# Section 6.10: Review for Chapter 6

Studying for a chapter examination is a personal process, one which nobody else can do for you. Simply take the time to review what you have done.

Here are the new terms in Chapter 6.

Algebra [6.1]
Binomial [6.1]
Binomial theorem [6.1]
Cell [6.3]
Common factor [6.2]
Comparison property [6.5]
Completely factored [6.2]
Consecutive integers [6.6]
Degree of a term [6.1]
Degree of a polynomial [6.1]
Difference of squares [6.6]
Division property [6.4]
Equation [6.4]
Equation properties [6.4]
Equivalent equations [6.4]
Evaluate an expression [6.3]
Expand [6.1]
Factor [6.2]
FOIL [6.1]
Inequality [6.5]
Inequality symbols [6.5]
Like terms [6.1]
Linear [6.1]
Linear equation [6.4]
Monomial [6.1]
Multiplication property [6.4]
Multiplication property of inequality [6.5]
Multiplicity [6.4]
Numerical coefficient [6.1]
Percent [6.8]
Percent problem [6.8]
Polynomial [6.1]
Property of proportions [6.7]
Proportion [6.7]
Ratio [6.7]
Replication [6.3]
Root [6.4]
Satisfy [6.4]
Similar terms [6.1]
Simplify [6.1]
Solution [6.4]
Solve a proportion [6.7]
Solve an inequality [6.5]
Solve an equation [6.4]
Substitution property [6.6]
Subtraction property [6.4]
Symmetric property of equality [6.4]
Term [6.1]
Trinomial [6.1]
Zero-product rule [6.4]

If you can describe the term, read on to the next one; if you cannot, then look it up in the text (the section number is shown in brackets).

IMPORTANT IDEAS
Can you explain each of these important ideas in your own words?

Binomial product (FOIL) [6.1]
Binomial theorem [6.1]
Procedure for factoring trinomials [6.2]
Difference of squares [6.2]
Evaluate an expression [6.3]
Equation properties [6.4]
Zero-product rule [6.4]
Linear inequalities [6.5]comparison property [6.5]addition property of inequality [6.5]positive Multiplication property of inequality [6.5]negative multiplication property of inequality [6.5]
Procedure for problem solving [6.6]
Property of proportions [6.7]
Procedure for solving proportions [6.7]
Change forms: fraction/decimal/percent [6.8]
Be able to estimate answers to percent problems [6.8]
Solve applied percent problems [6.8]
Guidelines for problem solving [6.9]

Problem-solving examples:
genetics [6.3]
linear inequalities [6.5]
number relationships [6.6.]
distance relationships [6.6]
Pythagorean theorem applications [6.6]
proportion problems [6.7]
percent problems [6.8]

Next, make sure you understand the types of problems in Chapter 6.

TYPES OF PROBLEMS
Simplify an algebraic expression. [6.1]
Multiply binomials mentally. [6.1]
Expand a binomial using the binomial theorem. [6.1]
Factor a polynomial. [6.1]
Evaluate an algebraic expression. [6.3]
Write spreadsheet expressions in ordinary algebraic notation. [6.3]
Use a spreadsheet to evaluate (including the replicate command). [6.3]
Use binomials to answer genetic applications. [6.3]
Solve equations (both linear and quadratic). [6.4]
Use a calculator to solve an equation. [6.4]
Solve linear inequalities. [6.5]
Solve applied problems; in particular, those involving number, distance, and Pythagorean
relationships. [6.6]
Set up and simplify ratios. [6.7]
Compare the size of fractions, decimals, and radicals. [6.7]
Solve proportion problems. [6.7]
Be able to change forms: fractions/decimals/percents. [6.8]
Estimate percents. [6.8]
Solve applied percent problems. [6.8]
Be able to change forms: fractions/decimals/percents. [6.8]
Estimate percents. [6.8]
Solve applied percent problems. [6.8]
Use problem-solving methods to answer uncategorized questions. [6.8]

Once again, see if you can verbalize (to yourself) how to do each of the listed types of problems. Work all of Chapter 6 Review Questions (whether they are assigned or not).

Work through all of the problems before looking at the answers, and then correct each of the problems. The entire solution is shown in the answer section at the back of the text. If you worked the problem correctly, move on to the next problem, but if you did not work it correctly (or you did not know what to do), look back in the chapter to study the procedure, or ask your instructor. Finally, go back over the homework problems you have been assigned. If you worked a problem correctly, move on the next problem, but if you missed it on your homework, then you should look back in the text or talk to your instructor about how to work the problem. If you follow these steps, you should be successful with your review of this chapter.

We give all of the answers to the Chapter Review questions (not just the odd-numbered questions), so be sure to check your work with the answers as you prepare for an examination.