[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-143394-105":59,"doc-detail-143394-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","hard-math-questions-from-august-2025-exam","HARD Math Questions from August 2025 Exam","","A set of challenging multiple-choice math problems covering a range of topics including linear functions, geometry of similar solids and triangles, angle relationships with parallel lines, and systems based on similarity. It also includes word problems involving pricing and revenue, percent and volume composition with water displacement, trigonometric identities, and algebraic equations with radicals and parameters. Each question requires selecting the correct option and computing exact values or expressions.",{"@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/hard-math-questions-from-august-2025-exam/143394/",{"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/hard-math-questions-from-august-2025-exam/143394.png","ImageObject",300,407,{"name":92,"@type":93},"Hazel","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-20","2026-08-25",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",23,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What math topics are covered in these August 2025 hard problems?","Question",{"text":113,"@type":114},"The problems span linear functions, similarity in triangles and solids, angle calculations with parallel lines, trigonometric identities, and algebra with radicals and parameters.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"Are the questions mostly multiple-choice?",{"text":118,"@type":114},"Yes. Each problem is presented with answer choices labeled A, B, C, and D.",{"name":120,"@type":111,"acceptedAnswer":121},"How can I approach a question involving similar solids’ surface area and volume?",{"text":122,"@type":114},"Use the similarity ratio: surface areas scale with the square of the linear factor, volumes scale with the cube. From the given surface areas you can find the linear factor, then compute the target volume(s).","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},143394,1787694876,{"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":19,"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":52},137441390410,"https://ap-avatar.wpscdn.com/avatar/2000252f4ab5702993?_k=1776741390130283984","# HARD Math Questions from August 2025 Exam\n\nMade by Abdulboriy-Telegram:@satmathclub800  \n1.  \nThe function fis defined by  \nf(x)=ax-b,where a and b are constants.In the xy-plane,the graph of y=f(x)passes through thepoints(c,5)and(2c,13),where cis a constant.Which of the following could be the value of b?  \nA.77  \nB.16  \nC.132  \nD.142  \nL  \n2.  \nIn quadrilateral KLMN shown,KL=3,LM=3,KN=27,and MN=27.Diagonals KM and LN(not shown)intersect at point G(not shown),where GK=1and GM=1.If the length of diagonal LNis √p+√w,wherep and w are integers,what is the value of p+w?  \n3.  \nThe table shows the volume of two similar solids,right circular cylinder A and right circular cylinder B.Theradius of right circular cylinder A is 2 units.The surface area of right circular cylinder A is kπ square units,and the surface area ofaright circular cylinder B is nπ square units,where k and n are constants.What isthe value of n-k?(The surface area of a right circular cylinder with radius rand height h is 2πr²+2πrh.)  \nRight circular cylinder A  \nVolume:32π  \nRight circular cylinder B  \nVolume:864π  \n800  \n2  \n4.  \nA line intersects two parallel lines,forming four acute angles and four obtuse angles.The measure of oneof the acute angles is (9w-650)°.The sum of the measures of one of the acute angles and three of theobtuse angles is (-18w+w)°.What is the value of w?  \nathclub8(  \n5.  \nA company developed a plan to set the selling price of a product.The company determined that for aselling price of $120.00,zero products would be sold.For each $1.50 decrease in the selling price,thenumber of products sold would increase by one.For a revenue of exactly $1,966.50,which of thefollowing could be the number of products sold?frevenue =price×number of products sold)  \n@satma  \nA.23  \nB.40  \nC.1,231  \nD.2,400  \n6.  \nOn a plot of land,48.0%of the square footage is farmland and the remaining square footage is pasture.There are buildings on exactly 28.5%of the square footage of the farmland,and there are buildings onexactly 11.0%of the square footage of the pasture.If there are buildings on exactly p%of the squarefootage of the plot of land,what is the value of p?  \n@satma  \n68  \n7.  \nRight rectangular prism Xis similar to right rectangular prism Y.The surface area of right rectangularprism Xis 58 square centimeters(cm²),and the surface area of right rectangular prism Yis 1,450 cm².The volume of right rectangular prism Yis 1,500 cubic centimeters(cm³).What is the sum of the volumes,in cm³,of right rectangular prism Xand right rectangular prism Y?  \nnathclub800  \n8.  \nIn the figure,a hollow steel pipe is in the shape of a right circular cylingder.The steel pipe has an outside @satmdiameter of 48 inches,a wall thickness ofP/inches,and a height of 144 inches.Which of the following isclosest to theolume,in cubic inches,of the wall of this steel pipe?  \nA.177  \nB.565  \nC.2,160  \nD.13,395  \n9.  \n△QPRis similar to △STR.The lengths represented by ST,QP,PR,and QR in the figure are 17,21,28,and  \n35,respectively.What is the length of SR?  \n@satm  \nAB  \nC.  \n10.  \nIn the figure,triangle ABF is congruent to triangle EDG,where B coresponds to D.The measure of angleDCFis 58°.What is the measure,in degrees,of angle ABF?  \nA.29  \nB.32  \nC.58sD.61  \n800  \n11.  \nAn ice cube is floating in water.The portion of the ice cube below the water's surface has a volume of  \n12.28 cubic centimeters and makes up 91.67%of the total volume of the ice cube.What is the volume,incubic centimeters,of the portion of the ice cube above the water's surface?  \n12.  \nFor two acute angles A and B,cos A-sin B=0.The measure of angle A is x degrees,where 8*sin(2x-  \n13)=321.What is the measure of angle Bin degrees?  \n@satma  \n13.  \nIn the given equation,cis a constant.A solution to the equation is k+7√2,where kis an integer.What isthe value of c?  \nx(x-18)=C  \nA.98  \nB.17  \nC.9  \nD.-67  \n14.a  \nWhich of the following equations is equivalent to the given equation,where b is a positive constant?y=4x²-bx-5@sat","cbCaidMz9CELpsm8","https://ap.wps.com/l/cbCaidMz9CELpsm8","pdf",1160868,"English","# Practice Questions\n## Functions and Equations\n## Geometry and Similarity\n## Angles and Trigonometry\n## Percent and Volume Word Problems","[{\"question\":\"What math topics are covered in these August 2025 hard problems?\",\"answer\":\"The problems span linear functions, similarity in triangles and solids, angle calculations with parallel lines, trigonometric identities, and algebra with radicals and parameters.\"},{\"question\":\"Are the questions mostly multiple-choice?\",\"answer\":\"Yes. Each problem is presented with answer choices labeled A, B, C, and D.\"},{\"question\":\"How can I approach a question involving similar solids’ surface area and volume?\",\"answer\":\"Use the similarity ratio: surface areas scale with the square of the linear factor, volumes scale with the cube. From the given surface areas you can find the linear factor, then compute the target volume(s).\"}]","HARD Math Questions from August 2025 Exam | PDF"]