[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-571858-105":53,"doc-detail-571858-en":126},{"code":4,"msg":5,"data":6},0,"success",[7,14,19,24,29,34,39,44,49],{"id":8,"doc_module":9,"doc_module_name":10,"category_name":11,"show_sort_weight":12,"slug":13},11,1,"Template","Presentations",90,"presentations",{"id":15,"doc_module":9,"doc_module_name":10,"category_name":16,"show_sort_weight":17,"slug":18},12,"Resumes",80,"resumes",{"id":20,"doc_module":9,"doc_module_name":10,"category_name":21,"show_sort_weight":22,"slug":23},14,"Invoices",70,"invoices",{"id":25,"doc_module":9,"doc_module_name":10,"category_name":26,"show_sort_weight":27,"slug":28},15,"Posters",60,"posters",{"id":30,"doc_module":9,"doc_module_name":10,"category_name":31,"show_sort_weight":32,"slug":33},16,"Social Media",50,"social-media",{"id":35,"doc_module":9,"doc_module_name":10,"category_name":36,"show_sort_weight":37,"slug":38},17,"Forms",40,"forms",{"id":40,"doc_module":9,"doc_module_name":10,"category_name":41,"show_sort_weight":42,"slug":43},18,"Letters",30,"letters",{"id":45,"doc_module":9,"doc_module_name":10,"category_name":46,"show_sort_weight":47,"slug":48},21,"Paper Templates",5,"papers-templates",{"id":50,"doc_module":9,"doc_module_name":10,"category_name":51,"show_sort_weight":4,"slug":52},158,"General","general-158",{"code":4,"msg":54,"data":55},"ok",{"site_id":56,"language":57,"slug":58,"title":59,"keywords":60,"description":61,"schema_data":62,"social_meta":119,"head_meta":121,"extra_data":123,"updated_unix":125},105,"en","algebra-cheat-sheet-basic-properties-facts","Algebra Cheat Sheet Basic Properties & Facts","","Algebra Cheat Sheet compiles core formulas and facts for arithmetic operations, exponents, inequalities, absolute value, distance, and complex numbers. It summarizes logarithm definitions, special logs, domain rules, and key logarithm properties, followed by essential factoring identities and solution methods such as the quadratic formula and square-root property. It also covers completing the square, function types and graph forms (lines, slopes, parabolas, circles, ellipses, hyperbolas), and common algebraic errors with reasons and corrections.",{"@graph":63,"@context":118},[64,80,101],{"@type":65,"itemListElement":66},"BreadcrumbList",[67,71,74,77],{"item":68,"name":69,"@type":70,"position":9},"https://docshare.wps.com","Home","ListItem",{"item":72,"name":10,"@type":70,"position":73},"https://docshare.wps.com/template/",2,{"item":75,"name":46,"@type":70,"position":76},"https://docshare.wps.com/template/paper-templates/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/algebra-cheat-sheet-basic-properties-facts/571858/",4,{"url":78,"name":59,"@type":81,"image":82,"author":87,"headline":59,"publisher":90,"fileFormat":93,"inLanguage":57,"description":61,"dateModified":94,"datePublished":95,"encodingFormat":93,"isAccessibleForFree":96,"interactionStatistic":97},"DigitalDocument",{"url":83,"@type":84,"width":85,"height":86},"https://docshare.wps.com/thumbnails/algebra-cheat-sheet-basic-properties-facts/571858.png","ImageObject",442,249,{"name":88,"@type":89},"Levi","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-10-15","2026-10-13",true,{"@type":98,"interactionType":99,"userInteractionCount":9},"InteractionCounter",{"@type":100},"ViewAction",{"@type":102,"mainEntity":103},"FAQPage",[104,110,114],{"name":105,"@type":106,"acceptedAnswer":107},"What are the basic exponent and inequality properties included in the cheat sheet?","Question",{"text":108,"@type":109},"The sheet lists exponent rules such as combining exponents and basic power identities, along with inequality translation rules when adding or subtracting the same quantity on both sides, and inequality directions when multiplying by positive vs. negative values.","Answer",{"name":111,"@type":106,"acceptedAnswer":112},"Which logarithm definition and core properties are summarized?",{"text":113,"@type":109},"It defines logb x via the equivalence x = by, includes special logarithms like natural log and common log, states the domain x > 0, and provides product/quotient and exponent-related log rules such as logb(xy) and logb(x^r).",{"name":115,"@type":106,"acceptedAnswer":116},"What methods are provided for solving quadratic equations?",{"text":117,"@type":109},"The sheet provides factoring formulas, the quadratic formula for ax^2 + bx + c = 0, and a completing-the-square workflow example, including square root property guidance for extracting solutions.","https://schema.org",{"og:url":78,"og:type":120,"og:title":59,"og:site_name":91,"og:description":61},"article",{"robots":122,"canonical":78},"index,follow",{"doc_id":124,"site_id":56},571858,1792053444,{"code":4,"msg":5,"data":127},{"doc_id":124,"user_id":128,"nickname":88,"user_avatar":129,"doc_module":9,"category_id":45,"category_name":46,"doc_title":59,"doc_description":61,"doc_content":130,"file_id":131,"file_url":132,"file_type":133,"file_size":134,"view_count":9,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":73,"language":135,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":136,"faqs":137,"seo_title":138,"seo_description":61,"update_tm":139,"read_time":9},7971461740909,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","Algebra Cheat Sheet Basic Properties & Facts \nArithmetic Operations \nab + ac = a (b + c) \nÊÁË ~~ ~~ab~~ ~~ ˆ¯˜ = a c bc \na c ad + bc ~~ ~~ + ~~ ~~ = ~~ ~~b d bd \na-b b-a ~~ ~~ = ~~ ~~c-d d-c \nab~~ ~~+a~~ ~~ac = b + c, a 􀂹 0 \nExponent Properties \nn m n+m \na a = a \nProperties of Inequalities \nIf a \u003C b then a + c \u003C b + c and a-c \u003C b-c If a \u003C b and c > 0 then ac \u003C bc and a \u003C bc c \nIf a \u003C b and c \u003C 0 then ac > bc and a > bc c \nProperties of Absolute Value \nÏa \na = ÌÓ-a \na 􀂳 0 \nab = ab \nifa 􀂳 0 \nif a \u003C 0 \na + b £ a + b Triangle Inequality \nDistance Formula \nIf P1 = ( x1, y1 ) and P2 = ( x2 , y2 ) are two points the distance between them is \n( )m \nn nm \na = a \na0 = 1, a 􀂹 0 d (P1 , P2 ) = \n( x2-x1 )2 + (y2-y1 )2 \nComplex Numbers \ni = -1 i2 = -1 -a = i, a 􀂳 0 \n( a + bi) + ( c + di) = a + c + ( b + d) i \n( a + bi)- (c + di) = a-c + ( b-d) i ( a + bi)( c + di) = ac-bd + (ad + bc) i ( a + bi)( a-bi) = a2 + b2 \na + bi = a2 + b2 Complex Modulus \n( a + bi) = a-bi Complex Conjugate \n( a + bi) ( a + bi) = a + bi2 \nFor a complete set of online Algebra notes visit [http://tutorial.math.lamar.edu](http://tutorial.math.lamar.edu). © 2005 Paul Dawkins \nLogarithms and Log Properties \nDefinition \ny = logb x is equivalent to x = by \nExample \nlog5 125 = 3 because 53 = 125 \nSpecial Logarithms \nln x = log e x natural log log x = log10 x common log where e = 2.718281828K \nLogarithm Properties logb b = 1 logb 1 = 0 logb bx = x blog b x = x logb ( x r) = r logb x \nlogb ( xy) = logb x + logb y logb ÊÁ ~~ ~~x~~ ~~ ˆ˜ = logb x-logb y \nË y ¯ \nThe domain of logb x is x > 0 \nFactoring and Solving \nFactoring Formulas \nx2-a2 = ( x + a) ( x-a ) x2 + 2ax + a2 = ( x + a)2 \nx2-2ax + a2 = ( x-a)2 \nx2 + (a + b) x + ab = (x + a)( x + b) x3 + 3ax2 + 3a2x + a3 = ( x + a )3 \nx3-3ax2 + 3a2x-a3 = ( x-a )3 x3 + a3 = ( x + a) ( x2-ax + a2 ) \nx3-a3 = ( x-a) ( x2 + ax + a2 ) x2n-a2n = ( xn-an)( xn + an) If n is odd then, \nxn-an = ( x-a) ( xn-1 + ax n-2 +L + an-1 ) n n \nx + a \n= ( x + a) ( xn-1-axn-2 + a2xn-3-L + an-1 ) \nQuadratic Formula \nSolve ax2 + bx + c = 0 , a 􀂹 0 \n-b ± b2-4ac x = ~~ ~~ \n2a \nIf b2-4ac > 0 -Two real unequal solns. If b2-4ac = 0 -Repeated real solution. If b2-4ac \u003C 0 -Two complex solutions. \nSquare Root Property \nIf x2 = p then x = ± \nAbsolute Value Equations/Inequalities \nIf b is a positive number \np = b \np \u003C b \np > b \nfi \nfi \nfi \np = -b or-b \u003C p \u003C bp \u003C -b or \np = b \np > b \nCompleting the Square \nSolve 2x2-6x-10 = 0 \n( 1) Divide by the coefficient of the x2 x2-3x-5 = 0 \n(2) Move the constant to the other side. x2-3x = 5 \n(3) Take half the coefficient of x, square it and add it to both sides \nx2-3x + ÁÊË - ~~ ~~32ˆ¯˜2 = 5 + ÁÊË - ~~ ~~32ˆ¯˜2 = 5 + ~~ ~~94 = ~~ ~~294 \n(4) Factor the left side \nÊ ~~ ~~3~~ ~~ ˆ˜2 ~~ ~~29 \nÁËx-2 ¯ = 4 \n(5) Use Square Root Property \n3 29 29 x- ~~ ~~ = ± ~~ ~~ = ± ~~ ~~ \n2 4 2 \n(6) Solve for x \n3 29 x = ± ~~ ~~ \n2 2 \nFor a complete set of online Algebra notes visit [http://tutorial.math.lamar.edu](http://tutorial.math.lamar.edu). © 2005 Paul Dawkins \nFunctions and Graphs \nConstant Function \ny = a or f ( x) = a \nGraph is a horizontal line passing through the point ( 0, a) . \nLine/Linear Function \ny = mx + b or f ( x) = mx + b Graph is a line with point ( 0,b) and slope m. \nSlope \nSlope of the line containing the two points ( x1 , y1 ) and ( x2 , y2 ) is \ny2-y1 rise \nm = = \nx-x run \n2 1 \nSlope – intercept form The equation of the line with slope mandy-intercept ( 0,b) is \ny = mx + b \nPoint – Slope form \nThe equation of the line with slope m \nand passing through the point (x1 , y1 ) is y = y1 + m( x-x1 ) \nParabola/Quadratic Function \ny = a ( x-h)2 + k f ( x) = a ( x-h)2 + k \nThe graph is a parabola that opens up ifa > 0 or down if a \u003C 0 and has a vertex at (h, k ) . \nParabola/Quadratic Function \ny = ax2 + bx + c f (x ) = ax2 + bx + c \nThe graph is a parabola that opens up ifa > 0 or down if a \u003C 0 and has a vertex \nÊ ~~ ","cbCaicz8xYTF05sy","https://ap.wps.com/l/cbCaicz8xYTF05sy","pdf",140621,"English","# Arithmetic Operations\n## Exponent and Inequality Properties\n## Absolute Value and Distance Formula\n# Exponent and Logarithm Properties\n## Logarithm Definition and Domain\n## Logarithm Rules\n# Factoring and Solving\n## Factoring Formulas\n## Quadratic Formula and Completing the Square\n# Functions and Graphs\n## Linear, Parabolic, and Conic Sections\n## Slope and Intercepts\n# Common Algebraic Errors","[{\"question\":\"What are the basic exponent and inequality properties included in the cheat sheet?\",\"answer\":\"The sheet lists exponent rules such as combining exponents and basic power identities, along with inequality translation rules when adding or subtracting the same quantity on both sides, and inequality directions when multiplying by positive vs. negative values.\"},{\"question\":\"Which logarithm definition and core properties are summarized?\",\"answer\":\"It defines logb x via the equivalence x = by, includes special logarithms like natural log and common log, states the domain x \\u003e 0, and provides product/quotient and exponent-related log rules such as logb(xy) and logb(x^r).\"},{\"question\":\"What methods are provided for solving quadratic equations?\",\"answer\":\"The sheet provides factoring formulas, the quadratic formula for ax^2 + bx + c = 0, and a completing-the-square workflow example, including square root property guidance for extracting solutions.\"}]","Algebra Cheat Sheet Basic Properties & Facts | PDF",1791924099]