Module 1 Study Guide. The first module covers the following sections of the textbook: , ,

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Vivian Carpenter
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1 Module 1 Study Guide The first module covers the following sections of the textbook: , , Sections I consider the entire first chapter to be a review of MAT092 (Algebra 1), so this material will not be covered as heavily as the material in the rest of the sections. Still, a few things may be new to you: * Interval Notation and Compound Inequalities the How To problem number 7 in section 1.1 does a good job of explaining how to express intervals of the number line in interval notation

$4 (make sure you can work with common denominators and combine fractions). Also, be able to work with simplifying algebraic terms.$

2 Also, Examples in that section cover how to simplify Union and Intersection of two sets: I expect that you know how to handle the material in sections (make sure you can work with common denominators and combine fractions). Also, be able to work with simplifying algebraic terms. For example, here is a snippet from section 1.4:

3 Verbal Problems are always problematic for students. You should be able to translate from words into algebraic expressions (section 1.5) and set up and solve Dry Mixture Problems (2.2 A) and Distance Problems (2.2 C). Definitely view all the publisher supplied videos for each of these topics and work through many, many problems! From section 2.1, make sure you can solve equations of all types IN YOUR SLEEP! You need to be an expert in this topic. A few topics in this section that may be a challenge: Equations containing fractions use the method of CLEARING DENOMINATORS. See these explanations from section 2.1:

4 Also, literal equations (equations that involve more than one variable) can be tricky. Here's another example I had scribbled down somewhere: A point of emphasis for this module is Inequalities (section 2.3). You need to be able to solve for, and either graph or express in interval notation, solution sets for inequalities. This includes simple inequalities (only a single inequality) and compound inequalities (more than one inequality, connected by an AND or an OR). Here are a few simple inequalities:

2. Sometimes, you'll end up with x on the right side of the inequality. For instance: 7 > x. How would you graph this? Well, this expression reads: the number 7 is larger than x.

5 Two things that trip students up: 1. You only switch the direction of the inequality when you multiply or divide by a negative number! That's it! Notice that in the how to problems 4 and 6 above, no change in direction occurs, because no multiplication or division of negatives occurred. However, in problem 5, we divide by -2, so > changes to <! 2. Sometimes, you'll end up with x on the right side of the inequality. For instance: 7 > x. How would you graph this? Well, this expression reads: the number 7 is larger than x. Isn't that the same thing as x must be smaller than 7? In other words: 7 > x is the same thing as x < 7! The graph of this would be <=============) > 7 which would be expressed as (,7) in interval notation. Solving and Simplifying Compound Inequalities When two inequalities are connected in the same problem, they MUST be connected with either an AND or an OR. This is true in spoken language as well. Consider the following statements about the students in this class: All the students with Blonde Hair AND Brown Eyes All the students with Blonde Hair OR Brown Eyes

So: the compound inequality: while the compound inequality: x>3 and x 1 is equivalent to (3, ) (members of both sets) x>3 or x 1 is equivalent to [1, ) (members of either set) Chapter 3 Functions

6 In the first example, because of the word AND, BOTH conditions must be met. This is equivalent to the Intersection of the two sets. In the second example, because of the work OR, EITHER one of the conditions must be met. This is equivalent to the Union of the sets. So: the compound inequality: while the compound inequality: x>3 and x 1 is equivalent to (3, ) (members of both sets) x>3 or x 1 is equivalent to [1, ) (members of either set) Chapter 3 Functions This is another point of emphasis on the quiz. You should be able to: Compute the distance between two points (memorize formula) Compute the midpoint between two points (memorize formula) Plot any ordered pair (x, y) on the rectangular coordinate system Determine the general shape of an equation of the form y =... by plotting points. Here are a few good examples from the book: In the problem above, you should be able to connect the dots forming a smooth curve.

Not all graphs are curvy. Some are linear: and others can be V-shaped: The point of graphing is to represent ALL POSSIBLE SOLUTIONS to an equation using a picture.

7 Not all graphs are curvy. Some are linear: and others can be V-shaped: The point of graphing is to represent ALL POSSIBLE SOLUTIONS to an equation using a picture. Functions The last topic covered in this module is an introduction to the idea of functions. You should spend extra time working on this section of the book (3.2). Important concepts include: Definition of a function: Why is the set { (2,3), (3,5), (4,5) } a function, but not { (2,3), (2,4), (3,5) }? What is function notation? f (x)=3 x 2 +2 How do I evaluate a function? f (4) = 3(4) 2 +2 = 3(16)+2 = 50 Relationship of functions to graphs. f (4)=50 is the same as the point (4, 50) on a graph. Domain and Range of a function. Spend extra time on this, especially Domain. Vertical Line test. Good luck preparing for the first quiz. Please post any questions to the module 1 discussion board. VIEW THE VIDEOS for each topic. They are EXCELLENT and will help you TREMENDOUSLY!

UNIT 1: NUMBER LINES, INTERVALS, AND SETS

UNIT 1: NUMBER LINES, INTERVALS, AND SETS ALGEBRA II CURRICULUM OUTLINE 2011-2012 OVERVIEW: 1. Numbers, Lines, Intervals and Sets 2. Algebraic Manipulation: Rational Expressions and Exponents 3. Radicals and Radical Equations 4. Function Basics