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Problems include solving exponential and radical equations, computing areas of regular polygons and composite figures, analyzing true statements about equation equalities, forming and using profit functions, evaluating polynomial expressions with parameters, and applying function composition with constraints. Additional tasks include solving ratio areas in inscribed shapes and word problems using linear equations based on spending patterns and group cost changes.",{"@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/wiut-01032025-original-examples/143967/",{"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/wiut-01032025-original-examples/143967.png","ImageObject",300,407,{"name":92,"@type":93},"Eden","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-04","2026-08-25",true,{"@type":102,"interactionType":103,"userInteractionCount":44},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What types of math problems are included in this set?","Question",{"text":112,"@type":113},"It includes algebra and equation solving, geometry and area calculations, function evaluation and composition, and modeling of real situations through profit/cost or spending relationships.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"Does the set cover functions and polynomial evaluation?",{"text":117,"@type":113},"Yes. It contains tasks such as finding f(13) from f(x)=2x^2-14x+k and evaluating expressions based on given component functions with domain constraints.",{"name":119,"@type":110,"acceptedAnswer":120},"Are there geometry problems involving polygons and inscribed shapes?",{"text":121,"@type":113},"Yes. It includes computing the area of a regular dodecagon and finding ratios or shaded areas for figures made from squares and triangles inscribed in each other.","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},143967,1787697761,{"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":44,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":14,"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":24},1374391974468,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","Subscribe to our Instagram channels where you can find more useful content:  \n[http://instagram.com/phd_shopulatov](http://instagram.com/phd_shopulatov)  \n[http://instagram.com/shopulatov_math_school](http://instagram.com/shopulatov_math_school)  \n(1) Solve the equation 27􀯫 = 3√􀯫  \n(2) Find the area of regular dodecagon (12 sides, 12 angles)  \n3) Total energy can be found by adding potential energy and kinetical energy. Find total energy if potential energy is~~ ~~−􀯘􀯥2 and kinetic energy is 􀯘22􀯥  \n4) ADEF is a square. ADEF is inscribed inside of right triangle ABC. AC=32AB. Find the ratio of shaded area to area of ABC.  \n5) Which statement is true for the equality: 􀯫~~ ~~29 = 􀯫~~ ~~3 + 􀯫~~ ~~3  \nA) 3 is the only solution  \nB) -3 is the only solution  \nC) 3 and-3 are solutions  \nD) No real solution  \n6) A company sells mobile phones for $200 each. The cost of producing 1 phone is $80 and there is a fixed cost of $800,000 . Find the profit function for this company.  \n7) f(x)=2x2-14x+k, f(11)=50. Find f(13)  \n8) Find 􀯙􀯚((􀯫􀯫)), if 􀝂(􀝔) = 􀝔 3 − 9x and 􀝃 (􀝔) = 􀝔 2 − 2􀝔 − 3. (x>3)  \n9) A man has 2 transportation options to travel to and from university: the subway, which costs $2.75 for a trip, and a taxi, which costs $18.5 per a trip. Over 5 days traveling to and from university he has spent $74.75. How many times did he take taxi?  \n10) A group of friends planned a trip with a total cost of $800, regardless of the number of participants. Initially, there were several people in the group, each expected to pay an equal share of the cost. However, two people decided to cancel, which caused the price for the remaining participants to increase by $20. Find the initial number of people in the group.  \n(11) A rectangle is inscribed inside of a circle. Sides of rectangle are 8 and 6. Find the area of shaded region.  \n12) The roots of the equation ax3 +bx2 +cx+d=0 are-1, -3, 5.  \nWhich of the following expressions is the factor of ax 3 +bx2 +cx+d?  \nA) x+5  \nB) x-3  \nC) x-1","cbCaic5kp2ixJrQE","https://ap.wps.com/l/cbCaic5kp2ixJrQE","pdf",297705,"English","# Problem Set\n## Algebra and Equations\n## Geometry and Area\n## Functions and Composition\n## Modeling and Word Problems","[{\"question\":\"What types of math problems are included in this set?\",\"answer\":\"It includes algebra and equation solving, geometry and area calculations, function evaluation and composition, and modeling of real situations through profit/cost or spending relationships.\"},{\"question\":\"Does the set cover functions and polynomial evaluation?\",\"answer\":\"Yes. It contains tasks such as finding f(13) from f(x)=2x^2-14x+k and evaluating expressions based on given component functions with domain constraints.\"},{\"question\":\"Are there geometry problems involving polygons and inscribed shapes?\",\"answer\":\"Yes. It includes computing the area of a regular dodecagon and finding ratios or shaded areas for figures made from squares and triangles inscribed in each other.\"}]","WIUT 01.03.2025 original examples | PDF"]