[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-455911-105":59,"doc-detail-455911-en":130},{"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":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","psat-10-practice-test-1-answer-explanations-455911","PSAT 10 Practice Test - 1 - Answer Explanations","","Answer explanations for students taking the digital PSAT 10 in non-digital format. Covers Math Module 1 questions, providing correct-choice identification and step-by-step reasoning for each item shown. Includes examples such as converting units (teaspoons to tablespoons), evaluating functions by substitution, solving for variables by balancing equations, working with percentages, simplifying expressions, and using geometric formulas like perimeter and area derived from population density. Also includes guidance for interpreting linear functions via slope and intercept, plus solving equations and trigonometric relationships.",{"@graph":69,"@context":122},[70,84,105],{"@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/psat-10-practice-test-1-answer-explanations-455911/455911/",{"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/psat-10-practice-test-1-answer-explanations-455911/455911.png","ImageObject",300,407,{"name":92,"@type":93},"dawugda","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-17","2026-09-30",true,{"@type":102,"interactionType":103,"userInteractionCount":39},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What are these PSAT 10 answer explanations for?","Question",{"text":112,"@type":113},"They are for students taking the digital PSAT 10 in a non-digital (paper) format.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How do the explanations handle Math Module 1 questions?",{"text":117,"@type":113},"Each question identifies the correct choice and explains the reasoning step by step, while also stating why the other choices are incorrect.",{"name":119,"@type":110,"acceptedAnswer":120},"What topics appear in the provided explanations?",{"text":121,"@type":113},"The excerpt includes function evaluation by substitution, solving linear equations, percentage comparisons, simplifying algebraic expressions, geometry using perimeter and area, and setting up slope-intercept form and right-triangle trigonometry.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},455911,1790792205,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":39,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"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":144,"read_time":145},3985747870947,"https://ap-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2","PSAT™ 10  \nPractice Test \\# 1   \nANSWER EXPLANATIONS  \nThese answer explanations are for students taking the digital PSAT 10 in nondigital format.  \n© 2023 College Board. College Board, SAT, and the acorn logo are registered trademarks of College Board.  \nMath  \nModule 1  \n(27 questions)  \nQUESTION 1  \nChoice C is correct. It’s given that 3 teaspoons is equivalent to 1 tablespoon. Therefore, 44 tablespoons is equivalent to (44 tablespoons)(~~ ~~3~~ ~~tea1~~ ~~tablspoonsespoon), or  \n132 teaspoons.  \nChoice A is incorrect. This is equivalent to approximately 15.66 tablespoons, not 44 tablespoons. Choice B is incorrect. This is equivalent to approximately  \n29.33 tablespoons, not 44 tablespoons. Choice D is incorrect. This is equivalent to approximately 58.66 tablespoons, not 44 tablespoons.  \nQUESTION 2  \nChoice D is correct. It’s given that f(x ) = ~~ ~~61x~~ ~~ . Substituting 3 for x in this equation yields f(3) = ~~ ~~63~~)~~ , or f (3) = ~~ ~~118 . Therefore, when x = 3, the value of f(x ) is 118 . Choice A is incorrect. This is the value of f(x ) when x = 0.5. Choice B is incorrect.  \nThis is the value of f(x ) when x = 1. Choice C is incorrect. This is the value of f(x ) when x = 1.5.  \nQUESTION 3  \nChoice C is correct. It’s given that x = 40. Adding 6 to both sides of this equation yields x +6 = 40 +6 , or x +6 = 46. Therefore, the value of x +6 is 46.  \nChoice A is incorrect. This is the value of x-6, not x +6 . Choice B is incorrect. This is the value of x , not x +6 . Choice D is incorrect. This is the value of x +24 , not x +6 .  \n34 PSAT 10 PRACTICE TEST \\#1 ANSWER EXPLANATIONS  \nQUESTION 4  \nChoice A is correct. 23% of 100 can be calculated by multiplying  23  by 100, which yields (~~ ~~12030)100 , or 23. 100  \nChoice B is incorrect. This is 46%, not 23%, of 100. Choice C is incorrect. This is 23% less than 100, not 23% of 100. Choice D is incorrect. This is 23% greater than 100, not 23% of 100.  \nQUESTION 5  \nChoice D is correct. The given expression shows addition of two like terms. Therefore, the given expression is equivalent to (50 +5)x2 , or 55x2 .  \nChoice A is incorrect. This expression is equivalent to (50)(5)x2 , not (50 +5)x2 . Choice B is incorrect. This expression is equivalent to (~~ ~~505)x2, not (50 +5)x2 . Choice C is incorrect. This expression is equivalent to (50-5)x2, not (50 +5)x2 .  \nQUESTION 6  \nThe correct answer is 370. It’s given that the population density of Cedar County is 230 people per square mile and the county has a population of 85,100 people. Based on the population density, it follows that the area of Cedar County is (85,100 people)(~~ ~~12sq3u0arepeomplilee), or 370 square miles.  \nQUESTION 7  \nThe correct answer is-9. Since w is in the denominator of a fraction in the given equation, w can’t be equal to 0. Since w isn’t equal to 0 , multiplying both sides of the given equation by w yields an equivalent equation, -54 = 6w. Dividing both sides of this equation by 6 yields-9 = w. Therefore, -9 is the solution to the given equation.  \nQUESTION 8  \nChoice B is correct. An equation defining a linear function can be written in  \nthe form f(x ) = mx +b , where m and b are graph of y = f (x ) in the xy-plane, and (0, b) given that for the function f , the graph of y  \nconstants, m is the slope of the is the y-intercept of the graph. It’s = f (x ) in the xy-plane has a slope  \nof 3. Therefore, m = 3. It’s also given that this graph passes through the point (0, -8). Therefore, the y-intercept of the graph is (0, -8), and it follows that b =-8. Substituting 3 for m and-8 for b in the equation f(x ) = mx +b yields f (x ) = 3x-8. Thus, the equation that defines f is f(x ) = 3x-8 .  \nChoice A is incorrect. For this function, the graph of y = f (x ) in the xy-plane passes through the point (0, 0), not (0, -8). Choice C is incorrect. For this function, the graph of y = f (x ) in the xy-plane passes through the point (0, 5), not (0, -8). Choice D is incorrect. For this function, the graph of y =","cbCaim9IbcC48Hr0","https://ap.wps.com/l/cbCaim9IbcC48Hr0","pdf",392772,17,"English","# Math\n## Module 1 (27 questions)\n## Question 1\n## Question 2\n## Question 3\n## Question 4\n## Question 5\n## Question 6\n## Question 7\n## Question 8\n## Question 9\n## Question 10\n## Question 11","[{\"question\":\"What are these PSAT 10 answer explanations for?\",\"answer\":\"They are for students taking the digital PSAT 10 in a non-digital (paper) format.\"},{\"question\":\"How do the explanations handle Math Module 1 questions?\",\"answer\":\"Each question identifies the correct choice and explains the reasoning step by step, while also stating why the other choices are incorrect.\"},{\"question\":\"What topics appear in the provided explanations?\",\"answer\":\"The excerpt includes function evaluation by substitution, solving linear equations, percentage comparisons, simplifying algebraic expressions, geometry using perimeter and area, and setting up slope-intercept form and right-triangle trigonometry.\"}]","PSAT 10 Practice Test - 1 - Answer Explanations | PDF",1790744658,43]