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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:

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 (
  • )
  • 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.

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

  • Exam #2 (question #3)
  • WebWork: “QuadraticFormula” set

#2: Graphing Quadratic Functions

  • “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)

Exam #3 Review / Homework Assignment

Listed below are the topics to review for Exam #3, which we will be on Tuesday, May 1.

For each topic you will see some exercises listed from the Final Exam Review Sheet. Please write out the solutions to these exercises and hand them in on the day of the exam–this will count as a homework assignment.  As always, show all your work.

[A copy of the Final Exam Review sheet was handed out in class, but you can also find the pdf (including answers, so you can check your solutions) here.]

  • Graphing a quadratic function y = -x^2 + bx + c
    • Final Exam Review: #2(c)
  • Solving a 3×3 linear system of equations
    • Final Exam Review: #6(a)
  • Solving a nonlinear system of equations
    • Final Exam Review: #7(a)(b)
  • Solving an exponential equation (using logarithms and a calculator)
    • Final Exam Review: #12(a)(b)
  • Evaluating logarithms:
    • Final Exam Review: #13(a)(b)(c)(d)
  • Trigonometry in the Coordinate Plane
    • Final Exam Review: #8(a)(c)

Also, a reminder to complete all open WebWork assignments, then go on to work on these exercises.

Exam #2 Review

Listed below are the topics and exercises (listed according to WebWork assignments in italics) to review for Exam #2, which we will be on Thursday, March 29.

The first two topics were included on Exam #1 (note that solutions to Exam #1 are available in the course profile’s Files):

  • ComplexFractions-Method1: #3-4, 6
    • textbook: Sec 5.4, Examples 1-5
    • Exam #1: #4
    • Final Exam Review: #3 (download FER sheet from Files)
  • ComplexNumbers: #3-8
    • textbook: Sec 6.8, Examples 5-7
    • Exam #1: #6
    • Final Exam Review: #5

The new topics that will be on this exam:

  • SquareRootProperty: #7-9
    • textbook: Sec 7.1, Examples 2-3, 5
    • Quiz #2 (solutions will uploaded to our course profile’s Files)
  • QuadraticFormula: all
    • textbook: Sec 7.2, Examples 1-2
    • Final Exam Review: #1
  • Graphs of Quadratic Functions: complete/review the handout HW!
    • ShiftingParabolas: all
    • ParabolaVertices-CtS: #1-2
    • Final Exam Review: #2
    • Quiz #3
  • Circles: #1-4
    • textbook: Sec 9.1, Examples 3-5
    • Final Exam Review: #4

First complete all the open WebWork assignments, then go on to reviewing the earlier material!

Note that you can always find links to Khan Academy videos for all the course material on the MAT1275 Student Video Resources OpenLab site, organized according to the syllabus. There are also links to the relevant pages within the “Set Info” section of each WebWork assignment (on the RHS of the webpage when you view the problem list for a given WebWork set).

On-Campus Math Tutoring Schedules

There is a lot of free on-campus math tutoring available that you can utilize:

1) There are math tutors available Mon-Fri in the Atrium Learning Center (AG-25; ground floor of the Atrium):

Atrium Learning Center - Math Tutoring



2) The Math Department runs a separate tutoring program, with tutors available Mon-Fri:

Math Department Tutoring



In addition, a complete list of tutoring services available at CityTech, across all departments, is available on the College website:



Extra Credit Assignment: Compound Interest (Part 1)

This is an extra credit assignment on compound interest.  Shown below is a worksheet which guides you through the mathematics of compound interest.  Also embedded below are the two videos you need to watch to complete the worksheet.

(In order to download the pdf to print it out, go to Files.)

MAT1275/D518: Compound Interest Extra Credit Assignment, Part 1



PatrickJMT — “Deriving the Annual Compound Interest Formula”: