Unit 1: Absolute Value and Symmetry

Section 1.2: Absolute Value

Two definitions of absolute value: A review

Example: Using the algebraic definition of absolute value to simplify expressions involving absolute value

Exercise Set 1.2A: Simplifying expressions involving absolute value.

  • Before attempting this exercise set, read the property summary at the bottom of page 7 of your text book.
  • page 9: # 27,29,33,35.

Exercise Set 1.2B: Using the geometric definition to represent the distances between points.

  • Page 9: #39,41,43,47

Using the geometric definition (of absolute value) to solve equations and inequalities.

Exercise set 1.2C: Using the geometric definition (of absolute value) to solve equations and inequalities.

  • Page 9: #49,51,53,59,60
  • Honorsp.10; #65 and #66

Section 1.3 : Solving equations

Because we did all of the stuff from section 1.3 in the text last year, I want you to read or skim the section to refresh your memory.

The reading starts on page 10:

  • Pay careful attention to the “Domain convention” box on page 11.
  • Pay careful attention to the words in bold. Most of these are pretty important.
  • Pay careful attention to the “Procedures that yield equivalent equations” box on page 12.
  • Pay careful attention to Example 2 starting on page 12 and read the blurb about extraneous roots on page 14.

Optional Exercises:

  • p.17, #13, 25, 35, 73

Section 1.4: Distance formula and Midpoint formula

This section is particularly important to our Precalculus studies. Luckily, you’ve already done this stuff. This section starts at the bottom of page 18 in your text.

Optional review video: Theory with examples.

Exercise Set 1.4

Optional Exercises:

  • Distance formula ->p.26: 5,8,9.
  • Midpoint formula-> p. 27: 17,19

1.4 Honors:

  • p.29 #31. Make this proof as clear as possible. Explain what you are doing by writing sentences about your steps or labeling pieces of your proof with their conceptual meanings. Also: Explain why part a.) by its self is not sufficient.  Also explain why part b.) shows that point M does lie on the segment PQ.
  •  p.31 Mini project.

Section 1.5: Graphs and graphing utilities

For this course you will be using a graphing utility (probably a graphing calculator) to make good estimates about their various properties. Since every graphing utility is different, there is no reason for me to make videos about whatever calculator I happen to have on hand. I’d like you to skim section 1.5, then make sure that you can do the following, mandatory (as in, not optional) exercises. You might need some in-class help with these, you might also need to spend some time with the user manual for your calculator (you can usually find a free pdf of this online).

Exercise Set 1.5: Using your graphing utility

  • Skim section 1.5: p.32 to p.39
  • p.41: #25,27,29,31,33
  • p.42: #41,43

Section 1.6: Equations of lines

We have done so much of this stuff that I simply can not bring myself to make any videos about it. That said, I’m happy to answer your questions in class.

Exercise Set 1.6

Optional:

  • Read/Skim section 1.6, which starts on page 43.
  • p.54: #15,17,23,31,35

Required: p. 53; #9,10,11,12

Honors:

  • p.56: #53, 54,55
  • p.57: Mini Project

Section 1.7: Symmetry and Graphs

X-axis symmetry: Theory and examples.

Y-axis symmetry: Test and Examples.

Origin symmetry: Test and Examples.

Equations of circles: Optional review (this will help with the required homework).

Exercise Set 1.7

Optional:

  • p. 67: #1,3,5
  • p. 68: 39,41 <-This pertains to graphing circles. Let me know if you want me to make a review video.

Required: 

  • p. 67: #7,9,15,17,29,51.
  • p.68: #45, 47 <- Graphing circles with completing the square. Click here for a review of completing the square. See example 7, p.65 for an example.

Honors:

  • p.69: #61,62,63
  • p.76 to 78: #Pick a challenging proof (or “show that …blah, blah is blah”-type problem) and do it. Write it up carefully so that in my haste, even I will be able to understand it. 

Please help me pick the due date: