Monthly Archives: September 2017

Exam #1: Review Exercises

Here are the topics and exercises to review for the exam this Wednesday (Sept 27), listed according to WebWork/homework assignments:

  • LinesReview: #2-4 (slopes and equations of lines)
  • LinearSystems: #1, 2, 4-7 (graphing lines, solving 2×2 linear systems)
  • Quiz #1: 3×3 linear system (solution is posted on OpenLab Files)
    • see also textbook pp280-281 (also posted on OpenLab Files)
  • DifferenceOfSquares (#1-3)
  • HW#2 (factoring quadratic polynomials & solving quadratic equations by factoring)
    • will be handed back at beginning of class Wed so that we can discuss; solutions will be posted to OpenLab later today
    • review GCF-Factoring if needed (in particular factoring by grouping, since that’s needed for the ac-method)
  • SquareRootProperty: #3-9
    • solving quadratic equations by completing the square and using the square root property
  • QuadraticFormula
  • ComplexNumbers (due Tuesday, 9/26 – complete this as review for the exam)

Video Playlists: Complex Numbers

I have mentioned in class that online videos are a good way to review material from class and to go through additional example, and I’ve previously posted a few videos on here from PatrickJMT (you can find all video posts at

This week we introduced imaginary and complex numbers. You can review that material via the following two video playlists:

The first one is via a website called “Math 1275 Student Video Resources” which was compiled by another CityTech math professor. It contains links to Khan Academy videos, organized according to the MAT1275 syllabus. Here is the page for Complex Numbers:


The 2nd one is a YouTube playlist of all 21 of PatrickJMT’s Complex Numbers videos:


Derivation of the Quadratic Formula

Here’s a snapshot of the derivation of the quadratic formula from the blackboard on Friday:

(Note that my “blackboard management” wasn’t ideal: the derivation starts in the middle board and the continues on LHS board. The RHS board has a numerical example, which follows the same steps as the general derivation.)

Also, here is PatrickJMT’s 7min video going thru the derivation:


You can also read the derivation on the Wikipedia page for the quadratic formula, or in Sec 7.2 of the textbook (p592).

PatrickJMT Videos: Factoring Differences of Squares

You may find online videos useful to review material from class and see additional examples. I particularly like the videos of a math teacher who goes by the name of “PatrickJMT.”  He has posted hundreds of short videos on his website, including many which cover topics we will cover in the course (all the videos are also available on YouTube–his YT channel is here.)

Here are three videos which present examples of factoring differences of squares:

Factoring the Difference of Two Squares – Ex 1


Factoring the Difference of Two Squares – Ex 2


Factoring the Difference of Two Squares – Ex 3