[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-143578-105":59,"doc-detail-143578-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","october-prediction-problem-set-practice","October prediction - Problem Set Practice","","A math problem set covering multiple algebra, geometry, and functions topics. The questions estimate population density from area and counts, use trigonometric relationships in triangles, and analyze line systems for infinitely many solutions. Geometry items include a circle inscribed in a square and properties of an isosceles right triangle, plus surface area of a right rectangular prism and a right triangular pyramid. Several number and function questions involve rates, absolute value functions, and identifying minimum values under domain constraints.",{"@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/october-prediction-problem-set-practice/143578/",{"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/october-prediction-problem-set-practice/143578.png","ImageObject",300,407,{"name":92,"@type":93},"Oliver","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",16,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How do you compute population density from a given area and estimated number of muskrats?","Question",{"text":113,"@type":114},"Divide the estimated population by the area in acres, then express the result in muskrats per acre.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What does it mean when a system of two linear equations has infinitely many solutions?",{"text":118,"@type":114},"It means the two lines coincide, so they represent the same line and share all intersection points.",{"name":120,"@type":111,"acceptedAnswer":121},"In the geometry problems, how is the perimeter of a square found when a circle is inscribed in it?",{"text":122,"@type":114},"Use the circle’s radius (from the circle equation) to determine the square’s side length, then compute perimeter as 4 times the side length.","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},143578,1787695838,{"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":34,"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":144},8796095461610,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","@DesmosMastery   @The_HawkMath  \n1. The number of muskrats in a 133-acre area is estimated to be 2,128. What is the estimated population density, in muskrat per acre, of this area?  \nA. 16  \nB. 133  \nC. 149  \nD. 2,144  \n2. In triangles RST and XYZ shown, XY is parallel to TS and tanR = 140/171. What is the value of sinX in triangle XYZ?  \nA. 140/311  \nB. 140/221  \nC. 171/221  \nD. 171/140  \n@DesmosMastery   @The_HawkMath  \n3. The graph of line g is shown in thexy-plane. Line k is defined by 165x+py = w, where p and w are constants. If line k is graphed in this xy-plane, resulting in the graph of a system of two linear equations, the system of two linear equations will have infinitely many solutions. What is the value of p + w?  \nStudent’s Response:  \nx² -4x + y² -8y-80 = 0  \n4. In the xy-plane, the graph of the given equation is a circle. If this circle is inscribed ina square, what is the perimeter of the square?  \nA. 20  \nB. 40  \nC. 80  \nD. 320  \n@DesmosMastery   @The_HawkMath  \n5. The cost of renting a piece of construction equipment for up to 5 days is $270 for the first day and $135 for each additional day. Which of the following equations gives the cost y, in dollars, of renting the equipment for a day, where æ is a positive integer and x≤5?  \nA. y = 135x + 135  \nB. y = 270x-135  \nC. y 270x + 135  \nD. y 135x + 270  \n6. A right triangular pyramid has exactly six edges. Each of these edges is 96 centimeters long. If the surface area of the pyramid is k√3 square centimeters, what is the value of k?  \nStudent’s Response:  \n@DesmosMastery   @The_HawkMath  \n7. The perimeter of an isosceles right triangle is 18 + 18√2 inches. What is the length, in inches, of the hypotenuse of this triangle?  \nA. 9  \nB. 9√2  \nC. 18  \nD. 18√2  \n8. The functions f and g are defined by the given equations below, where x ≥ 0. Which of the following equations displays, as a constant or coefficient, the minimum value of the function it defines, where x ≥ 0?  \nI. f(x) = 18(1.4)x+5  \nII. g(x) = 18(1.16)(1.4)x+3  \nA. I only  \nB. II only  \nC. I and II  \nD. Neither I nor II  \n@DesmosMastery   @The_HawkMath  \n9. The positive number a is 2,352% of the sum of the positive numbers b and c, and b is 84% of c. What percent of b is a?  \nA. 5,152%  \nB. 2,436%  \nC. 51.52%  \nD. 24.36%  \n10. A set designer is hammering nails along the top edge of a wall with a length of 3x feet, where x is an integer, that will be used to hang garland. The designer hammers the first nail at the left edge of the wall. The designer then hammers an additional nail every 3/8 feet along the entire length of the wall, starting from the first nail and with the last nail being hammered at the right edge of the wall. Which equation best represents this situation, where y is the number of nails the designer hammers along the entire length of the wall?  \nA. y = (3/8)x  \nB. y = (3/8)x + 1  \nC. y = 8x  \nD. y = 8x + 1  \n@DesmosMastery   @The_HawkMath  \n11. The function q is defined by q(x) = a|x-9|2-87|x – 9| + b, where a and b are constants, and a > b > 87. If q(639) = h and q(-621) = k, where h and k are constants, what is the value of 9(-639)h-k+ 621(9)k-h?  \nStudent’s Response:  \n12. The functions f and g are defined by the equations shown, where a and b are integer constants, a \u003C b and b \u003C 0. If y = f(x) and y = g(x) are graphed d in the xy-plane, which of the following equations displays, as a constant or coefficient,  \nthey-coordinate of the y intercept of the graph of the corresponding function?  \nI. f(x) = a(3.3)x + b  \nII. g(x)=a(3.3)x + b  \nA. I only  \nB. II only  \nC. I and II  \nD. Neither I nor II  \n@DesmosMastery  @The_HawkMath  \n13. A right rectangular prism has a base area of 28p square centimeters (cm²). The length of the base of the rectangular prism is 12 cm, and the height of the rectangular prism is 4 cm. Which expression represents the surface area, in cm2, of the right rectangular prism?  \nA. (512/3) p  \nB. 224 p/3 + 96  \nC. 56p + 192  \nD. 560p + 96  \nf(x) = ax²+2x+c  \n14. In","cbCaigihbjKeSBu1","https://ap.wps.com/l/cbCaigihbjKeSBu1","pdf",89260,"English","# Practice Problems\n## Algebra and Systems\n## Trigonometry\n## Geometry and Measurement\n## Functions and Absolute Value","[{\"question\":\"How do you compute population density from a given area and estimated number of muskrats?\",\"answer\":\"Divide the estimated population by the area in acres, then express the result in muskrats per acre.\"},{\"question\":\"What does it mean when a system of two linear equations has infinitely many solutions?\",\"answer\":\"It means the two lines coincide, so they represent the same line and share all intersection points.\"},{\"question\":\"In the geometry problems, how is the perimeter of a square found when a circle is inscribed in it?\",\"answer\":\"Use the circle’s radius (from the circle equation) to determine the square’s side length, then compute perimeter as 4 times the side length.\"}]","October prediction - Problem Set Practice | PDF",18]