# Exam #4 Topics/Review

Listed below are the topics and exercises to review for the 4th midterm exam on Wednesday Dec 13.

Note that the MAT1275 Final Exam Review sheet is available as a pdf inÂ Files, and is also available in the Final Exam Review post.

This exam will also include one algebra topic from earlier in the semester:

• Solving systems involving nonlinear equations
• Final Exam Review: #7
• Exam #2: question #5
• Algebra textbook, Sec 9.4: Example 1(b) (p777), Example 4 (p779)

# Final Exam Review – Study Guide

Our final exam will be Monday, Dec 18 (at the usual class time, 10-11:40am).

The questions on the final exam will be very similar in format to the exercises on the Math Departmentâ€™s Final Exam Review sheet:

MAT1275 Final Exam Review

(A hardcopy of the Final Exam Review sheet was handed out in class, and the pdf is also available online at http://www.citytech.cuny.edu/mathematics/docs/review/MAT1275FinalRview.pdfÂ or on OpenLab: https://openlab.citytech.cuny.edu/groups/mat1275en-ganguli-fall2017/files/).

Note that many of the exercises on our midterm exams and quizzes were very similar in format to these exercises. Â The best way to review for the final is to work through the Final Exam Review sheet, and study the related midterm exam solutions and quiz solutions as you do so.Â  All the midterm and quiz solutions are on OpenLab–download them!

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.

#1: Solving Quadratic Equations (using the quadratic formula)

• Quiz #3 (question #2)
• Quiz #4 (question #3)
• Exam #1 (question #3)
• WebWork: â€śQuadraticFormulaâ€ť set

#2: Graphing Quadratic Functions (by completing the square to identify the vertex)

• â€śGraphing Quadraticsâ€ť class handout (pdf available on OpenLab)
• Quiz #4
• Exam #2 (question #3)
• Exam #3 (question #1)

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

• Exam #2 (question #2)
• Exam #3 (question #6)
• WebWork: “ComplexFractions-Method1” set, Problem 6

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

• Quiz #5 (question #1)
• Exam #2 (question #4)
• WebWork: â€śCirclesâ€ť set, Problems 1-4

#5: Complex Numbers (multiplying via â€śFOILâ€ť; dividing using the complex conjugate)

• Exam #2 (question #2)
• Quiz #8 (question #3)
• WebWork: “ComplexNumbers” set, Problems 5-8

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

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

#7: Solving systems involving nonlinear equations

• Exam #2 (question #5)
• 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 #5)
• WebWork: â€śCoordinatePlaneTrigâ€ť set, Problems 4 & 5
• Trigonometry textbook, Sec 1.3: Example #5 (p26)

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

• Exam #4 (TBD)
• Trig textbook, Sec 7.1: Example 1 (pp317-318)
• Sec 7.2: Examples 2 & 3 (pp331-332)

#10: Verifying Trig Identitiesâ€“use the fundamental trig identities and algebra

• Exam #4 (TBD)
• Trig textbook, Sec 1.4: Examples 2-4 (pp32-33)
• Trig textbook, Sec 5.1: Examples 1 & 2 (pp212-213)

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

• Exam #4 (TBD)
• Quiz #8 (question #2)
• WebWork: â€śSolvingTrigEquationsâ€ť set (Problems 1-7)

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

• Exam #3 (question #3)
• Quiz #7 (question #1)
• Algebra textbook, Sec 8.7: Example 7 (p722)

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

• Exam #3 (question #2)
• Quiz #6 (questions #1(c) & #1(d))
• WebWork: â€śLogarithmicFunctionsâ€ť (Problems 6-10)
• Algebra textbook, Sec 8.4: Examples 1 & 2 (pp682-683)