Topics [Study] [List of skills] [Exam]

Unit 1 should be mostly review. The focus will be on solutions of equations. We will review how to solve linear equations, quadratic equations, radical equations, "quadratic type" equations, and equations with absolute values. Finally, we will also review procedures for solving application problems, and study several typical types of applications that involve linear and quadratic equations.

• Solving equations
  • Linear equations (1.1)
  • Quadratic equations (1.3)
  • Radical equations (1.4)
  • "Quadratic type" equations (1.4)
  • Equations with absolute values (1.6)
• Inequalities
  • Linear inequalities (1.5)
    • Interval notation
  • Inequalities with absolute values (1.6)
• Applications
  • Setting up applied problems (1.2)
  • Applications of linear equations (1.2)
    • Interest problems
    • Mixtureproblems
    • Uniform motion problems
    • Constant rate job problems
  • Applications of quadratic equations (1.3)
  • Applications involving inequalities (1.5)

Study Guidelines [Topics] [List of skills] [Exam]

These reading and problem assignments are designed to help you learn the course material. You should complete all of these problems, check your answers in the back of the textbook, and get help with the problems that you missed. Most of the problems are odd-numbered, so you can check the solutions in the Solutions Manual.

The only way to learn mathematics is to do mathematics, so while these problems will not be collected or graded, you will probably not do well in the course if you do not complete these and check your work as described above. After completing these problems, go on to the Unit Exam Description below and follow directions.

• Sections R.1-6, R.8-9: Review
  • Read and review sections R.1-6 and R.8-9 as necessary. Work through a representative sampling of the problems from these sections until you feel comfortable with the material.
    
    
  
  
• Section 1.1: Equations
  • Reading: section 1.1
    Read and work through examples 1-8 and their matched problems (see Pencil Icon, "Now Work Problem #__").
    Pay special attention to the "Procedures that result in equivalent equations" on page 85
    and the "Steps for solving equations" on page 87.
  • Practice Problems: 1.1 #1-7 odd, 9, 15, 19, 25, 29, 33, 37, 41, 43, 47, 51, 55, 59, 61, 63, 65, 67, 69, 73, 83, 85, 87, 89, 91, 93
    
    
• Section 1.2: Setting Up Equations: Applications
  • Reading: section 1.2
    Read and work through examples 1-8 and their matched problems (see Pencil Icon, "Now Work Problem #__").
    Pay special attention to the "Steps for setting up applied problems" on page 96.
    Be sure that you know how to solve the four types of problems discussed here: interest problems, mixtureproblems, uniform motion problems, and constant rate job problems.
  • Practice Problems: 1.2 #1, 3, 5, 7, 11, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 43, 47, 53
    
    
• Section 1.3: Quadratic Equations
  • Reading: section 1.3
    Read and work through examples 1-12 and their matched problems (see Pencil Icon, "Now Work Problem #__").
    Make sure that you know the quadratic formula and the significance of the discriminant (page 111).
  • Practice Problems: 1.3 #3, 7, 9, 13, 17, 23, 25, 27, 31, 33, 37, 43, 47, 51, 53, 55, 59, 63, 67, 71, 75, 79, 81, 83, 85, 89, 91, 93, 95
    
    
• Section 1.4: Radical Equations; Equations Quadratic in Form
  • Reading: section 1.4
    Read and work through examples 1-6 and their matched problems (see Pencil Icon, "Now Work Problem #__").
    There is a lot of variation of problems here, so it is very important that you do lots of problems. These types of problems get easier with more experience.
  • Practice Problems: 1.4 #1, 5, 9, 13, 17, 19, 25, 29, 31, 35, 41, 45, 49, 55, 59, 63, 65, 71
    
    
• Section 1.5: Solving Inequalities
  • Reading: section 1.5
    Read and work through examples 1-13 and their matched problems (see Pencil Icon, "Now Work Problem #__").
    The most important property to remember is that the inequality is reversed if you multiply or divide both sides by a negative number (see example 5).
  • Practice Problems: 1.5 #1-6, 9, 11, 13, 17, 19, 21, 25, 27, 29-41 (odd), 43, 47, 51, 55, 59, 63, 67, 71, 73, 77, 81, 85, 95, 103
    
    
• Section 1.6: Equations and Inequalities Involving Absolute Value
  • Reading: section 1.6
    Read and work through examples 1-6 and their matched problems (see Pencil Icon, "Now Work Problem #__").
    Equations involving absolute value are solved by using property (1) on page 135.
    Inequalities involving absolute value are solved by using properties (2) and (3) on page 136, and properties (4) and (5) on page 137. Note that there are two basic cases, |x|<a and |x|>a, with very different solution sets.
  • Practice Problems: 1.6 #3, 7, 9, 15, 21, 23, 25, 27, 29, 33, 35, 39, 43, 45, 47, 55, 57, 63, 65
    
    
• Supplementary material (optional) for sections 1.1-6:
  • Student Solutions Manual for Chapter 1
  • Video lectures are available on reserve in the CR library.
  • For tutoring help, visit the Prentice Hall Math Tutor Center. Tutors can be contacted by phone, fax, or e-mail. To register, you will need to first obtain an access code from me.
  • Graphing Calculator Help
  
  
• Here is more supplementary material on application problems:(added June 9)
  • Interest (and Multiple Investment) Problems:
    • PurpleMath has a page about "Investment" Problems. The first two are straightforward, but the ones you really need to focus on are after that. They involve multiple investments. Read the problems and try to work them out on your own before reading through the way they did them. Then compare your work to their work.
    • Here is another example from the MathForum
  • Mixture Problems: Go to this PurpleMath page on Mixture problems. Read the example problems (tickets and acid solution) and try to work them out on your own. Then compare your work to their work. Try some of the other practice problems too.
  • Uniform Motion Problems:
    • In this PurpleMath page on Distance Problems in general, there are several general distance problems, but the 6th (A boat travels for threehours with a current ...) and 7th (With the wind, an airplane travels ... ) examples have to do with Uniform Motion, so, depending on your level of experience with distance problems, you may want to work some of these but in particular, you should do the ones on the boat with and against the current and the airplane with and against the wind.
    • Here is another example from the MathForum. Scroll way down to where "Karen can row a boat..."
  • Constant Rate Job Problems:
    • There are several "work" problems on this PurpleMath page! Work lots of these (no pun intended), but especially the painter, the pipe, and the tub faucet ones.
    • Two more examples from the MathForum.

List of Miscellaneous Things to Know and Be Able To Do [Study] [Topics] [Exam]

To be successful in Unit #1, you should have the following knowledge and skills:

• Know what "solve" means
• solving linear equations
• inverse operations
• fractions -- how to add, subtract, multiply
• how to clear fractions
• how to find LCD of rational expressions
• factoring polynomials
• zero product property
• solving equations with squares
• solving equations with quadratics
• recognizing quadratic situations
• solving equations with radicals (sq rt, cube rt, etc)
• fractional exponents (rational exponents)
• rules of exponents
• inequalities
• double inequalities
• interval notation
• absolute value equations
• absolute value inequalities
• graphical solutions
• solving proportions (helpful)
• ratios
• percent
• how to solve application problems
• mean average
• perimeter of triangles, rectangles
• area of rectangles
• sales commision
• investment combinations
• uniform motion problems (eg with current or tailwind)
• "work" problems -- constant rate job problems

Unit Exam #1 [Topics] [Study] [List of skills]

After completing the above work, do the following:

1. Read the exam description:
   • This exam has 20 questions, and will Unit Exams count for 35% of your grade. 
   • This exam has a one hour time limit.
   • Calculators may be used on this exam.
   • Some questions in this unit are multiple choice or multiple selection. For the other questions, be sure to look under the entry box for the expected format of the answer.
     • Some problems (for example, solutions of quadratic equations) expect a list of several values or formulas separated by semicolons, such as -3;4. In this case, the order of the values is not important.
     • All answers on this exam must be exact.
     • There are several application questions on this exam. Remember you should not add any units such as "miles" or "meters" or "seconds" to your answers.
2. Complete the online Unit 1 Pretest assignment. You may use your book if you wish, and redo the pretest as many times as you like. Your pretest score will be scaled to 10 points maximum.
   • Directions: At the Optimath testing web site, choose the Unit 1 Pretest/HW.
   • The pretest must be completed by the deadline date listed at the top of this page.
     However, you may redo the pretest as many times as you like before the deadline date. Your best score counts, and it will be rescaled to 10 points maximum.
   • See the instructions for pretests.
3. If you are having trouble with any of the problems listed above or on the practice exams, make use of the help resources listed on the Help page.
4. Go to the Academic Support Center (or specified proctored location closer to you) to take the online proctored Unit 1 Exam assignment (see the instructions for proctored exams). Remember to bring identification, and remember that you will not be able to take the unit exam after the deadline date given at the top of this page. You may NOT use your book or notes on this exam.
   • Directions: At the testing web site, choose Unit 1 Exam.
   • The proctored unit exam must be completed by the deadline date listed at the top of this page, and may be repeated under certain conditions. See the Detailed Schedule page for specific dates.

   Note: Remember that you can always go back and take practice exams on this unit after the deadline has passed. In particular, this will help you prepare for the midterm and final exams.

   • Directions: At the testing web site, choose Unit 1 Practice Exam.

Math 30 home page