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Tasks include solving systems for infinite solutions, vector and perpendicularity relationships, finding distances between points, determining shaded areas, and handling standard form with large exponents. The set also includes trigonometric identities, log expressions, and practical modeling through workers’ production rates, tuition payment schedules, savings growth, and optimization of cylinder dimensions using volume and surface material reasoning.",{"@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/azamath-24062025/144003/",{"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/azamath-24062025/144003.png","ImageObject",300,407,{"name":92,"@type":93},"Quinn","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-29","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},"What types of math topics are included in AzaMath 24.06.2025?","Question",{"text":113,"@type":114},"The document includes algebra and equations, logarithms, trigonometry, vectors/perpendicularity, geometry (distance and shaded area), and applied word problems.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"Are there questions that involve solving systems of equations?",{"text":118,"@type":114},"Yes. One question asks for the value at which a system of equations has an infinite number of solutions.",{"name":120,"@type":111,"acceptedAnswer":121},"Does the set include real-life application problems?",{"text":122,"@type":114},"Yes. It contains problems about car price depreciation, changes in rectangle area, worker production rates, education payment schedules, and savings growth over weeks.","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},144003,1787697906,{"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},962075114765,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","WIUT 24.06.2025  \nAzaMath  \n1. If 2􀝔 = 5􀝕 , find 􀯬􀯫~~ ~~ .  \n2. If the width of the rectangle is increased by 20% and the length is decreased by 20%, how much will the area of the figure change?  \n3. Every year the price of a car drops by 15% . If a new car cost $20000, how many years later will the price become $12200?  \n4. Four friends can choose one of four different games. What is the number of ways in which all friends will choose different games?  \n5. At what value of 􀝇 will the system of equations have an infinite number of solutions?  \n{2􀝔4􀝔3􀝕􀝇􀝕612  \n6. Find 􀝔 + 􀝕, if 􀝉1 ||􀝉2 and 􀝉3 is perpendicular to 􀝉1 and 􀝉2.  \n7. Find 􀝔 .  \n8. Find the value of 􀜽 , if 􀝂 (􀝔) = 4􀝔 − 5 and 􀝂 (􀜽) + 1 = 3􀜽 .  \n9. lg(8 − 􀝔) + 2 lg √6 − 􀝔 = 0  \n10. Show in a standard form: 8 ∙ 107 ∙ 2 ∙ 10 −12  \n11. Find a distance between two points 􀜣(−1; −3) and 􀜤 (3; 5) .  \n12. ~~ ~~2~~  2~~ = (􀝔 + 2) −~~ ~~13 (􀯫+2) − 3  \n13. 2􀝔 + 􀝕 is 80% of 5􀝕 . Find 􀯬􀯫~~ ~~ .  \n14. By 7 􀜣􀜯 , 14 of students were at school, then 80 of them entered the school, making 34 of students. How many students were at school?  \n15. 9􀯬 = 27􀳤9−1  \n16. (􀝔 + 2)2 − 6(􀝔 + 2) + 9 = 0  \n17. Find 􀝔 .  \n18. Find the shaded area, if 􀜣(0; 6) and 􀜤 (−6; 0)  \n19. sin 122° cos 32° − sin 32° cos 122°  \n20. log1 (􀝔2 + 􀝔) − log1 (􀝔2 − 􀝔) = −1  \n2 2  \n21. Worker 􀜣 makes a toy in 10 minutes, while Worker 􀜤 makes it in 12 minutes. How many more toys will Worker 􀜣 make than Worker 􀜤 in 5 hours?  \n22. A student must pay $24, 000 for 12 years of education. For the first 6 years, she pays 3 times more than for the second 6 years. How much did she pay for the first year?  \n23. There is a cylinder with a volume of 800 􀝉 3. What is the radius and the height of the cylinder to use the minimum amount of steel required to make such a cylinder?  \n24. The dimensions of the brick are 30 􀜿􀝉 × 40 􀜿􀝉 × 50 􀜿􀝉, with a density of 2 . 8 􀝃/􀜿􀝉3. Find the mass of the brick.  \n25. A person begins to save money. The first week he saved $10, the second week $20, the third week $40, and so on. How much will he have to save in 6 months (week 26)?  \n26. The temperature is set by the function 􀜶 = 4􀯧2 Find the value of 􀝐 , when the temperature 􀯧+2 .  \nequals to zero.  \n27. If the radius of the cylinder is twice the radius of the cone, and the height of the cylinder is half the height of the cone. Find the ratio of the volume of the cylinder to the volume of the cone.  \nНаши социальные сети","cbCaifY3b14bpJTj","https://ap.wps.com/l/cbCaifY3b14bpJTj","pdf",325731,"English","# Questions\n## Algebra and Equations\n## Logs, Trigonometry, and Vectors\n## Geometry and Measurement\n## Word Problems and Applications","[{\"question\":\"What types of math topics are included in AzaMath 24.06.2025?\",\"answer\":\"The document includes algebra and equations, logarithms, trigonometry, vectors/perpendicularity, geometry (distance and shaded area), and applied word problems.\"},{\"question\":\"Are there questions that involve solving systems of equations?\",\"answer\":\"Yes. One question asks for the value at which a system of equations has an infinite number of solutions.\"},{\"question\":\"Does the set include real-life application problems?\",\"answer\":\"Yes. It contains problems about car price depreciation, changes in rectangle area, worker production rates, education payment schedules, and savings growth over weeks.\"}]","AzaMath 24.06.2025 | PDF"]