Math 103 Study Guide

Textbook:   "Introductory Algebra, 3rd Edition"


  • ALWAYS read the text, study the examples, and do the Practice problems throughout each section.

  • Then, on a separate sheet of paper, do the Suggested Problems (listed below) from the Exercise Set at the end of each section. Write out your steps and check your answers in the back of the book.

  • Worked-out solutions for the odd-numbered problems may be viewed in the Math Learning Center (MLC) , 1-112 Wilson, or may be purchased at Cards 'N Copies in the SUB.

  • The list of problems given for each section is a suggested minimum number of problems. Do more problems in any section where you feel you need more practice to be successful.

    Chapter 1 -- Beginning Concepts

    1.1 Operations with Real Numbers
    1, 3 - 6, 9, 10, 12 - 14, 19, 20, 22 - 27, 29 - 42

    1.2 Algebraic Expressions
    1 - 11, 13 - 15, 17, 21, 23, 25 - 27, 29, 31, 33 - 36

    1.3 Solving Linear Equations
    Solving equations is one of the most important topics in algebra.
    Do all: 1 - 46

    1.4 Applications of Linear Equations
    1 - 20

    1.5 Solving Linear Inequalities
    1 - 9, 11, 13, 16, 19, 22, 25 - 29

    Chapter Review
    1 - 60

    Using Sample Exams - Never take the actual exam without first completing the Sample Exam. Do this as a "practice test". Follow each of these steps:.
  • Become familiar with the wording of the questions and the answer choices.
  • Copy each problem onto a piece of paper and use a pencil and a calculator.
  • Check over your own work as you would on an exam.
  • Imagine you are in the actual testing situation. Do not look back in the chapter or at your notes during this "practice test".
  • When finished, check your answers in the back of your book.
  • If you made any mistakes, go back and find out why. Seek help if necessary.
  • Use the chart below to find an explanation and examples relating to each type of problem, as well as other, similar problems.
  • You will have 16 problems on your actual exam and cannot miss more than 4 problems to pass the test. Aim high!

    Chapter 1 Sample Exam
    Sample exam problems come from these sections:

          Problem          Comes From Section Number    
          Number          and Key Idea:    
    1 Chap. 0, C
    2 1.1 A
    3 1.1 B
    4 1.1 C
    5, 6, 7 1.1 D
    8, 9 1.2 A
    10, 11, 12, 13, 14 1.2 B
    15, 16, 17, 18 1.3 A
    19, 20, 21, 22, 23, 24 1.3 B
    25 1.3 C
    26, 27 1.4 A
    28, 29 1.4 B
    30, 31 1.4 C
    32 1.5 B
    33 1.5 C
    34 1.5 A
    35, 36 1.5 D


    For a similar list of information about the 16 actual test questions, see Math 103 Test Information . This is especially helpful if you don't pass the test and need to study before taking it again.

    Don't forget to pick up your Free Testing Coupon from a course supervisor in the Math Learning Center after your first try on the Unit 01 exam (whether or not you pass).




    Chapter 2 -- Linear Equations in Two Variables

    For more accurate graphs, use the graph paper provided at the back of your textbook, pages 391 - 400.

    2.1 Solutions of Linear Equations in Two Variables
    1, 3, 4, 6, 7, 9, 10, 12, 13, 14, 16 - 18

    2.2 Graphing Linear Equations
    1 - 24, 25 - 33, 34, 35, 36, 39, 41, 43, 44, 45, 47

    2.3 Slope - Intercept Form of an Equation
    1 - 6, 7, 10 - 12, 13, 14, 16, 17, 19, 20, 22, 23, 26, 27

    2.4 Finding an Equation of a Line
    1 - 10, 11 - 14, 16 - 18, 19, 21, 22, 24, 25, 27, 29, 32

    Chapter Review
    1 - 3, 5, 6, 8, 10, 13, 14, 16, 17, 19 - 22, 24, 25, 27, 29 - 37, 40 - 45

    Chapter 2 Sample Exam (see "Using Sample Exams" in the Chapter 1 section above.)
    Sample Exam problems come from these sections:

          Problem          Comes From Section Number    
          Number          and Key Idea:    
    1, 2 2.1 A
    3 2.1 B
    4, 5 2.2 A
    6, 7 2.2 C
    8 2.2 B
    9, 10 2.2 D
    11, 12 2.3 A
    13 2.3 B
    14 2.3 A
    15, 16 2.3 C
    17, 18, 19 2.3 D
    20 2.4 A
    21 2.4 B
    22 2.4 C
    23, 24, 25 2.4 D
    26 2.4 E


    For a similar list of information about the actual test questions, see Math 103 Test Information




    Cumulative Test A -- covering Chapters 1 & 2

    Now that you have mastered Units 01 and 02, the next test you must take is Cumulative Test A.

    Remember a cumulative test may only be taken once and the score you receive is used when computing your course grade.

    Prepare thoroughly. In addition to your review of chapters 1 and 2 and their sample exams, a review worksheet for Cumulative Test A is available in the Math Learning Center, 1-112 Wilson Hall.

    Don't forget to pick up your Free Testing Coupon after taking each Cumulative Test. Your coupon is available from the course supervisor in the MLC.




    Chapter 3 -- Systems of Equations and Inequalities

    3.1 Introductions to Linear Systems in Two Variables and Solving Systems of Equations using the GRAPHING method
    For more accurate graphs, use the graph paper provided at the back of your textbook, pages 391 - 400.
    1, 3, 4, 5, 7, 8, 12, 14, 16

    3.2 Solving Systems of Equations using the SUBSTITUTION method
    1 - 3, 5, 8, 10, 11, 12, 14, 15

    3.3 Solving Systems of Equations using the ADDITION method
    1 - 6, 8 - 10, 13, 15

    3.4 Problem Solving
    1 - 12 all. Read the examples in section 3.4 first!

    3.5 Systems of Linear Inequalities in Two Variables
    Use graph paper.
    1, 4, 5, 6, 7, 9, 10, 13, 14, 16

    Chapter Review
    1 - 4, 6, 7, 8, 9, 11, 16, 19, 20 - 23, 26, 27, 28, 29, 32, 33

    Chapter 3 Sample Exam (see "Using Sample Exams" in the Chapter 1 section above.)
    Sample Exam problems come from these sections:

          Problem          Comes From Section Number    
          Number:           and Key Idea:    
    1, 2 3.1 A
    3 3.1 B
    4 3.1 C
    5, 6 3.1 B
    7 3.1 C
    8, 9, 10 3.2 A
    11 3.2 B
    12 3.3 A
    13, 14, 15 3.3 B
    16, 17, 18, 19 3.4 A
    20, 21 3.5 A
    22, 23, 24, 25, 26 3.5 B


    For a similar list of information about the actual test questions, see Math 103 Test Information




    Chapter 4 -- Polynomials

    4.1 Integer Exponents
    The laws of exponents require practice and memorization. Turn back to this section later to practice again. Practice until the rules are completely memorized.
    1 - 40 all

    4.2 Scientific Notation
    1, 2, 4, 5, 7, 8, 9, 10, 13, 14, 17, 18, 19, 21, 23, 24 - 30

    4.3 Polynomials
    Know the terminology from this section.
    1, 2, 4, 5, 6, 8, 9 - 14, 15, 17, 19, 22, 25 - 30, 31, 35

    4.4 Adding and Subtracting Polynomials
    You must be especially careful when subtracting polynomials.
    1, 2, 7, 8, 10, 14, 16, 17, 19, 20

    4.5 Multiplying and Dividing with Monomials
    1, 2, 4, 5, 7, 8, 9, 10 - 12, 14, 17, 19, 20

    4.6 Multiplying Polynomials
    You must master this section for success in chapter 5. Be sure you understand and can perform the FOIL method.
    1 - 8, 10, 11, 15 - 17, 19 - 23

    Chapter Review
    1 - 48

    Chapter 4 Sample Exam (see "Using Sample Exams" in the Chapter 1 section above)
    Sample Exam problems come from these sections:

          Problem          Comes From Section Number    
          Number          and Key Idea:    
    1, 2 4.1 C
    3 4.1 A
    4 4.1 C
    5 4.1 A
    6 4.1 C
    7, 8 4.1 D
    9, 10 4.2 A
    11, 12, 13 4.2 B
    14, 15 4.3 A
    16 4.3 B
    17, 18 4.3 C
    19 4.4 A
    20 4.4 B
    21 4.4 A & 4.4 B
    22 4.5 A
    23 4.5 B
    24, 25 4.5 C
    26, 27, 28 4.6 A
    29 4.6 B


    For a similar list of information about the actual test questions, see Math 103 Test Information




    Cumulative Test B -- covering Chapters 3 & 4

    Now that you have mastered Units 03 and 04, the next test you must take is Cumulative Test B.

    Remember a cumulative test may only be taken once and the score you receive is used when computing your course grade.

    Prepare thoroughly. In addition to your review of chapters 3 and 4 and their sample exams, a review worksheet for Cumulative Test B is available in the Math Learning Center, 1-112 Wilson Hall.

    Don't forget to pick up your Free Testing Coupon.




    Chapter 5 -- Factoring Polynomials

    You must master Factoring in Chapter 5 for success in Chapter 6.

    5.1 Common Factors
    You should begin each factoring problem by first asking, "Is there a greatest common factor?"
    1, 2, 4, 7, 9 - 13, 15, 16 - 23, 25, 27 - 29, 31, 34, 35, 38

    5.2 Factoring Trinomials
    1 - 8, 10 - 12, 14 - 18, 22, 25, 26, 28, 31, 33 - 35

    5.3 Factoring Binomials
    Be able to recognize the perfect squares listed at the bottom of page 238.
    1, 2, 4, 5, 7, 9, 11, 12, 14, 16, 18, 20 - 22, 24, 25, 27 - 29, 32

    5.4 Solving Problems Using Factoring
    When solving, always write the equation so that one side equals zero, then factor to solve.
    1 - 8, 10 - 12, 14, 16, 17, 21, 22, 25 - 34

    Chapter Review
    1, 3, 4, 6, 7 - 20, 26, 30 - 36, 39 - 43, 45, 47, 48, 50, 51 - 55

    Chapter 5 Sample Exam (see "Using Sample Exams" in the Chapter 1 section above)
    Sample Exam problems come from these sections:

          Problem          Comes From Section Number    
          Number          and Key Idea:    
    1, 2 5.1 A
    3, 4 5.1 B
    5 5.1 C
    6 5.2 A
    7 5.1 B
    8 5.2 A
    9, 10, 11 5.2 C
    12, 13 5.2 B
    14 5.2 C
    15 5.1 B & 5.1 C
    16 5.3 B
    17, 18, 19 5.3 A
    20, 21 5.3 B
    22 5.3 A
    23 5.2 C & 5.3 B
    24 5.4 A
    25, 26, 27, 28, 29, 30 5.4 B
    31, 32, 33 5.4 C


    For a similar list of information about the actual test questions, see Math 103 Test Information




    Chapter 6 -- Rational Expressions and Equations

    6.1 Simplifying Rational Expressions
    Notice: you have two tasks to do - find the restrictions and simplify.
    1 - 5, 8, 9, 13 - 17, 19, 20
    Note - on problems 8, 13 - 15, & 17 you will factor out a (-1) as shown in Example 4 (a) and (b) - read the paragraph above Example 4 on page 264 and look over that whole example carefully. This is a very important skill.

    6.2 Multiplying and Dividing Rational Expressions
    2, 3, 6, 7, 10 - 12, 15 - 17, 19, 20

    6.3 Adding and Subtracting Rational Expressions
    1 - 5, 9 - 13, 17 - 21, 24, 25, 29, 31 - 33, 36

    6.4 Solving Rational Equations
    Note: there is a big difference between adding/subtracting rational expressions (no equal sign) and solving a rational equation (has an equal sign). Be sure you can keep the problems straight. Review the comparison on page 286.
    1, 2, 5 - 7, 12, 13, 15 - 19, 22, 24, 26, 27, 31 - 33

    6.5 Applications Using Rational Equations
    2, 4, 7, 10, 12 (Ratio Problems); 14 - 16, 20, 21, 23 (Work Problems)

    6.6 Direct and Inverse Variation
    Be sure to memorize these two formulas.
    1 - 6, 11, 12, 16 - 20

    Chapter Review
    1, 3, 4, 6, 7, 9, 12, 13, 16, 17, 18, 21, 22, 24, 25, 28, 30 - 36, 37 - 40, 42 - 46

    Chapter 6 Sample Exam (see "Using Sample Exams" in the Chapter 1 section above)
    Sample exam problems come from these sections:

          Problem          Comes From Section Number    
          Number          and Key Idea:    
    1 6.1 A
    2, 3 6.1 B
    4, 5 6.2 A
    6 6.2 B
    7, 8 6.3 A
    9, 10 6.3 B
    11, 12, 13, 14 6.3 C
    15, 16, 17, 18, 19, 20 6.4 A
    21 6.5 A
    22, 23 6.5 B
    24, 25 6.6 A
    26 6.6 B


    For a similar list of information about the actual test questions, see Math 103 Test Information




    Cumulative Test C -- covering Chapters 5 & 6

    Now that you have mastered Units 05 and 06, the next test you must take is Cumulative Test C.

    Remember a cumulative test may only be taken once and the score you receive is used when computing your course grade.

    Prepare thoroughly. In addition to your review of chapters 5 and 6 and their sample exams, a review worksheet for Cumulative Test C is available in the Math Learning Center, 1-112 Wilson Hall.

    Don't forget your Free Testing Coupon.




    Chapter 7 -- Square Roots and Radicals

    7.1 Introduction to Square Roots
    1 - 8 (be sure you understand the difference between exact form and approximate form), 9 - 15, 19, 20 (notice if you are finding the principal root, the negative root, or both), 21 - 32 (study Example 3 on pages 316 - 317 for a discussion on replacement values)

    7.2 Multiply and Divide Square Roots
    1, 3, 4, 7 - 11, 13 - 18, 19 - 24, 25 - 30, 32, 33, 36 - 43, 49, 50

    7.3 Addition and Subtraction of Square Roots
    Notice it is necessary to have like terms before adding or subtracting.
    1 - 5, 9 - 13, 16 - 18, 23, 28, 30

    7.4 Solving Equations with Square Roots
    There are two types of problems here; pay attention to the difference. In the first type, the variable is not under the square root symbol. In the second type, the variable IS under the square root symbol. If the variable was originally under a square root symbol you MUST check your answer(s) in the original equation.
    1 - 17, 20, 22

    7.5 Using Square Roots
    Memorize the Pythagorean Theorem; it will not be given on the exam. The distance formula and quadratic formula WILL be given on the exam if needed.
    1, 2, 4, 5, 9, 12 - 16, 17, 18, 20, 23, 24

    Chapter Review
    1 - 8, 9 - 12, 16, 17, 19, 21, 23, 25, 26, 28, 29, 30, 32, 35, 36, 37, 41, 42, 43, 46, 47, 49, 50, 52 - 59

    Chapter 7 Sample Exam (see "Using Sample Exams" in the Chapter 1 section above)
    Sample Exam problems come from these sections:

          Problem          Comes From Section Number    
          Number          and Key Idea:    
    1, 2 7.1 A
    3, 4 7.1 B
    5, 6 7.2 A
    7, 8, 9, 10 7.2 B
    11 7.2 C
    12 7.2 C & 7.2 D
    13, 14, 15, 16 7.3 A
    17, 18 7.4 A
    19, 20, 21 7.4 B
    22, 23, 24 7.5 A
    25 7.5 B
    26 7.5 C


    For a similar list of information about the actual test questions, see Math 103 Test Information




    The FINAL -- covering all chapters, with extra emphasis on Chapter 7

    Now that you have mastered Unit 07, the only thing left is the final. Hooray!

    Remember that the final may be taken twice if you allow time. If you take it twice, the higher score is the one that counts. The score you receive is doubled so the final carries twice as much weight in your course grade as a cumulative test or your attendance. You should take this test very seriously and study carefully. Don't wait till the last day (noon on the Wed. of finals week is your last chance); leave enough time for a second try.

    In addition to your review of all the chapters and their sample exams, a review worksheet for the Final is available in the Math Learning Center, 1-112 Wilson Hall.