# Study Guide for the Final Exam (& the Take-Home Exam)

The take-home midterm exam will be due at the beginning of our next class meeting, on Tuesday, May 22. Our final exam will be Thursday, May 24 (at the usual class time, 10-11:40am).

Note that the questions on the take-home exam are similar in format to a subset of the exercises on the Math Department’s Final Exam Review sheet, and that the final exam questions will also be similar to the Final Exam Review questions.

(A hardcopy of the Final Exam Review sheet was handed out in class, and the pdf is also available on our course OpenLab profile; see this previous post: https://openlab.citytech.cuny.edu/mat1275-ganguli-spring2018/2018/04/19/mat1275-final-exam-review-sheet/.)

Here are some recommendations for approaching the take-home midterm, and for preparing the for the final exam

• we worked through similar examples in class, so study those examples in your class notes
• try to work through the similar exercises on the Final Exam Review sheet, and/or study the YouTube videos that go through the Final Exam Review exercises (https://www.youtube.com/playlist?list=PLutj_7uIurpn51xePnCtTNVC_QNz9vw3n
• )
• many of the exercises on our midterm exams and quizzes were very similar in format to the Final Exam Review exercises, so study the related midterm exam solutions and quiz solutions

Below is a guide to the exercises on the Final Exam Review sheet, with similar exam questions, WebWork exercises, and textbook examples listed for further review.

• Exam #2 (question #3)

• “Graphing Quadratics” class handout (pdf available on OpenLab)
• Quiz #3
• Quiz #4
• Exam #2 (question #4)
• Exam #3 (question #1)

#3: Simplifying Complex Fractions (using least common denominators)

• Quiz #1 (question #2)
• Exam #1 (question #4)
• Exam #2 (question #1)
• WebWork: “ComplexFractions-Method1” set, Problem 6

#4: Graphing Circles (by completing the squares to identify the center and radius)

• Exam #2 (question #5)
• WebWork: “Circles” set, Problems 1-4

#5: Complex Numbers (multiplying via “FOIL”; dividing using the complex conjugate)

• Exam #1 (question #6)
• WebWork: “ComplexNumbers” set, Problems 5-8

#6: Solving a system of 3 linear equations in 3 variables

• Quiz #5
• Exam #3 (question #3)
• Algebra textbook, Sec 3.6: Example 1 (pp280-281)

#7: Solving systems involving nonlinear equations

• Exam #3 (question #2)
• WebWork: “NonlinearSystems” set, Problems 4-6
• Algebra textbook, Sec 9.4: Example 1(b) (p777), Example 4 (p779)

#8: Finding the values of the trig functions based on the value of one trig function (and information about the sign of one other trig function):

• Exam #3 (question #6)
• WebWork: “CoordinatePlaneTrig” set, Problems 4 & 5
• Trigonometry textbook, Sec 1.3: Example #5 (p26)

#9: Using the Law of Sines or Law of Cosines

• WebWork: “LawOfSines” set, Problems TBA; LawOfCosines set, Problems TBA
• Trig textbook, Sec 7.1: Example 1 (pp317-318)
• Sec 7.2: Examples 2 & 3 (pp331-332)

#10: Verifying Trig Identities–use the fundamental trig identities and algebra

#11: Solving Trig Equations (using the unit circle)

#12: Solving an exponential equation (using logarithms):

• Exam #3 (question #5)
• WebWork: “ExponentialEquations-Calc” (Problems 1-3)
• Algebra textbook, Sec 8.7: Example 7 (p722)

#13: Evaluating logarithms (using the definition of logarithms)

• Exam #3 (question #4)
• WebWork: “LogarithmicFunctions” (Problems 6-10)
• Algebra textbook, Sec 8.4: Examples 1 & 2 (pp682-683)