[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-144049-105":59,"doc-detail-144049-en":131},{"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":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","wuit-math-test-8-april-2009-solutions","WUIT Math Test - 8 April 2009 - Solutions","","WIUT Math Test (8 April 2009) provides fully worked solutions to six algebra, geometry, and finance-style questions. Topics include solving cubic equations by factoring, simplifying algebraic expressions to a constant, calculating yearly planting and monthly cleaning costs for a garden split into shaded and unshaded regions, and computing triangle area formed by two intersecting lines with the x-axis. Additional problems determine angles using parallel-line and isosceles/angle-sum relationships, and compute the total savings after annual salary increases with a fixed saving fraction over 10 years.",{"@graph":69,"@context":123},[70,84,106],{"@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/wuit-math-test-8-april-2009-solutions/144049/",{"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/wuit-math-test-8-april-2009-solutions/144049.png","ImageObject",300,407,{"name":92,"@type":93},"Seraphina","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-24","2026-08-25",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",17,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How do you solve Question 1’s equation x^3 - x^2 - 20x = 0?","Question",{"text":113,"@type":114},"Factor out x and reduce to a quadratic. Compute the quadratic roots using the discriminant, giving x = 0, x = 5, and x = -4 as the solutions stated in the answer.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What is the yearly cost in Question 3 for keeping the garden?",{"text":118,"@type":114},"Calculate planting cost from the shaded area times 10,000 Uzbek soom per square meter, then compute monthly cleaning cost for the white area using 1,000 per square meter. Multiply the monthly cleaning by 12 and add the one-time planting, resulting in 10,400,000 soom per year.",{"name":120,"@type":111,"acceptedAnswer":121},"How are the angles found in Question 6?",{"text":122,"@type":114},"Use parallel-line angle relationships and angle sums in triangles. For part (a), derive angles via supplementary angles and triangle angle sum to get ∠EFG = 20°. For part (b), set equal angles using HI = HK and HJ = JI, then solve 3x = 120° and convert to ∠IHK = 100°.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},144049,1787698098,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":14,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":130,"read_time":24},962075114101,"https://ap-avatar.wpscdn.com/avatar/e000253a75eb197efd?x-image-process=image/resize,m_fixed,w_180,h_180&k=1780044092746381165","WIUT Math Test  \n8 April 2009  \nQuestion 1  \nSolve x3 – x2 – 20x = 0. Sxlux2onx−: 20) = 0  \n1) x = 0; 2) x 2 − x − 20 = 0  \nD = (−1)2 − 4 ⋅1⋅ (− 20) = 1 + 80 = 81  \nx 1  \n− (−1) +=  \n2 ⋅1  \n81 1 + 9  \n= = 5 ; 2  \n− (−1) − 81 1 − 9  \nx = = = −4 .  \n2  \n2 ⋅1 2  \nAnswer: x = – 4; x = 0 or x = 5.  \nQuestion 2  \na 2 − a − 2  \nSimplify A = ~~ ~~a2~~ ~~−25a230 × ~~ ~~(a~~ ~~−~~ ~~2a(a1+~~ ~~4)  \na 2 + 5a  \nSolution:  \na 2 − a − 2  \nA = ~~ ~~a2~~ ~~−25a230 × ~~ ~~(a~~ ~~−a2a2(a15+a~~ ~~4) = ~~ ~~a2~~ ~~−25a230 × ~~ (~~aa~~ ~~−2~~)~~24~~)~~ : ~~ ~~a~~ ~~a2~~ ~~~~ ~~15a = ~~ ~~a2~~ ~~−25a230 × ~~ (~~aa~~ ~~−2~~)~~−+24~~)~~ × ~~ ~~a~~ ~~2a~~ ~~~~ ~~51a == a(a~~(~~55a)(~~)~~a~~(~~54a)~~)~~ × ~~ (~~(aa−22~~)~~)~~(~~(aa14)~~)~~ × ~~ ~~a~~ ~~15) = a5−5a = −~~ ~~5(5−−aa~~ ~~) = −1 .  \nAnswer: A = – 1.  \nQuestion 3  \nA 30x30 meter garden is split into 9 equal squares as shown. The shaded areas are planted with flowers, at a cost of 10,000 Uzbek soom per square meter. The white areas are cleaned up every month at a cost of 1,000 Uzbek soom per square meter. If planting happens only once a year, and cleaning every month, what is theyearly cost of keeping the garden?  \nSolution:  \n10  \n10  \n10  \n10 10 10  \nYearly cost = Planting cost + Cleaning cost  \nPlanting cost = Shaded Area x Unit cost = 12 ⋅ 20 ⋅ 20 x 10,000 = 200 x 10,000 = 2,000,000 . Cleaning cost = 12 x White area x Unit cost = 12 x (Full area – Shaded area) x 1,000 == 12 x (30x30 – 200) x 1,000 = 12 x 700 x 1,000 = 8,400,000 .  \nYearly cost = 2,000,000 + 8,400,000 = 10,400,000 .  \nAnswer: The garden costs 10,400,000 soom per year  \nQuestion 4  \nDraw the lines y = 3x + 4 and y = 4x + 3 showing clearly the point where they meet and work out the area of the triangle formed between these two lines and the x-axis.  \nSolution:  \ny = 3x + 4  \nx = 0 => y = 3 .0 + 4 = 4 => (0, 4)  \ny = 0 => 0 = 3x + 4 => x = – 4/3 => A (– 4/3, 0)  \ny = 4x + 3  \nx = 0 => y = 4 .0 + 3 = 3 => (0, 3)  \ny = 0 => 0 = 4x + 3 => x = – 3/4 => B (– 3/4, 0)  \n⎧y  \n⎨  \n⎩y  \n= 3x + 4  \n⇒ 3x + 4 = 4x + 3 =>= 4x + 3  \nx = 1, y = 3. 1 + 4 = 7 => C (1, 7)  \nS = S − S =  1 AD ⋅ CD −  1  BD ⋅ CD =  \nABC ACD BCD 2 2  \n= 12 ⋅ ⎜1 − ⎜ − ~~ ~~43⎟⎟ ⋅ 7 − ~~ ~~12 ⋅ ⎜ 1 − ⎜⎛⎝ − ~~ ~~34⎟⎟ ⋅ 7 =  \n49 49 49 1  \n= ~~ ~~ − ~~ ~~ = ~~ ~~ = 4 ~~ ~~ .  \n6 8 12 12  \nAnswer: 4 ~~ ~~112 .  \nQuestion 5  \nA person is employed at a salary of £18,000 (eighteen thousand pounds) per year, to be increased by £1,800 a year at the end of each year. He saves one quarter of his salary every year. Find the total saved at the end of 10 years.  \nSolution:  \n18,000, 19,800, ... a1 = 18000 , d = 1800  \na10 = a1 + 9d = 18000 + 9 ⋅1800 = 18000 +16200 = 34200 S10 = a1~~ ~~a10~~ ~~ ⋅10 = 18000~~ ~~+2~~ ~~34200 ⋅10 = 52200 ⋅ 5 = 261,000  \n14 S10 = 14 ⋅ 261,000 = 65,250 . Answer: 65,250 .  \nQuestion 6  \nFind a) the angle ∠EFG if AB is parallel to CD,  \nand b) the angle ∠IHK if HI = HK, HJ = JI and ∠JHK = 60° .  \na) b)  \nSolution: a) ∠ FMP = FKG = 60o ; ∠ FPM = 180o – ∠ BPF = 180o – 80o = 100o ;  \nFor ΔFMP : 60o + 100o + ∠ MFP = 180o => ∠ MFP = 20o = ∠ EFG.  \nb) HI = HK => ∠ HIJ = ∠ HKJ = x; HJ = JI => ∠ HIJ = ∠ JHI = x  \nFor ΔHIK : x + x + (x + 60o) = 180o => 3x = 120o => x = 40o => ∠ IHK = 40o + 60o = 100o.  \nAnswer: a) ∠EFG = 20o and b) ∠IHK = 100o","cbCairx3vsX9TL34","https://ap.wps.com/l/cbCairx3vsX9TL34","pdf",49241,"English","# Question 1\n## Solving a cubic equation\n# Question 2\n## Simplifying an algebraic expression\n# Question 3\n## Yearly cost for planting and monthly cleaning\n# Question 4\n## Area of a triangle between lines and the x-axis\n# Question 5\n## Total savings over 10 years with salary growth\n# Question 6\n## Finding angles with parallel lines and isosceles conditions","[{\"question\":\"How do you solve Question 1’s equation x^3 - x^2 - 20x = 0?\",\"answer\":\"Factor out x and reduce to a quadratic. Compute the quadratic roots using the discriminant, giving x = 0, x = 5, and x = -4 as the solutions stated in the answer.\"},{\"question\":\"What is the yearly cost in Question 3 for keeping the garden?\",\"answer\":\"Calculate planting cost from the shaded area times 10,000 Uzbek soom per square meter, then compute monthly cleaning cost for the white area using 1,000 per square meter. Multiply the monthly cleaning by 12 and add the one-time planting, resulting in 10,400,000 soom per year.\"},{\"question\":\"How are the angles found in Question 6?\",\"answer\":\"Use parallel-line angle relationships and angle sums in triangles. For part (a), derive angles via supplementary angles and triangle angle sum to get ∠EFG = 20°. For part (b), set equal angles using HI = HK and HJ = JI, then solve 3x = 120° and convert to ∠IHK = 100°.\"}]","WUIT Math Test - 8 April 2009 - Solutions | PDF"]