[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-452283-105":59,"doc-detail-452283-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","mock-upcat-1-answer-key-with-solutions","MOCK UPCAT 1 - ANSWER KEY WITH SOLUTIONS","","Mock UPCAT 1 answer key with step-by-step solutions across a set of multiple-choice math problems labeled 1 through 35. The material includes algebraic simplifications, factoring and exponent rules, solving equations for variables and ages, arithmetic sequence term computations, ratio and percent growth comparisons, average speed and time-difference calculations, coordinate geometry distance properties, and geometry proofs using triangle angle sum, isosceles triangle, and linear pair theorems.",{"@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/mock-upcat-1-answer-key-with-solutions/452283/",{"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/mock-upcat-1-answer-key-with-solutions/452283.png","ImageObject",300,407,{"name":92,"@type":93},"Fahsai","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-25","2026-09-30",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",11,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What does the document provide for each UPCAT item?","Question",{"text":113,"@type":114},"It gives the selected answer letter (e.g., A, B, C, D) and includes the corresponding solution steps for that problem.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What math topics are covered in the solutions?",{"text":118,"@type":114},"The solutions include algebraic manipulations, arithmetic sequence calculations, percent/ratio word problems, time and speed computations, and geometry including properties of triangles and parallelograms.",{"name":120,"@type":111,"acceptedAnswer":121},"Are geometry questions solved using formal proof reasoning?",{"text":122,"@type":114},"Yes. The document includes a structured reasoning table using triangle theorems (like isosceles triangle and angle sum) and properties such as linear pairs and supplementary angles.","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},452283,1790974723,{"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":144,"read_time":145},549768702563,"https://ap-avatar.wpscdn.com/avatar/8000c4aa63b76e948b?x-image-process=image/resize,m_fixed,w_180,h_180&k=1786536092046926083","MOCK UPCAT 1: ANSWER KEY WITH SOLUTIONS  \n1. D  \n0.04 = \"!\\#\\# = \"$% = 􀀦􀀧􀀨􀀩􀀧  \n2. A  \n$$ = $$ =  3. C  \n(2a)2 = (22)(a2)= 4a2  \nx5-x3 = (x3)(x2-1)  \na3+ a3 = (a3)(1+1) = 2a3  \n(x+y)2 = x2+2xy+y2  \n4. C  +  =  +  = +**  \n√3- √2 = 1.732 – 1.414 = 0.318  \n(x-y)2 = x2-2xy + y2  \n5. B  \n($($!\"2))((13!!\\#$)) = (1$)~~ ~~(!\"1$(1)~~ ~~(!\\#$!)$) = 4($1!!\"%5)((1$!!\\#$)) = 4($1!!\"%5)((1$!!\\#$)) =  \n($()41~~$~~!%!)$5($($!)\\#) = ($)1(%!\\#) = (($1))~~ ~~((~~1~~1!!\\#\\#)~~)~~ = 􀀡􀀢 6. C  \ns = 68;:;6 sty – sr = rst + xy  \nsty – xy = rst + sr  \n(y)(st – x) = (rs)(t + 1)  \nr = 􀀡 (􀀣􀀤 – 􀀧)  \n􀀩 (􀀪+􀀬)  \n7. B  \n[( √\" 􀀤  ) (%√􀀤 )]\"\\# = [(􀀤 \"/1)(􀀤 \"/% )]\"\\#= (􀀤 \"\\#⁄1) (􀀤 \"\\#⁄%) = (􀀤 \"\\#⁄1) (􀀤 $ )= 􀀤 ~~ ~~!\"&.$ = 􀀤 ~~ ~~!\"&.'\" = 􀀤 \"3⁄1 = 􀀨√􀀪 􀀦􀀿  \n8. C  \n(–8a5b2c3)(–2a2b7c)2  \n= (–8a5b2c3) [(–2)2(a2)2(b7)2(c2)2]=(–8a5b2c3) (4a4b 14c2)= –32a5+4b2+14c3+2 = –32a9b16c5  \n9. C  \nm = 188$@ 3mt – 2hm = 4t  \n3mt – 4t = 2hm (3m – 4)(t) = 2hmt =  􀀭􀀮􀀯   \n􀀰􀀯1􀀲  \n10. C  \n-8 +24 -8 +24 -8 +24 32 24 48 40 64 56 xx = 56 + 24 = 80  \n11. C  \nSum of terms in a sequence  \n=(Average)(\\# of terms) Average = \"AB~~ ~~BCDE~~ ~~.$FGAB~~ ~~BCDE  \n= $\"~~ ~~.$~~ ~~2$ = 46.5 Number of terms  \n= FHGIABEBCDEEIJ\"MAMCBDBCCDJEHC + 1  \n= 2$~~ ~~1–~~ ~~$\" + 1 = %\"1 + 1 = 18  \nSum = (46.5)(18) = 837  \n12. C  \nIn an arithmetic sequence, the 8th term =[1st term + (7)(common difference)] and the 15th term = [1st term + (14)(common difference)] .  \nLet A 1 be the 1st term  \nd be the common difference  \nA 1 + 14d = 30  \n- A 1 + 7d = 9  \n7d = 21  \nd = 3  \nA 1 + 14d = 30  \nA 1 = 30 – 14d  \nA 1 = 30 –(14)(3) = 30 – 42 = –12  \n13. C  \n1  \n\"$%  \n= 0.024  \n0.028 – 0.024 = 0.004 = \"\\#!\\#\\# = 􀀨~~ ~~􀀦􀀩􀀧 14. C  \nLet x be the price of spaghetti; y be the price of juice  \nx + y = 230  \nx = y + 100  \ny + 100 + y = 2y + 100 = 230 2y = 130  \ny = 65  \n15. C  \nrate: 50 envelopes/minute  \ntime:OPQ+R6~~ ~~S6T*R8ROURVSWR7  \nn/50  \n16. C  \nLet x be the price of refrigerator (5%)(x) = (0.05)(x) = P500.00 x = X\\#%\\#\\#\\#% = P10 000  \n17. B  \nrate: 7 tables/day  \ntime:OPQ+R66*S8TR~~ ~~8*+VR7  \nt/7  \n18. A  \nLCM (9, 21): 63  \nThe bells will ring simultaneously 63 minutes after 12 noon or at 1:03 p.m.  \n19. B  \nLet x be the mother’s age;  \n(3x – 7) be the son’s age  \nIf x = 15, then 3x – 7 = 45 – 7 = 38  \nShe gave birth 15 years ago and her age was then 38 – 15 = 23 years old.  \n20. D  \nLet x be Trina’s age;  \n37-x be Trisha’s age;  \nx-5 be Trina’s age 5 years ago;  \n32-x be Trisha’s age 5 years ago;  \nx – 5 = (2)(32 – x)  \nx – 5 = 64 – 2x  \n3x = 64 + 5 = 69  \nx = 23  \n21. B  \nLet x be the \\# of tables w/ 4 chairs  \n20 – x be the \\# of tables w/ 6 chairs  \n(4)(x) + (6)(20-x) = 92 4x + 120 – 6x = 92  \n-2x = -28 x = 14  \n22. C  \nTotal cost of taxed goods  \n=P540 + (P540) (12%)  \n=P540 + (P540) (0.12)  \n=(P540) (1.12)  \n=P604.80  \nTotal cost of all goods  \n= taxed goods + untaxed goods = P604 .80 + P66  \n23. A  \nLet x be mother’s age  \n2x be Grandmother’s age  \n2x – 60 be Tanisha’s age  \nx + 2x + 2x – 60 = 150;  \n5x – 60 = 150;  \n5x = 210;  \nx = 42;  \n2x – 60 = (2)(42)– 60 = 84 – 60 = 24  \n24. D  \nIf growth of sales of Pet Habitat this year is 20%, it’s sales next year is 1.2 times as this year. So, the sales of an indicated year are 1.2 times as that of its previous year.  \nRatio: 1.2 :1 = 6:5  \n25. C  \nAve. speed = 8S8*V8S8Z*V[788*[QOR\\R = \"$$\\#·1$^@6Q7 = $%!\\#@Q7=48 km/hr = 48 kph  \n26. A  \n2:25 pm = 14:25 (military time)  \n10:00 to 14:25 = 4 hrs and 25 mins  \n8:00 – 7:00 = 1 hour time difference  \n4 hrs. & 25 min.– 1 hr = 3 hrs. & 25 mins.  \n27. D  \nTime = Z[77W8*RORZ\\R=$~~ ~~%%^Q^Q/@= 0.2 hr (0.2 hr) 03\\#~~ ~~S[OPP68R71 = 12 mins.  \nHe will arrive 12 minutes past 9:00 or at  \n9:12 a.m.  \n28. DAt 6:15:  \nTrain A:  \n(6:15 – 5:00)(10kph) = 12.5 km from station  \nTrain B:  \n(6:15 – 5:30)(8kph)= 6 km from station  \nDistance: 12.5km – 6km = 6.5 km = 􀀦􀁟􀀨 􀀲􀀳 29. A  \nf(x) = ::$\"\" = (:~~ ~~\u003C).(.\")= :~~ ~~\", x≠ ±1 g(x) = 1:$:.2  \nf[g(x)] = \")$*)\u003C\" = \")$*)\u003C$$)) = ~~ ~~\")),$)\" 􀀨 􀁠  \n= )$*)+  = 􀁠.􀁡  \n30. C  \n28x – 4y – 12 = 0;  \n28x – 1","cbCaiePEuSAKXwGx","https://ap.wps.com/l/cbCaiePEuSAKXwGx","pdf",324806,"English","# Solutions and Answer Key\n## Algebra and Equation Solving\n## Sequences, Ratios, Speed, and Time\n## Geometry Concepts and Proofs","[{\"question\":\"What does the document provide for each UPCAT item?\",\"answer\":\"It gives the selected answer letter (e.g., A, B, C, D) and includes the corresponding solution steps for that problem.\"},{\"question\":\"What math topics are covered in the solutions?\",\"answer\":\"The solutions include algebraic manipulations, arithmetic sequence calculations, percent/ratio word problems, time and speed computations, and geometry including properties of triangles and parallelograms.\"},{\"question\":\"Are geometry questions solved using formal proof reasoning?\",\"answer\":\"Yes. The document includes a structured reasoning table using triangle theorems (like isosceles triangle and angle sum) and properties such as linear pairs and supplementary angles.\"}]","MOCK UPCAT 1 - ANSWER KEY WITH SOLUTIONS | PDF",1790736843,18]