[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-274529-105":3,"doc-detail-274529-en":81,"detail-sidebar-cat-0-en-105":97},{"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","mathematics-exam-a-answers","Mathematics Exam A - Answers","","Mathematics Exam A provides step-by-step explanations for solutions to a sequence of multiple-choice problems labeled 58 through 79. The answer walkthroughs cover a range of algebra and arithmetic skills, including simple interest, exponents and converting mixed numbers, distributive and additive inverse properties, angle sums and vertical angles, mean calculations from discarded values, fraction addition with common denominators, percent and proportion problems, coordinate reasoning on number lines, and solving linear equations and ratios. It concludes with evaluated expressions and selected correct options.",{"@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/mathematics-exam-a-answers/274529/",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/mathematics-exam-a-answers/274529.png","ImageObject",300,407,{"name":42,"@type":43},"Emma Mercer","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-21","2026-09-15",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",14,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What topics are included in the Mathematics Exam A answer explanations?","Question",{"text":63,"@type":64},"The explanations cover topics such as simple interest, exponents, mixed-number to improper-fraction conversion, linear equations using properties, triangle angle sums, mean calculations, fraction addition, percent problems, proportions, and number-line reasoning.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How are some equations solved in the answers?",{"text":68,"@type":64},"Many solutions use algebraic properties such as the distributive property, additive inverse, and multiplicative inverse, with steps that combine like terms and solve by dividing or subtracting on both sides.",{"name":70,"@type":61,"acceptedAnswer":71},"What is the typical method for percent and proportion questions in the document?",{"text":72,"@type":64},"Percent questions are solved by multiplying the given quantity by the percent expressed as a decimal, while proportion questions introduce a variable for the unknown and set ratios equal before solving for the 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},274529,1789478409,{"code":4,"msg":82,"data":83},"success",{"doc_id":79,"user_id":84,"nickname":42,"user_avatar":85,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":86,"file_id":87,"file_url":88,"file_type":89,"file_size":90,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":91,"language":92,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":93,"faqs":94,"seo_title":95,"seo_description":12,"update_tm":80,"read_time":96},962084925502,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","Sample Test – Mathematics Explanations of Correct Answers  \n58 . (5) Simple interest (y) is calculated by multiplying the initial deposit (p), the interest rate (r), and time (t)  .  \nprt = y  \n(2,500)( 0.04)t = 500  \n100t = 500  \nt = 5  \n59 . (–9) 6 − 9 ÷  −3 + (−2)3 × 1 ~~ 12 ~~ Calculate the exponent and convert the mixed number to an improper fraction  \n6 − 9 ÷  −3 + (−8) × ~~ 32 ~~ Next, cathe absolcl uutlaete value  \n6 − 9 ÷ 3 + (−8) × ~~ 32 ~~ iPerndiforcatmedthe multiplication and division  \n6 − 3 + (−12) Perform the addition and subtraction  \n3 + (−12) = −9  \n60 . (4) 7x + 3 − 2 ( 2x + 1) = 13 Apply the  \ndistributive property;  \nmultiply the –2 by 2x and 1  \n7x + 3 − 4x − 2 = 13 Combine like  \nterms  \n3x + 1 = 13 Apply the additive inverse property; subtract 1 from both sides of the equation  \n3x = 12 Apply the multiplicative inverse property; divide both sides of the equation by 3  \nx = 4  \n61 . (55) Since vertical angles are congruent, the right triangle in the figure has acute angles with measures of 35° and x°  . The interior angles of a triangle sum to 180°, so set up an equation to solve for x:  \n90 + 35 + x = 180  \n125 + x = 180 x = 55  \n62 . (19  .2) First, find the sum of the original 8 numbers  . Let x equal the sum of those numbers and use the mean formula to solve for x:  \nx~~8~~ = 17  \nx = 136  \nNext, subtract the 3 discarded numbers from the sum:  \n136 − 9 − 11 − 20 = 96  \nFinally, calculate the mean of the remaining 5 numbers by dividing the new sum, 96, by 5:  \n~~965~~ = 19.2  \n\n| 63 . (C) | 34 + 74 = 81 + 2,401 = 2,482 |  |\n| --- | --- | --- |\n| 64 . (E) | To solve, add the three given fractions:\u003Cbr>1 ~~ 34 ~~ + 2 ~~ 23~~ + ~~ 78~~\u003Cbr>The common denominator is 24: |  |\n|  | = 1 ~~ 1824 ~~ += 4 ~~ 1024 ~~ += 5 ~~ 724~~ | 2 ~~ 1624 ~~ + ~~ 2214~~\u003Cbr>2124 |\n\n65 . (C) Calculate 215% of 220:  \n2.15 ( 220) = 473  \n\n| 66 . (F) | First, use a proportion to find out how many minutes it will take the sign to complete 8 revolutions  . Let x equal the total number of minutes:\u003Cbr>x   90 8 = 1 x = 720\u003Cbr>Next, convert 720 minutes into hours and minutes:\u003Cbr>~~72060~~ = 12 hours\u003Cbr>Finally, 12 hours after 2:30 p . m  . is\u003Cbr>2:30 a  . m  . |\n| --- | --- |\n| 67 . (D) | First, find where Y is located on the number line  . Point X is the midpoint of WY  . Since there are 2 units between Wand X, there must also be 2 units between X and Y  . Thus, Y is located at 4 on the number line  .\u003Cbr>Point Y is the midpoint of WZ  . Use the same reasoning as above  . Since there are 4 units between W and Y, there must be 4 units between Y and Z  . So, Z is located at 8 on the number line  . |\n| 68 . (F) | ~~8110~~ = ~~ ~~~~ ~~ Cross multiply\u003Cbr>81n = 9(10) Apply the multiplicative inverse property; divide both sides of the equation by 81;\u003Cbr>n = ~~ 9081~~ = 1 ~~ 981~~ = 1 ~~ 19 ~~ thethesaimpctioly |\n\n69 . (A) The expression 3n + 3 is equal to 3( n + 1) , and it is given that this is an even number  . The expression ( n + 1) must also represent an even number, because 3 is an odd number and the product of an odd number and an even number is an even number  . If ( n + 1) is an even number, then n must be an odd number  . Choose an odd number to substitute for n in the answer options to find which expression represents an even number:  \nLet n = 3 .  \nOption A:  \n5n + 1 = 5 ( 3) + 1 = 16  \nOption B:  \n4n + 5 = 4 ( 3) + 5 = 17  \nOption C:  \n2n + 3 = 2 ( 3) + 3 = 9  \nOption D:  \nn + 2 = 3 + 2 = 5  \nSince 16 is the only even number, the correct answer is option A  .  \n\n| 70 . (F) | First, find the pairs of positive integers that multiply to 65: 1 ´ 65 and 5 ´ 13 .\u003Cbr>The sums of the pairs are 66 and 18 .\u003Cbr>18 is the option that is provided in the answer choices  . |\n| --- | --- |\n\n71 . (D) The two greatest integers less than –3 .25 are –4 and –5 . Since –4 is even, the answer is –5 .  \n\n| 72 . (F) | First, calculate how many pages Mikah has left to read:\u003Cbr>420 − 160 = 260\u003Cbr>Then, divide 260 by 4 to calculate the mean number of pages h","cbCaimySuGrwLVfK","https://ap.wps.com/l/cbCaimySuGrwLVfK","pdf",723063,11,"English","# Answer Explanations\n## Problem Set 58-79","[{\"question\":\"What topics are included in the Mathematics Exam A answer explanations?\",\"answer\":\"The explanations cover topics such as simple interest, exponents, mixed-number to improper-fraction conversion, linear equations using properties, triangle angle sums, mean calculations, fraction addition, percent problems, proportions, and number-line reasoning.\"},{\"question\":\"How are some equations solved in the answers?\",\"answer\":\"Many solutions use algebraic properties such as the distributive property, additive inverse, and multiplicative inverse, with steps that combine like terms and solve by dividing or subtracting on both sides.\"},{\"question\":\"What is the typical method for percent and proportion questions in the document?\",\"answer\":\"Percent questions are solved by multiplying the given quantity by the percent expressed as a decimal, while proportion questions introduce a variable for the unknown and set ratios equal before solving for the value.\"}]","Mathematics Exam A - Answers | PDF",28,{"code":4,"msg":82,"data":98},[99,103,107,110,115,120,125,130,135,138,142],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":100,"show_sort_weight":101,"slug":102},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":104,"show_sort_weight":105,"slug":106},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":108,"slug":109},70,"exam",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":112,"show_sort_weight":113,"slug":114},5,"Comic",60,"comic",{"id":116,"doc_module":4,"doc_module_name":25,"category_name":117,"show_sort_weight":118,"slug":119},6,"Technology",50,"technology",{"id":121,"doc_module":4,"doc_module_name":25,"category_name":122,"show_sort_weight":123,"slug":124},7,"Healthcare",40,"healthcare",{"id":126,"doc_module":4,"doc_module_name":25,"category_name":127,"show_sort_weight":128,"slug":129},8,"Research & Report",30,"research-report",{"id":131,"doc_module":4,"doc_module_name":25,"category_name":132,"show_sort_weight":133,"slug":134},9,"Religion & Spirituality",20,"religion-spirituality",{"id":133,"doc_module":4,"doc_module_name":25,"category_name":136,"show_sort_weight":133,"slug":137},"World Cup","world-cup",{"id":139,"doc_module":4,"doc_module_name":25,"category_name":140,"show_sort_weight":139,"slug":141},10,"Lifestyle","lifestyle",{"id":143,"doc_module":4,"doc_module_name":25,"category_name":144,"show_sort_weight":111,"slug":145},19,"General","general"]