[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-463359-105":59,"doc-detail-463359-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","math-111-exam-1-review","Math 111 - Exam 1 review","","Math 111 Exam 1 review sheet providing practice and self-testing problems focused on set operations, algebraic manipulation, and function-like transformations. Exercises include finding intersections and unions in interval notation, simplifying expressions to lowest terms, performing indicated operations with algebraic simplification, factoring completely, and converting expressions to simple fractions. Additional coverage evaluates exponential and radical expressions, rationalizes denominators, and includes an answer key for selected problems.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/math-111-exam-1-review/463359/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/math-111-exam-1-review/463359.png","ImageObject",300,407,{"name":92,"@type":93},"Rizky","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-04","2026-09-30",true,{"@type":102,"interactionType":103,"userInteractionCount":81},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What topics are covered in the Math 111 Exam 1 review exercises?","Question",{"text":112,"@type":113},"The review covers set operations with intervals, algebraic operations and simplification, factoring completely, fractions in lowest terms, evaluating exponents, working with radicals, and rationalizing denominators.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How should answers be written for the set interval problems?",{"text":117,"@type":113},"Answers for interval notation problems must be expressed in interval notation, including union results when applicable.",{"name":119,"@type":110,"acceptedAnswer":120},"Are solutions provided for the practice problems?",{"text":121,"@type":113},"Yes. The document includes an ANSWERS section listing the responses for the corresponding problems.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},463359,1790766459,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":81,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":81,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":129,"read_time":39,"preview_page_count":4},962085564807,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","MATH 111  \nExam 1 review  \nThe following are review exercises for the Math 111 first exam. These exercises are provided for you to practice or test yourself for readiness for the first exam.  \n1. Given A = {x | −3 \u003C x ≤ 7}, B = {x | x ≥ 5}, C = {x | x > 10} find the following and express your answer using interval notation.  \n(a)A ∩ B (b) A ∪ C (c) A ∩ C  \n2. Perform the indicated operation and express your answer in simplest form. x − 3 x2 − x − 2 3x + 9 3 2  \n(a) (8x + 4) ÷ ~~ ~~ (b) ~~ ~~ · ~~ ~~ (c) ~~ ~~ − ~~  ~~2x2 − 5x − 3 x + 3 2x + 2 5x2 y 3xy2  \n 3x   5   x − 2   3   \n(d) x2 − 9 + 2x3 − 6x2 (e) 3x2 − 12x − x2 − 8x + 16  \n3. Perform the indicated operation and simplify.  \n(a) 􀀐− 2x2 y 􀀑 2 􀀐 2xy3 􀀑 3 (b) 􀀐 2x2~~ ~~yxy43 􀀑 2 􀀐 3xy62 􀀑 3 (c) 􀀐 25 a6 b4 􀀑􀀐 ~~ ~~10ab43 􀀑  \n4. Perform the indicated operation and express your answer in simplest form with positive exponents only.  \n(a) ~~ ~~1(1aabcc)−21~~ ~~ (b) ~~ ~~15m325m−22~~ ~~n−41 !−3 (c) ~~ ~~􀀐x~~ ~~1/2y~~ ~~1/3􀀑~~ ~~−2xyx/41/3y~~ ~~1/4􀀑~~ ~~−12  \n5. Factor completely.  \n(a) 6n2 + 5n − 4 (b) y 2 + 9 − 6y − 4x2 (c) 81y4 − 256 (d) 64x3 − 125  \n(e) 3y(y − 2)2 + (y − 2) (f) y 2/3 − 4y1/3 + 3 (g) 2x(x2 + 1)−1/3 + (x2 + 1)2/3  \n6. Express the following as a simple fraction reduced to lowest terms.  \n(a)  \n3x2 y  \n 2ab   \n9x  \n16a2  \n(b)  \n5  \nx + y  \n5  \nx − y  \n(c)  \n2x2 − 3x − 2  \nx2 − 1  \n2x2 + 5x + 2 x2 + x − 2  \n7. Evaluate each of the following.  \n(a) 8−4/3 (b) −243−4/5  \n8. Perform the indicated operation and express your answer in simplest radical form.  \n(a) √ 12 √ 75 (b) 3 √ 8 − 5 √ 32 + 2 √ 27 (c) √12a3 b9 (d) √3 20ab5 √3 50b4 (e) 􀀐4a √10b􀀑􀀐 3b √2a􀀑 (f) ~~ ~~a13a4b2b5~~ ~~ (g) 2b2 √48a7 b6 − 5a √27a5 b 10  \n9. Rationalize the denominator.  \n 3x   5xy   \n(a) (b)    \n√4y  p3 x2 y  \nANSWERS  \n1a) [5 , 7] 1b) (−3, 7] ∪ (10 , ∞ ) 1c) ϕ  \n2a) 4(2x + 1)2  2b) ~~ ~~3(x~~ ~~2) 2c) ~~ ~~9y15−x210y2x 2d) ~~ ~~26x2x(3x53x)~~ ~~(+x~~ ~~3)  \nx2 − 15x + 8  \n2e)  \n3x(x − 4)2  \n3a) 32x7 y 11 3b) ~~ ~~x5~~ ~~y24~~ ~~ 3c) 4a9 11a2 b 125p3 1  \n4a) ~~ ~~ 4b) ~~ ~~ 4c) ~~ ~~  \nc 27m15 n6 x6 y47/12  \n5a) (2n − 1)(3n + 4) 5b) (y − 3 − 2x)(y − 3 + 2x) 5c) (9y2 + 16)(3y − 4)(3y + 4)  \n5d) (4x − 5)(16x2 + 20x + 25) 5e) (y − 2)(3y2 − 6y + 1) 5f) (y1/3 − 3)(y1/3 − 1) 5g) (x2 + 1)−1/3(x + 1)2  \n8axy   x − y   x − 2  \n6a) 6b) 6c)  \n3b x + y x + 1  \n 1   1   \n7a) 7b) −  \n16 81  \n8a) 30 8b) −14 √2 + 6 √3 8c) 2ab4 √3ab 8d) 10b3 √3 a 8e) 24ab √5ab 8f) ~~ ~~a3b~~ ~~ 8g) −7a3 b5 √3a  \n9a) ~~ ~~3x2√yy~~ ~~ 9b) 5 p3 xy 2","cbCaivtsPGbxqrw6","https://ap.wps.com/l/cbCaivtsPGbxqrw6","pdf",107069,"English","# Set and Interval Notation\n# Algebraic Operations and Simplification\n## Factoring\n## Rational Expressions and Fractions\n## Exponents and Radicals\n# Rationalizing Denominators\n# Answers","[{\"question\":\"What topics are covered in the Math 111 Exam 1 review exercises?\",\"answer\":\"The review covers set operations with intervals, algebraic operations and simplification, factoring completely, fractions in lowest terms, evaluating exponents, working with radicals, and rationalizing denominators.\"},{\"question\":\"How should answers be written for the set interval problems?\",\"answer\":\"Answers for interval notation problems must be expressed in interval notation, including union results when applicable.\"},{\"question\":\"Are solutions provided for the practice problems?\",\"answer\":\"Yes. The document includes an ANSWERS section listing the responses for the corresponding problems.\"}]","Math 111 - Exam 1 review | PDF"]