Algebra Practice. Dr. Barbara Sandall, Ed.D., and Travis Olson, M.S.
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1 By Dr. Brr Sndll, Ed.D., Dr. Melfried Olson, Ed.D., nd Trvis Olson, M.S. COPYRIGHT 2006 Mrk Twin Medi, Inc. ISBN Printing No EB Mrk Twin Medi, Inc., Pulishers Distriuted y Crson-Dellos Pulishing Compny, Inc. The purchse of this ook entitles the uyer to reproduce the student pges for clssroom use only. Other permissions my e otined y writing Mrk Twin Medi, Inc., Pulishers. This product hs een correlted to stte, ntionl, nd Cndin provincil stndrds. Visit to serch nd view its correltions to your stndrds. All rights reserved. Printed in the United Sttes of Americ.
2 Tle of Contents Tle of Contents Introduction to the Mth Prctice Series...iv Common Mthemtics Symols nd Terms...1 Alger Rules...6 Chpter 1: Review of Numer Systems...7 Rel Numers...7 Checking Progress: Numer Systems...10 Chpter 2: Review of Properties of Numers...11 Properties of Numers Identity, Commuttive, Inverse, Distriutive...11 Checking Progress: Properties Identity, Commuttive, Inverse, Distriutive Chpter 3: Exponents nd Exponentil Expressions...17 Exponents...17 Comining Terms Multipliction nd Division; evluting Exponentil Expressions...19 Rising to Power nd Negtive Exponents...22 Checking Progress: Exponents nd Exponentil Expressions...25 Chpter 4: Roots nd Rdicl Expressions...26 Squre, Cue, nd Higher Roots nd Negtive Rdicls...26 Simplifying Rdicl Expressions...29 Frctionl Roots nd Rdicl Expressions...36 Checking Progress: Roots nd Rdicl Expressions...38 Chpter 5: Opertions...39 Opertions on Algeric expressions...39 Checking Progress: Opertions on Algeric Expressions...44 Chpter 6: Equtions nd Prolem Solving...45 Equtions Liner, Qudrtic, Polynomil...45 Checking Progress: Equtions Liner, Qudrtic, Polynomil...56 Chpter 7: Grphing...57 The Crtesin Coordinte System...57 Checking Progress: Grphing With the Crtesin Coordinte System...60 Chpter 8: Functions...61 Functions Tles, Grphs, Nottion...61 Checking Progress: Functions Tles, Grphs, Nottion...66 iii
3 Tle of Contents Tle of Contents (cont.) Chpter 9: Liner Functions...67 Stndrd Form, Grphing, Slope, nd Writing Equtions for Line...67 Checking Progress: Stndrd Form, Grphing, Slope, nd Writing Equtions for Line...74 Chpter 10: Qudrtic Functions...75 Stndrd Form, Grphing Qudrtic Functions...75 Checking Progress: Qudrtic Functions...81 Check-Up Prolems...82 Numer Systems...82 Properties...83 Exponents nd Exponentil Expressions...84 Roots nd Rdicl Expressions...85 Opertions on Algeric Expressions...86 Equtions nd Prolem Solving...87 Grphing...88 Functions...89 Liner Functions...91 Qudrtic Functions...92 Answer Keys...93 Prctice Answer Keys...93 Check-Up Answer Keys References iv
4 Chpter 1: Review of Numer Systems Chpter 1: Review of Numer Systems Bsic Overview: Rel Numers Rel numers re comintion of ll the numer systems. Rel numers include nturl numers, whole numers, integers, rtionl numers, nd irrtionl numers. Exmples of rel numers could e ny numer. Summry of Numers Rel Numers Comintion of ll the numer systems Includes these susets Rtionl Numers Cn e expressed s the rtio of two whole numers Irrtionl Numers Cnnot e expressed s rtio Includes the suset of Integers Nturl numers, their opposites or negtive numers, nd zero Includes the suset of Whole Numers Nturl numers plus zero Includes the suset of Nturl Numers Sometimes clled counting numers Exmples of Numer Systems Rel Numers Rel numers mke up ll of the numers represented y the mrks with numers nd ll of the points in etween the mrks. Rememer tht the rrows indicte tht this numer line goes on into infinity or forever in oth directions
5 Nme: Dte: Chpter 1: Review of Numer Systems Chpter 1: Review of Numer Systems (cont.) Prctice: Numer Systems Directions: Using the words listed elow, fill in the lnks with the correct numer type(s). Rel Numer Rtionl Numer Integer Whole Numer Irrtionl Numer 1.!s ( 7 ) π
6 Nme: Dte: Chpter 1: Review of Numer Systems Chpter 1: Review of Numer Systems (cont.) π 4π Tq Qu Chllenge Prolems: Numer Systems Directions: Find vlues for nd such tht: is n integer. is undefined. is irrtionl is zero. is rtionl numer ut not n integer. 9
7 Nme: Dte: Chpter 1: Review of Numer Systems Chpter 1: Review of Numer Systems (cont.) Checking Progress: Numer Systems Directions: Using the words listed elow, fill in the lnks with the correct numer type(s). Rel Numer Rtionl Numer Integer Whole Numer Irrtionl Numer Numer Type or Types π 5π 45π
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