[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-446952-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-446952-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","psatnmsqt-practice-test-1-answer-explanations-math-module-1","PSAT/NMSQT Practice Test #1 Answer Explanations - Math Module 1","","Math Module 1 contains PSAT/NMSQT practice questions with answer choices and step-by-step solution explanations. The content demonstrates how to convert units and interpret ratios, evaluate linear functions by substitution, solve simple algebraic equations, and compute expressions with like terms. It also explains applications involving area from population density, solving linear equations with variables in denominators, determining slope and intercept from points, and using triangle perimeter to find unknown side lengths, along with trigonometric tangent in right triangles.",{"@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/psatnmsqt-practice-test-1-answer-explanations-math-module-1/446952/",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/psatnmsqt-practice-test-1-answer-explanations-math-module-1/446952.png","ImageObject",300,407,{"name":42,"@type":43},"WPS_1786070896","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-21","2026-09-29",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",7,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"How does the document explain converting teaspoons to tablespoons?","Question",{"text":63,"@type":64},"It states that 3 teaspoons equals 1 tablespoon, then uses that conversion to determine the equivalent number of tablespoons for the given quantity.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How are linear function values found in these explanations?",{"text":68,"@type":64},"For f(x)=mx+b, the solutions substitute the given x value into the equation, or derive m (slope) and b (y-intercept) from the graph’s slope and a point like (0, b).",{"name":70,"@type":61,"acceptedAnswer":71},"How does the document handle equations where the variable is in the denominator?",{"text":72,"@type":64},"It notes the denominator can’t be zero, multiplies both sides by the nonzero denominator to get an equivalent equation, and then solves for the variable.","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},446952,1791209382,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,109,114,119,122,126],{"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":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":106,"show_sort_weight":107,"slug":108},"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":96,"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":144,"read_time":107},549768072016,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","Math  \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 WHDVSRRQV􀀑  \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 WDEOHVSRRQV􀀏 QRW 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 \\LHOGV f(3) = ~~ ~~61~~(~~3~~)~~ 􀀏 RU f (3) = ~~ ~~118 . Therefore, when x = 3, the value of f(x ) LV 118 . Choice A is incorrect. This is the value of f(x ) when x = 0.5. Choice B is incorrect. This is the value of f(x ) when x = 1􀀑 Choice C is incorrect. This is the value of f(x )  \nwhen 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 􀀑 TKHUHIRUH􀀏 WKH YDOXH RI 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/NMSQT PRACTICE TEST \\#1 ANSWER EXPLANATIONS  \nQUESTION 4  \nChoice A LV FRUUHFW􀀑 23% of 100 FDQ EH FDOFXODWHG E\\ PXOWLSO\\LQJ  23  by 100, which yields (~~ ~~12030)100 , or 23. 100  \nChoice B LV LQFRUUHFW􀀑 TKLV LV 46% 􀀏 QRW 23%, of 100. Choice C LV LQFRUUHFW􀀑 TKLV LV 23% OHVV WKDQ 100􀀏 QRW 23% RI 100. Choice D LV LQFRUUHFW􀀑 TKLV LV 23% greater than 100􀀏 QRW 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 􀀏 RU 55x2.  \nChoice A LV LQFRUUHFW􀀑 TKLV H[SUHVVLRQ LV HTXLYDOHQW WR (50)(5)x2 , not (50 +5)x2 . Choice B LV LQFRUUHFW􀀑 TKLV H[SUHVVLRQ LV HTXLYDOHQW WR (~~ ~~505)x2􀀏 QRW (50 +5)x2 . Choice C LV LQFRUUHFW􀀑 TKLV H[SUHVVLRQ LV HTXLYDOHQW WR (50-5)x2􀀏 QRW (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 LQ WKH HTXDWLRQ f(x ) = mx +b yields f (x ) = 3x-8. Thus, the equation that defines f LV f(x ) = 3x-8 .  \nChoice A LV LQFRUUHFW􀀑 )RU WKLV IXQFWLRQ􀀏 WKH JUDSK RI y = f (x ) in the xy-plane passes through the point (0, 0)􀀏 QRW (0, -8). Choice C is incorrect. For this IXQFWLRQ􀀏 WKH JUDSK RI y = f (x ) in the xy-plane passes through the point (0, 5), not (0, -8). Choice D LV LQFRUUHFW􀀑 )RU WKLV IXQFWLRQ􀀏 WKH JUDSK RI y = f (x ) in the xy-plane passes through the point (0, 11), not (0, -8).  \n35 PSAT/NMSQT PRACTICE TEST \\#1 ANSWER EXPLANATIONS  \nQUESTION 9  \nChoice A is correct. The perimeter of a triangle is the sum of the lengths of its three sides. The triangl","cbCaigaU4Cmu6Urt","https://ap.wps.com/l/cbCaigaU4Cmu6Urt","pdf",597488,16,"English","# Math Module 1\n## Question 1-12","[{\"question\":\"How does the document explain converting teaspoons to tablespoons?\",\"answer\":\"It states that 3 teaspoons equals 1 tablespoon, then uses that conversion to determine the equivalent number of tablespoons for the given quantity.\"},{\"question\":\"How are linear function values found in these explanations?\",\"answer\":\"For f(x)=mx+b, the solutions substitute the given x value into the equation, or derive m (slope) and b (y-intercept) from the graph’s slope and a point like (0, b).\"},{\"question\":\"How does the document handle equations where the variable is in the denominator?\",\"answer\":\"It notes the denominator can’t be zero, multiplies both sides by the nonzero denominator to get an equivalent equation, and then solves for the variable.\"}]","PSAT/NMSQT Practice Test #1 Answer Explanations - Math Module 1 | PDF",1790717885]