Review for Final Exam (Day 80)

This week is the last week of school before winter break. On an early start calendar, this is the last week of the semester, hence finals week. This is exactly the reason why there is an early start calendar in the first place -- so that finals can occur before the students forget everything that they learned during winter break.

In the district whose calendar I'm following, Wednesday, Thursday, and Friday are the official finals days this week. This means that today and tomorrow are excellent days for review -- technically, there was a little review last Friday as well.

Now I don't presume to know what your district is giving for a final. Most likely, your district is already giving some sort of common final, so I wouldn't need to post my own final. But I've decided that I will post my own final this week, as well as a review for that final. You, as a teacher, can still give my final review, if it can help your students review for your final.

All of these questions are based on the SPUR objectives from the U of Chicago text. I chose to leave out Chapter 1, since we only covered parts of that chapter. For Chapters 2-7, the breakdown by chapter will be as follows:

Chapter 2: 8 questions
Chapter 3: 10 questions
Chapter 4: 6 questions (including Wu rotations)
Chapter 5: 8 questions
Chapter 6: 9 questions
Chapter 7: 9 questions

Like most high school finals, the exam will be multiple choice -- since most teachers don't have time to grade free-response finals before grades are due. But the review worksheets for this final will not be multiple choice, since it's just the review.

A few notes about the questions included on this review worksheet, which covers mostly Chapters 2 through 4 of the U of Chicago text (with two questions that require parallels from Chapter 5):

Question 8 requires a TI calculator, since it's a TI-BASIC question from Chapter 2. On the actual final, if the students don't have a calculator, they can simply use the formula to compute the number of diagonals in some polygon without needing a calculator at all.

Questions 11 and 17 require the students to draw angles of a certain measure. Hopefully, the students at least have protractors. The multiple choice questions on the final will be written such that students won't need the protractors.

Questions 14 and 18 require constructions -- that is, straightedge and compass. If these are not available to the students, then they can just freehand the necessary lines. Also, even though I do not provide a separate worksheet for the following constructions, they are mentioned in the Common Core Standards:

CCSS.Math.Content.HSG.CO.D.13
Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

I recommend that these be included as bonus questions, since I couldn't find any other point to include them in my curriculum (but they do sort of fit here in Chapter 7, since regular polygons were mentioned in Section 7-6). The regular hexagon is the easiest, since the side length of the hexagon equals the radius of the circle. Just keep the compass set to the radius of the circle and make six arcs equally spaced around the circle. If one only connects three of the arcs, the equilateral triangle is constructed instead of a circle. The best way to construct the square is to draw in a diameter and then find its perpendicular bisector -- these are the diagonals of the square.