[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-452231-105":59,"doc-detail-452231-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","mock-upcat-1-answer-key-with-solutions-part-1","MOCK UPCAT 1 - ANSWER KEY WITH SOLUTIONS - Part 1","","Mock UPCAT 1 answer key with step-by-step solutions for a set of multiple-choice problems. The material covers algebraic simplifications and factoring, radical calculations, quadratic relationships, distance and midpoint reasoning, time and rate conversions, least common multiple applications, ratio and growth problems, sequence and arithmetic sequence term computations, and word problems using variables for ages and prices. It also includes geometry proof reasoning using table-form statements and reasons.",{"@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/mock-upcat-1-answer-key-with-solutions-part-1/452231/",{"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-part-1/452231.png","ImageObject",300,407,{"name":92,"@type":93},"\tCallum ","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-08","2026-09-30",true,{"@type":102,"interactionType":103,"userInteractionCount":29},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What topics are included in the Mock UPCAT 1 answer key?","Question",{"text":112,"@type":113},"The solutions span algebra (factoring and equations), sequences (including arithmetic sequences), rate/time problems, and geometry reasoning with proof statements and reasons.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How are sequence and arithmetic sequence questions solved?",{"text":117,"@type":113},"They use formulas for sums and terms, such as determining common difference and computing a specified term from the first term plus a multiple of the common difference.",{"name":119,"@type":110,"acceptedAnswer":120},"How does the document handle geometry questions with reasoning tables?",{"text":121,"@type":113},"It lists statements in a table alongside corresponding reasons, referencing triangle properties, linear pair/supplementary definitions, and equality properties to justify each step.","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},452231,1791157870,{"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":29,"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},137451211410,"https://ap-avatar.wpscdn.com/avatar/2000bb0a9246f588df?x-image-process=image/resize,m_fixed,w_180,h_180&k=1786362646172706240","MOCK UPCAT 1: ANSWER KEY WITH SOLUTIONS  \n1. D  \n0.04 = = =  \n2. A = =  \n3. 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√ - √ = 1.732 – 1.414 = 0.318  \n(x-y)2 = x2-2xy + y2  \n5. B  \n( ) ( ) ( )= = = =  \n( )  \n= = =  \n6. Cs =  \nsty – sr = rst + xy  \nsty – xy = rst + sr  \n(y)(st – x) = (rs)(t + 1)  \n–  \nr = 7. B  \n[( √ √ = [( )(  \n= ( ⁄ ( ⁄ ) = ( ⁄= = = ⁄ = √  \n8. C  \n(–8a5b2c3)(–2a2b7c)2  \n= (–8a5b2c3) [(–2)2(a2)2(b7)2(c2)2]  \n=(–8a5b2c3) (4a4b 14c2)  \n= –32a5+4b2+14c3+2 = –32a9b16c5  \n9. Cm =  \n3mt – 2hm = 4t  \n3mt – 4t = 2hm  \n(3m – 4)(t) = 2hm  \nt = 10. 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)  \nAverage = ~~ ~~  \n= ~~ ~~ = 46.5 Number of terms  \n= ~~ ~~  \n–  \n= ~~ ~~ ~~ ~~  \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 ~~ ~~ = 0.024  \n0.028 – 0.024 = 0.004 = ~~ ~~ = ~~ ~~  \n14. C  \nLet x be the price of spaghetti;  \ny be the price of juice  \nx + y = 230  \nx = y + 100  \ny + 100 + y = 2y + 100 = 230  \n2y = 130  \ny = 65  \n15. C  \nrate: 50 envelopes/minute  \ntime:~~ ~~  \nn/50  \n16. C  \nLet x be the price of refrigerator  \n(5%)(x) = (0.05)(x) = P500.00  \nx = ~~ ~~ = P10 000  \n17. B  \nrate: 7 tables/day  \ntime:~~ ~~  \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  \n= 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 = ~~ ~~ = ~~ ~~  \n= ~~ ~~ =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 = ~~ ~~ = ~~ ~~ = 0.2 hr (0 .2 hr) ( ) = 12 mins.  \nHe will arrive 12 minutes past 9:00 or at  \n9:12 a.m.  \n28. DAt 6:15: Train 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) = ~~ ~~ = ~~ ~~ = ~~ ~~ , x≠ ±1  \ng(x) = ~~ ~~  \nf[g(x)] = ~~  ~~ = ~~   ~~ = ~~   ~~  \n= ~~   ~~ = ~~ ~~  \n30. C  \n28x – 4y – 12 = 0;  \n28x – 12 = 4y;  \n7x – 4 = y;  \ny = 7x – 4; (slope-intercept form)  \nslope = 7  \n31. C  \nx2 – y2 = (x + y)(x – y) = 77  \nx + y = 11  \nx – y = ~~ ~~ = 7  \nx + y = 11  \n+x – y = 7  \n2x = 18; x = 9  \n32. B  \nA midpoint ofa line segment is equidistant from the 2 end points.  \nDistance (-14,-6) = |-14 –(-6)| = |-8| = 8  \n-6 + 8 = 2  \n33. C  \n\n| Statement | Reason |\n| --- | --- |\n| \u003Cbr>1. BD = CD ;\u003Cbr>\u003Cbr>AD = BD | 1. Definition of isosceles triangle |\n| \u003Cbr>2. AD = CD | 2. Transitive Property of Equality |\n| 3. m∠DBC = m∠","cbCaieTgTtGrl0B9","https://ap.wps.com/l/cbCaieTgTtGrl0B9","pdf",10475722,86,"English","# Item Solutions\n## Algebra and Functions\n## Sequences and Arithmetic Sequences\n## Rates, Time, and Word Problems\n## Geometry and Proofs","[{\"question\":\"What topics are included in the Mock UPCAT 1 answer key?\",\"answer\":\"The solutions span algebra (factoring and equations), sequences (including arithmetic sequences), rate/time problems, and geometry reasoning with proof statements and reasons.\"},{\"question\":\"How are sequence and arithmetic sequence questions solved?\",\"answer\":\"They use formulas for sums and terms, such as determining common difference and computing a specified term from the first term plus a multiple of the common difference.\"},{\"question\":\"How does the document handle geometry questions with reasoning tables?\",\"answer\":\"It lists statements in a table alongside corresponding reasons, referencing triangle properties, linear pair/supplementary definitions, and equality properties to justify each step.\"}]","MOCK UPCAT 1 - ANSWER KEY WITH SOLUTIONS - Part 1 | PDF",1790736749,217]