[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-437076-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-437076-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","practice-problems-in-algebra-trigonometry-and-analytic-geometry","PRACTICE PROBLEMS IN ALGEBRA, TRIGONOMETRY, AND ANALYTIC GEOMETRY","","Mathematics placement examination practice problems targeting Algebra, Trigonometry, and Analytic Geometry. The document explains that the provided problems help students identify weak subject areas before taking the NJIT placement exam and notes that not all incoming students are expected to solve every exercise. It emphasizes correct problem-solving across equation solving, factoring, graphing, logarithms, systems of equations, polynomial division, and fundamentals of slopes and intercepts. Calculators are not permitted.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/practice-problems-in-algebra-trigonometry-and-analytic-geometry/437076/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/practice-problems-in-algebra-trigonometry-and-analytic-geometry/437076.png","ImageObject",300,407,{"name":42,"@type":43},"Grenda","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-22","2026-09-29",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",6,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What is the purpose of these practice problems?","Question",{"text":63,"@type":64},"They help students identify which subject areas need attention when preparing for the Mathematics Placement Examination.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"Which topics does the placement examination cover?",{"text":68,"@type":64},"The exam covers Algebra, Trigonometry, and Analytic Geometry.",{"name":70,"@type":61,"acceptedAnswer":71},"Are calculators allowed on the placement exam?",{"text":72,"@type":64},"No. The document states that the use of calculators is not permitted on the placement exam.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},437076,1790764122,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,104,109,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":93,"slug":94},70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":101,"show_sort_weight":102,"slug":103},"Technology",50,"technology",{"id":105,"doc_module":4,"doc_module_name":25,"category_name":106,"show_sort_weight":107,"slug":108},7,"Healthcare",40,"healthcare",{"id":110,"doc_module":4,"doc_module_name":25,"category_name":111,"show_sort_weight":112,"slug":113},8,"Research & Report",30,"research-report",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":96,"slug":129},19,"General","general",{"code":4,"msg":82,"data":131},{"doc_id":79,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":105,"language":139,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":12,"update_tm":143,"read_time":144},7971474921005,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","PRACTICE PROBLEMS IN ALGEBRA, TRIGONOMETRY, AND ANALYTIC GEOMETRY  \nThe accompanying problems from the subjects covered on the Mathematics Placement Examination can be used by students to identify subject areas that need attention in preparation for the examination. The examination covers the subjects of Algebra, Trigonometry, and Analytic Geometry which students traditionally learn in high school. It is not expected that all incoming students can work all of the following exercises. The placement examination is used to determine what preparatory courses, if any, are needed to be successful at NJIT. THE USE OF CALCULATORS ISNOT PERMITTED ON THE PLACEMENT EXAM .  \n1. Evaluate È25 􀁢 \"%% .  \n\\#Þ Expand (x ~~\"~~​\\# 􀁢 C ~~\"~~​\\# Ñ\\# .  \n$Þ Combine into a single fraction and simplify: B\" 􀁣 B$􀁢\" .  \n%Þ Combine into a single fraction and simplify: B~~\\#~~􀁢$ 􀁢 Ð~~􀁢~~$Ñ~~\"~~​\\#B .  \n&Þ Solve for x: B$ 􀁣 'B \\# 􀁣 \\#(B œ !  \n'Þ Write and simplify as a fraction without negative exponents: BB\\#\"$~~\\#~~3\\# .(Þ Simplify: B~~\\#􀁢\\# ~~~~ ~~B~~\"􀁢\\# ~~ .  \n)Þ Solve for x: 􀁣 2x\\# 􀁣 )B 􀁢 \" œ !.  \nIn Problems 9,10, and 11, solve for x and check your answers in the original equation:  \n9. B􀁢 È\"\\#B 􀁢\\#& œ 􀁣$\"!Þ B 􀁢 \\# 􀁣 ÈB œ %\"\"Þ B 􀁣 $ œ 􀁣 È\\#& 􀁣 \"\\#B\"2. Solve for y: ~~\"~~​C œ  􀁣 $& .  \n13. Combine into a single fraction  􀁢 $, 􀁣 ~~'~~​-  \nIn Problems 14,15, and 16, P91 will refer to P91 \"! , that is Log to the base 10.  \n14. Solve for x: Ð Log BÑ œ \\#  \n\"&Þ Solve for x: ÐP91BÑ\\# 􀁢 P91ÐB $ Ñ 􀁢 \\# œ !\"'Þ Evaluate numerically: Log 5 + Log 2  \n17. Express the solutions for x as Logarithms: \"!\\#B 􀁣 &Ð\"! BÑ 􀁢 ' œ !.\")+ÑÞ Simplify: (x$ Ñ\\# .  \n\"),ÑÞ Write as a power of x: ÈÐB$ ÑB\\#  .  \nIn problems 19, 20, and 21, write the given expression in the form: +ÐB 􀁢 ,Ñ\\# 􀁢 - , giving the values ofa, b and c.  \n\"* . B\\# 􀁣 %B 􀁢 & 20. 3x\\# 􀁢&B􀁣\\#\\#\"Þ %B 􀁣 B\\# 􀁢 &  \nIn problems 22 and 23, describe the set ofall x which satisfy the given inequality:  \n22. ¸ \\#B 􀁢 & ¸ 􀁿 $\\#$ . ¸ 􀁣 $B 􀁢 \" ¸ 􀂀 &  \n\\#% . Write the expression in terms of Log x +8. Log(x-1): P91Ð ~~ ~~ÈBB\" Ñ .  \n25. Solve for x: ~~ ~~ 􀁣 \\#Ð*BÑ œ !\\#'Þ Solve for x: ~~ ~~ 􀁣 %B\\# œ !\\#( . Solve for x: 􀁣 \\# 􀁢 \\#ÐB$Ñ\\# œ !\\#) . Solve for x: P91\"! ÐB 􀁣 \\#Ñ œ \"  \n\\#*Þ Solve for x: ~~ ~~\\#BÐB\\#~~ ~~􀁣BÑ~~\"~~​$~~ ~~Ð\\#B􀁣\"Ñ 􀁢 ÐB \\# 􀁣 BÑ ~~\\#~~$ œ !; x Á !$!. Factor and simplify: [x\\# 􀁢 $B 􀁣 \"!Ó $\\# .  \n$\"Þ Evaluate and simplify the given expression when B œ 9: x ~~\"~~​\\# 􀁣 B $\\# .  \n$\\#Þ Simplify: B~~ ~~􀁣B$%~~\"~~​B~~\"\\#~~$\"!  \n$$Þ Simplify: B~~  ~~$\"'~~ ~~BB$%~~\"~~​)B~~ ~~􀁣~~ ~~\"'  \nFor problems 34-37, sketch the graph of the function and find the coordinates of the intercepts (if any) with the x and y axes:  \n34. C œ ÐB 􀁢 \\#Ñ\\# 􀁢 \"$&Þ C œ B\\# 􀁣 %B $'Þ B œ %C \\# 􀁣 $C $(Þ B\\# œ * 􀁣 C \\#  \n38. Evaluate-9=Ð2E\u003C->+8Ð$% ÑÑ .  \n$* . Use the quadratic formula to find the roots of 5x\\# 􀁣 \"$B 􀁢 ' œ ! and then write the expression 5x\\# 􀁣 \"$B 􀁢 ' in factored form Þ  \n%!Þ Given the fact that one root of the given polynomial is B œ \\#ß Completely factor it. 2x$ 􀁣 ~~\"\"~~​$ B\\# 􀁣 B 􀁢 ~~\\#~~$  \n%\"Þ Find the roots of the equation: 2x\\# 􀁢 ~~\"~~​$ B 􀁣 ~~\"~~​$ œ !.  \n42. Divide 2x$ 􀁣 ~~\"\"~~​$ B\\# 􀁣 B 􀁢 ~~\\#~~$ by ÐB 􀁣 \\#Ñ .  \n%$Þ Find the equation of the line Ðin C œ 7B 􀁢 , formÑ through Ð 􀁣 %ß \"Ñ with slope = 􀁣 ~~\"~~​&  \n%%Þ Find the equation of the line (in C œ 7B 􀁢 , form) with x-intercept = $ andy-intercept = 5.  \n%&Þ Solve the system of equations: C œ 􀁣 ~~\"~~​&B 􀁢 ~~\"~~​&  \nB œ C \\# 􀁣 'C 􀁢 \"  \n%'. Find the equation of the line (in C œ 7B 􀁢 , formÑ through the point Ð 􀁣 2ß 5Ñ with an angle of inclination of 45 degrees.  \n47. Find the equation of the line Ðin C œ 7B 􀁢 , formÑ through the point Ð 􀁣 \"ß $Ñ with an angle of inclination of \"\\#0 degrees.  \n48. Find the equation of the line Ðin C œ 7B 􀁢 , formÑ through the point Ð\"ß 􀁣 ~~)~~$Ñ and the point Ð 􀁣 \\#ß ~~\"~~​$ Ñ .  \n%* . Use polynomial division to simplify: B$$~~ ~~B\\#\\#􀁢􀁢~~ )~~$  \n&!Þ Expand and simplify: ÐB È& 􀁢 C È\\# ÑÐB È& 􀁣 C È\\# Ñ .  \n&\"Þ Expand ( È\\# B 􀁣 &Ñ\\# .  \n&\\#Þ Find and ","cbCaienoAxjS4Mx8","https://ap.wps.com/l/cbCaienoAxjS4Mx8","pdf",48888,"English","# Practice problems\n## Algebra problem set\n## Trigonometry problem set\n## Analytic geometry problem set","[{\"question\":\"What is the purpose of these practice problems?\",\"answer\":\"They help students identify which subject areas need attention when preparing for the Mathematics Placement Examination.\"},{\"question\":\"Which topics does the placement examination cover?\",\"answer\":\"The exam covers Algebra, Trigonometry, and Analytic Geometry.\"},{\"question\":\"Are calculators allowed on the placement exam?\",\"answer\":\"No. The document states that the use of calculators is not permitted on the placement exam.\"}]","PRACTICE PROBLEMS IN ALGEBRA, TRIGONOMETRY, AND ANALYTIC GEOMETRY | PDF",1790680108,18]