Concept 1: Before the Course
1. To be motivated to complete a course, it is helpful to have a very clear reason for taking the course. List
your goals for taking this course.
2. Budgeting enough time to do homework and to study for a class is one of the most important steps to
success in a class. Use the weekly calendar to help you plan your time for your studies this week. Also write other obligations such as the time required for your job, for your family, for sleeping, and for eating. Be realistic when estimating the time for each activity.
Time Mon. Tues. Wed. Thurs. Fri. Sat. Sun. 7–8 8–9 9–10 10–11 11–12 12–1 1–2 2–3 3–4 4–5 5–6 6–7 7–8 8–9 9–10
3. Taking 12 credit hours is the equivalent of a full-time job. Often students try to work too many hours while
taking classes at school.
a. Write down how many hours you work per week and the number of credit hours you are taking this term.
number of hours worked per week _______________ number of credit hours this term _______________
b. The next table gives a recommended limit to the number of hours you should work for the number of
credit hours you are taking at school. (Keep in mind that other responsibilities in your life such as your family might also make it necessary to limit your hours at work even more.) How do your numbers from part (a) compare to those in the table? Are you working too many hours?
4. It is important to establish a place where you can study—someplace that has few distractions and is readily
available. Answer the questions about the space that you have chosen.
a. Is there enough room to spread out books and paper to do homework? b. Is this space available anytime?
c. Are there any distractions? Can you be interrupted?
d. Is the furniture appropriate for studying? That is, is there a comfortable chair and good lighting? 5. Organization is an important ingredient to success. A calendar or pocket planner is a valuable resource for
keeping track of assignments and test dates. Write the date of the first test in this class.
Number of Maximum number of
credit hours hours of work per week
3 40
6 30
9 20
12 10
Concept 2: During the Course
6. Taking notes can help in many ways. Good notes provide examples for reference as you do your
homework. Also, taking notes keeps your mind on track during the lecture and helps make you an active listener. Here are some tips to help you take better notes in class.
a. In your next math class, take notes by drawing a vertical line about of the way
across the paper as shown. On the left side, write down what your instructor puts on the board or overhead. On the right side, make your own comments about important words, procedures, or questions that you have.
b. Revisit your notes as soon as possible after class to fill in the missing parts that
you recall from lecture but did not have time to write down.
c. Be sure that you label each page with the date, chapter, section, and topic. This
will make it easier to study from when you study for a test.
7. Many instructors use a variety of styles to accommodate all types of learners. From
the following list, try to identify the type of learner that best describes you.
Auditory Learner Do you learn best by listening to your instructor’s lectures? Do you tape the lecture so that you can listen to it as many times as you need? Do you talk aloud when doing homework or study for a test?
Visual Learner Do you learn best by seeing problems worked out on the board? Do you understand better if there is a picture or illustration accompanying the problem? Do you take notes in class?
Tactile Learner Do you learn best with hands-on projects? Do you prefer having some sort of physical objects to manipulate? Do you prefer to move around the classroom in a lab situation?
Concept 3: Preparation for Exams
8. When taking a test, go through the test and work all the problems that you know first. Then go back and
work on the problems that were more difficult. Give yourself a time limit for each problem (maybe 3 to 5 minutes the first time through the test). Circle the importance of each statement.
not somewhat very important important important
a. Read through the entire test first. 1 2 3
b. If time allows, go back and check 1 2 3
each problem.
c. Write out all steps instead of doing the 1 2 3
work in your head.
9. One way to lessen test anxiety is to feel prepared for the exam. Check the ways that you think might be
helpful in preparing for a test.
Do the chapter test in the text.
Get in a study group with your peers and go over the major topics. Write your own pretest.
Use the online component that goes with your textbook.
Write an outline of the major topics. Then find an example for each topic.
Make flash cards with a definition, property, or rule on one side and an example on the other. Re-read your notes that you took in class.
Write down the definitions of all key terms introduced in the chapter.
3 4
1. Basic Definitions
The study of algebra involves many of the operations and procedures used in arith- metic. Therefore, we begin this text by reviewing the basic operations of addition, subtraction, multiplication, and division on fractions and mixed numbers.
In day-to-day life, the numbers we use for counting are the natural numbers: and
the whole numbers: .
Whole numbers are used to count the number of whole units in a quantity. A frac- tion is used to express part of a whole unit. If a child gains , the child has gained two whole pounds plus a portion of a pound. To express the additional half pound mathematically, we may use the fraction,12.
212 lb
0, 1, 2, 3, . . . 1, 2, 3, 4, . . .
10. The following list gives symptoms of math anxiety.
• Experiencing loss of sleep and worrying about an upcoming exam. • Mind becoming blank when answering a question or taking a test. • Becoming nervous about asking questions in class.
• Experiencing anxiety that interferes with studying.
• Being afraid or embarrassed to let the instructor see your work. • Becoming physically ill during a test.
• Having sweaty palms or shaking hands when asked a math question.
Have you experienced any of these symptoms? If so, how many and how often?
11. If you think that you have math anxiety, read the following list for some possible solutions. Check the
activities that you can realistically try to help you overcome this problem. Read a book on math anxiety.
Search the Web for help tips on handling math anxiety. See a counselor to discuss your anxiety.
See your instructor to inform him or her about your situation.
Evaluate your time management to see if you are trying to do too much. Then adjust your schedule accordingly.
Concept 4: Where to Go for Help
12. Does your college offer free tutoring? If so, write down the room number and the hours of the tutoring center. 13. Does your instructor have office hours? If so, write down your professor’s office number and office hours. 14. Is there a supplement to your text? If so, find out its price and where you can get it.
15. Find out how to access the online tutoring available with this text.
Section R.2
Fractions
Concepts
1. Basic Definitions 2. Prime Factorization 3. Simplifying Fractions to Lowest Terms 4. Multiplying Fractions 5. Dividing Fractions 6. Adding and SubtractingFractions
The denominator of a fraction indicates how many equal parts divide the whole. The numerator indicates how many parts are being represented. For instance, suppose Jack wants to plant carrots in of a rectangular garden. He can divide the garden into five equal parts and use two of the parts for carrots (Figure R-1).
2 5
5 equal parts
2 parts
Figure R-1
The shaded region represents of the garden.25