts; sketch a graph of the function and label all of these features):
  3. Difference quotient or inverse of a function:
    • see WebWork “Functions – Difference Quotient”; Exam #1
    • see WebWork “Functions – Inverse Functions”; textbook Example 7.6 (pp89-90)
  4. Polynomial function (show all algebra necessary for factoring and finding roots, including long division; sketch a graph of the function and label the x-intercept(s) and y-intercept)
    • see WebWork “Polynomials – Graphs”; Quiz #3; Exam #2
    • see this example
  5. skip this exercise
  6. Logarithmic function or logarithmic properties:
    • see WebWork “Logarithmic Functions – Graphs”; textbook Example 13.3
    • see WebWork “Logarithmic Functions – Properties”; textbook Example 14.3
  7. Trigonometric function and graph:
    • see textbook Definition 17.9 and Example 17.10 (pp246-247)
    • sketch a graph of the function and label the period, amplitude, and phase shift
  8. Trigonometric equation (show algebra needed to simplify the equation, and then justify your solutions in terms of either the unit circle or the graph of the trig function involved)
    • see WebWork “Trigonometry – Equations”
  9. Application of exponential function:
  10. skip this exercise

Class #28 Agenda – Wed Dec 9

Class Info

Topics

  • finish Trigonometric Functions – Graphs & Equations (Ch 17)
  • instructions for Practice Final Exam exercises

 

To-Do:

  • Work on Practice Final Exam (submit written work for WebWork exercises – due Monday Dec 14)
  • work on remaining WebWork (also due Monday Dec 14):
    • “Trigonometry – Unit Circle”
    • “Exponential Functions – Growth and Decay” and “Trigonometry – Equations” (both of these sets will be counted as extra credit)

Unit Circle and Trigonometry

Here is a useful image of the unit circle labeled with the “special angles” and the coordinates of the corresponding points on the unit circle:

unit-circle-trig

(via http://etc.usf.edu/clipart/43200/43215/unit-circle7_43215.htm)

This image of the unit circle is useful since you can use it to find the sine and cosine of any of the given angles, using the definitions of sin t and cos t as the y- and x-coordinates, respectively, of the point on the unit circle corresponding to the angle t:

186px-Unit_circle.svg
« Older posts Newer posts »