[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-143297-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-143297-en":131},{"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","day-4-question-set","Day 4 - Question set","","This problem set focuses on core academic math skills, combining geometry, algebra, equations, and word problems. It includes right-triangle side-length calculations, mean and sequence analysis, systems of equations with parameters and infinite solutions, root-sum/product problems, and area problems for circles, semicircles, and triangles within given boundaries. Real-world contexts appear through a leak water-tank rate model and a ticket sales revenue breakdown, requiring equation setup and solving.",{"@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/day-4-question-set/143297/",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/day-4-question-set/143297.png","ImageObject",300,407,{"name":42,"@type":43},"Aurora","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-20","2026-08-25",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",13,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What types of mathematics topics are included in the Day 4 question set?","Question",{"text":63,"@type":64},"The set covers geometry (triangles, circles, semicircles), algebra (means, sequences), systems of equations, and absolute value/root problems, plus word problems that require modeling real situations.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How is the water-tank leak problem framed?",{"text":68,"@type":64},"The tank starts full with 1500 gallons and loses 5 gallons per week. The question asks for the number of weeks until the tank is half full, which requires setting up a linear equation.",{"name":70,"@type":61,"acceptedAnswer":71},"What do Q3 and its system of equations ask for?",{"text":72,"@type":64},"Q3 presents a system where w is a constant and states the system has infinitely many solutions. The task is to determine the value of w that makes the system consistent.","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},143297,1787694280,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,115,120,123,127],{"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":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},7,"Healthcare",40,"healthcare",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":112,"show_sort_weight":113,"slug":114},8,"Research & Report",30,"research-report",{"id":116,"doc_module":4,"doc_module_name":25,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":25,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":25,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":25,"category_name":129,"show_sort_weight":96,"slug":130},19,"General","general",{"code":4,"msg":82,"data":132},{"doc_id":79,"user_id":133,"nickname":42,"user_avatar":134,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":140,"language":141,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":12,"update_tm":80,"read_time":145},4810365810221,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","# Day 4 . Question set.\n\nQ1 . Given a right triangle with one leg (base) of 6 cm andthehypotenuse of 10 cm, find the length of the other leg.  \nQ2 . If the numbers in a certain data set are 4 , 8 , 20, 25 and 32,what is the mean?  \nQ3 . In the given system of equations, w is a constant. The systemhas infinitely many solutions . What is the value ofw?  \n45x + 33y − 200 = −3592wx + 11y = −53  \nQ4 . Find the sum of the roots of the equation: √3 x − x = 0  \nQ5 . What is the area of the circle inscribed in an equilateraltriangle with side length of 12  \nQ6 . Find m ⋅ n inthe following system of equations:  \n–4n = –9m + 85n = –8m–10  \nQ7 . A water tank develops a leak. Each week, the tank  \nloses 5 gallons of water due to the leak. Initially, the tank is full andcontains 1500 gallons . After how many weeks will the tank be half-full?  \nQ8 . Find the product of solutions to the equation: ∣ 2x − 2∣ = x + 1  \nQ9 . A carnival receives $10 for each adult admission ticket sold and$5 for each child admission sold. On a particular day, the carnivalreceived a total of $4, 100 from selling adult and child admissiontickets . If 220 adult admission tickets were sold on that day, howmany child tickets were sold?  \nQ10 . Scarlett bought an ant farm with 80 ants . If from the followingweek forward the ant population tripled, when (week) will it reach  \nQ11 . 2 + lg √ 1 + x + 3 lg √ 1 − x = lg √ 1 − x2Solve the equation for x. (Note that lga = log 10 a )  \nQ12 . Using the information in the given image, find the area of the  \nsemicircle .  \nQ13 . Find the sum of the solutions to the equation:  \n∣x2 − 4∣ = x + 2  \nQ14 . The sum of the first three terms of a geometric sequence isequal to 4242 . The sum of the squares ofthe same terms is equalto 1092 . Find the first three terms of the sequence .  \nQ15 . Find the area of the colored region.  \nQ16 . A rectangular garden should be twice as wide as itis long. Ifthe fenced area is greater than 98 m2 , what can we say about thewidth of the garden?  \nQ17 . How many solutions does the following equation have?  \n x x − 3  \n2  \n−   =  \nx + 3  \n 18 x2 − 9  \nQ18 . Find the area of the blue triangle .  \n9  \nQ19 . Find the radius of the circle .  \n5  \n6  \n5  \nQ20 . Work out the area of the pink triangle .  \nQ21 . The triangle bounded by the lines y = 0 , y = 2xandy=−0 . 5x+k, with k positive, is equal to 80 square units .Find k.  \nQ22 . Determine the value of x.  \nQ23 . Given a semicircle . Calculate the area of the blue region.","cbCaimyy21serw1K","https://ap.wps.com/l/cbCaimyy21serw1K","pdf",553999,14,"English","# Question set\n## Geometry\n## Algebra and Equations\n## Word Problems","[{\"question\":\"What types of mathematics topics are included in the Day 4 question set?\",\"answer\":\"The set covers geometry (triangles, circles, semicircles), algebra (means, sequences), systems of equations, and absolute value/root problems, plus word problems that require modeling real situations.\"},{\"question\":\"How is the water-tank leak problem framed?\",\"answer\":\"The tank starts full with 1500 gallons and loses 5 gallons per week. The question asks for the number of weeks until the tank is half full, which requires setting up a linear equation.\"},{\"question\":\"What do Q3 and its system of equations ask for?\",\"answer\":\"Q3 presents a system where w is a constant and states the system has infinitely many solutions. The task is to determine the value of w that makes the system consistent.\"}]","Day 4 - Question set | PDF",35]