[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-158598-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-158598-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","psat-89-practice-test-2-answer-explanations","PSAT 8/9 Practice Test #2 - Answer Explanations","","PSAT™ 8/9 Practice Test #2 provides detailed answer explanations for students completing the digital PSAT 8/9 in nondigital format. The material walks through step-by-step reasoning across multiple math questions, including interpreting solutions from linear equation graphs, reading values from models, comparing quantities from bar charts, solving equations with distributive property, evaluating functions, and using inequalities and percent relationships. It also includes guidance for identifying incorrect choices and common conceptual or calculation mistakes.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/psat-89-practice-test-2-answer-explanations/158598/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/psat-89-practice-test-2-answer-explanations/158598.png","ImageObject",300,407,{"name":42,"@type":43},"Mia  ","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-09-11","2026-08-29",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",5,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"How do the explanations determine whether an ordered pair is a solution to a system of equations?","Question",{"text":63,"@type":64},"They check whether the point lies on both lines in the graph. If the lines intersect at that point, the ordered pair is the system’s solution.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"What method is used to solve the equation in Question 4?",{"text":68,"@type":64},"The explanations apply the distributive property on the left-hand side, then perform inverse operations (subtracting and dividing) to isolate x.",{"name":70,"@type":61,"acceptedAnswer":71},"How is a percent question like “21 is 21% of ___” handled?",{"text":72,"@type":64},"They define the unknown as the number that 21% equals 21, set up an equation using percent as a decimal, and solve for the missing value.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},158598,1788005471,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,99,104,109,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":93,"slug":94},70,"exam",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":96,"show_sort_weight":97,"slug":98},"Comic",60,"comic",{"id":100,"doc_module":4,"doc_module_name":25,"category_name":101,"show_sort_weight":102,"slug":103},6,"Technology",50,"technology",{"id":105,"doc_module":4,"doc_module_name":25,"category_name":106,"show_sort_weight":107,"slug":108},7,"Healthcare",40,"healthcare",{"id":110,"doc_module":4,"doc_module_name":25,"category_name":111,"show_sort_weight":112,"slug":113},8,"Research & Report",30,"research-report",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":55,"slug":129},19,"General","general",{"code":4,"msg":82,"data":131},{"doc_id":79,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":139,"language":140,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":12,"update_tm":80,"read_time":144},687207024478,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","PSAT™ 8/9  \nPractice Test \\# 2   \nANSWER EXPLANATIONS  \nThese answer explanations are for students taking the digital PSAT 8/9 in nondigital format.  \n© 2024 College Board. College Board, SAT, and the acorn logo are registered trademarks of College Board.  \nMath  \nModule 1  \n(27 questions)  \nQUESTION 1  \nChoice B is correct. If a point ^x, yh lies on both lines in the graph of a system of two linear equations, the ordered pair ^x, yh is a solution to the system. The graph shown is the graph of a system of two linear equations, where the two lines in the graph intersect at the point ^3, 4h. Therefore, the point ^3, 4h lies on both lines, so the ordered pair ^3, 4h is the solution to the system.  \nChoice A is incorrect. The point ^2, 3h lies on one, not both, of the lines in the graph shown. Choice C is incorrect. The point ^4, 5h lies on one, not both, of the lines in the graph shown. Choice D is incorrect. The point ^5, 6h lies on one, not both, of the lines in the graph shown.  \nQUESTION 2  \nChoice C is correct. It’s given that x represents years after 2010. Therefore, 2010 is represented by x = 0. On the model shown, the point with an x-coordinate of 0 has ay-coordinate of 20,000. Thus, the model estimates that in 2010, the city had 20,000 residents.  \nChoice A is incorrect. This is the value of x that represents the year 2010.  \nChoice B is incorrect and may result from conceptual or calculation errors.  \nChoice D is incorrect. This is approximately the number of residents the model estimates the city had in 2014, not 2010.  \nQUESTION 3  \nChoice B is correct. It’s given that the bar graph shows the number of each typeof monkey in a sanctuary. The bar representing the number of mandrills has a height of 5; therefore, there are 5 mandrills in the sanctuary. The bar representing vervets has a height of 11; therefore, there are 11 vervets in the sanctuary.  \nTherefore, there are 11-5, or 6, more vervets in this sanctuary than mandrills.  \n30 PSAT 8/9 PRACTICE TEST \\#2 ANSWER EXPLANATIONS  \nChoice A is incorrect. This is the number of vervets in the sanctuary. Choice C is incorrect. This is the number of mandrills in the sanctuary. Choice D is incorrect and may result from conceptual or calculation errors.  \nQUESTION 4  \nChoice A is correct. Applying the distributive property on the left-hand side of the given equation yields 3x+5x+20 = 76, or 8x+20 = 76. Subtracting 20 from each side of this equation yields 8x = 56. Dividing each side of this equation by 8 yields x = 7.  \nChoice B is incorrect and may result from conceptual or calculation errors.  \nChoice C is incorrect and may result from conceptual or calculation errors.  \nChoice D is incorrect. This is the solution to the equation x+4 = 76, not 3x+5 ^x+4h = 76.  \nQUESTION 5  \nChoice A is correct. It’s given that f^xh = ~~ ~~1x6. Substituting 17 for x in this function yields f^17h = ~~ ~~1617. Therefore, when x = 17, the value of f^xh is 1617.  \nChoice B is incorrect. This is the value of the reciprocal of f^xh when x = 17.  \nChoice C is incorrect. This is the value of f^xh when x = 1. Choice D is incorrect. This is the value of x when x = 17.  \nQUESTION 6  \nThe correct answer is 3. It’s given that the y-intercept of the graph shown is ^0, yh. The graph passes through the point ^0, 3h. Therefore, the value of y is 3.  \nQUESTION 7  \nThe correct answer is 5. Let p represent the number of packages of dinner rolls that should be bought for the party. It’s given that dinner rolls are sold in packages of 12. Therefore, 12p represents the number of dinner rolls that should be bought for the party. It’s also given that 50 dinner rolls are needed; therefore, 12p$50. Dividing both sides of this inequality by 12 yields p$5012~~ ~~ , or approximately p$4 .17. Since the number of packages of dinner rolls must be a whole number, the minimum number of packages that should be bought for the party is 5.  \nQUESTION 8  \nChoice D is correct. Let x represent the number that 21 is 21% of. It follo","cbCaigjoU6ZEpUcb","https://ap.wps.com/l/cbCaigjoU6ZEpUcb","pdf",460987,17,"English","# Answer Explanations\n## Math - Module 1","[{\"question\":\"How do the explanations determine whether an ordered pair is a solution to a system of equations?\",\"answer\":\"They check whether the point lies on both lines in the graph. If the lines intersect at that point, the ordered pair is the system’s solution.\"},{\"question\":\"What method is used to solve the equation in Question 4?\",\"answer\":\"The explanations apply the distributive property on the left-hand side, then perform inverse operations (subtracting and dividing) to isolate x.\"},{\"question\":\"How is a percent question like “21 is 21% of ___” handled?\",\"answer\":\"They define the unknown as the number that 21% equals 21, set up an equation using percent as a decimal, and solve for the missing value.\"}]","PSAT 8/9 Practice Test #2 - Answer Explanations | PDF",43]