[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-397207-105":59,"doc-detail-397207-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","math121-practice-test-comprehensive-final-for-aleks-students-solution-1","MATH121 Practice Test Comprehensive Final for ALEKS students - SOLUTION 1","","Comprehensive final practice test solutions for MATH121 students, covering a broad set of algebra and analytic geometry tasks. The problems include solving quadratic equations and absolute value inequalities using interval notation, finding distances between points, determining x-intercepts, and computing slopes of perpendicular lines. Additional items address maxima/minima and relative extrema, midpoint and circle problems in standard form, transforming equations, and logarithmic or exponential form conversions. Written problems request centers, radii, intercepts, graphs, and additional function quotient computations.",{"@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/math121-practice-test-comprehensive-final-for-aleks-students-solution-1/397207/",{"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/math121-practice-test-comprehensive-final-for-aleks-students-solution-1/397207.png","ImageObject",300,407,{"name":92,"@type":93},"asda1da","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-09-26",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",15,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How do you solve the quadratic equation x² - x - 2 = 0 in this test?","Question",{"text":113,"@type":114},"Set the equation to zero and factor the quadratic to find the roots. Select the option that matches the computed solutions.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What interval notation is used for the inequality |x| \u003C 1/2 (as shown in the test context)?",{"text":118,"@type":114},"Convert the absolute value inequality into a compound inequality, then express the solution set as an open interval. Choose the option corresponding to that interval notation.",{"name":120,"@type":111,"acceptedAnswer":121},"How is the midpoint of two points found in the problems?",{"text":122,"@type":114},"Use the midpoint formula by averaging the x-coordinates and averaging the y-coordinates. The answer is the point ( (x1+x2)/2, (y1+y2)/2 ).","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},397207,1790710779,{"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":39,"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":46,"preview_page_count":4},3985747861852,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","Multiple Choice Section.Write the letter of your answer in the box provided  \n   \n1.Solve the equation x²-x-2=0 for x.  \n(a)   x=2,1 (b)x=-2,1 (c)x=2,-1(d)x=-2,-1 (e)None of the above  \n206one x=2 cr×=一1hono6oeAns Cc)Cx-2)(x+1)=0x²一×一2=O  \n2.Write the solution to the inequality |x|\u003C12 using interval notation.(a)(-12,12)(b)(-∞,12)(c)(12,∞)  (d)(-∞,-12)U(12,c)  \n(e)None of theAn)(一 12,12)  \nabove  \n3.Find the distance between the points(-1,-3)and(2,3).  \n(b)√36 (c)√45 (d)(-3,0)(a)9=-11“+.(×,,y,)=(-1,-3)(×₂,92)=(2,3)  \n(e)None of the above=√(2-(-1)²+(3-(-3)²  \n=  J(2+1)²+(3+3)3²=√3²+6²=√9+36=√45Answer:(c)  \n4.The x-intercepts of x²+y²=16 are  \n(a)(-4,0),(4,0)  \n(b)(4,0)  \n(c)(-16,0),(16,0)   (d)(0,-4),(0,4)  \nCirde wi(ucntox (00)Ans(a)and radiu=4  \n5.Find the slope of the line that is perpendicular to 2x-5y=7.(a)-5     (e)None of the above.Ams (b)oof mi  lie=y=号一  \nAbslouto maximum valne off occuys henef(x)=0 happes at tx=1cx=5)Nob:Diffecno tetwau alsdul arelatwe maximym C minimum)eBTP1n Tnis graph,B.aD are Locahons of  \n6.Find the midpoint of the line segment joining the points(e)√32 (d)(2,-6)(a)(1,-3)  \n(e)None of the aboveAnswer:(一)  \nYeltive maxima:hoWeuer,①is c  \nocchum  匹e asolute maximum  \n9.Determine the absolute maximum value off.(b)4(c)-2(a)3  \n(e)None of the above  \n(d-1  \nb  \nAnswer:  \n9n切心Cae e absolnLe max(mum  \nsunce  \n7.Find the equation of the circle in standard form that has center(1,-3)and radius of√5.  \na人reCfwe maximum ne  \n(a)(x+1)²+(y-3)²=√5  \n(b)(x-1)²+(y+3)²=√5  \nttene心only me maximum Sen  \n(c)(x+1)²+(y-3)²=5(d)(x-1)²+(y+3)²=5(e)None of the aboveAnswer:() x-1^2++32=5S (X-^2(y-)2i,)1,  \n10.Find a value of x for which f(x)=0  \n(a)x=2  \n(b)x=1  \n(c)x=-2  \n(e)None of the above  \n(d)x=3  \nAnswer:(b)fr e giwen fmckwwey=O ou te grzph  \nNoto fC×)=0  \n8.Find the average rate of change of f(x)=3*from x=1tox=2.(a)4.5(c)6 (d)9(b)-6(e)None of the above  \nf(×₂)--GX)  \nAverg Yake chanye)  \n11.Find the coordinates of the relative (local)maximum.(c).(-1,4)(b)(1,0)(a)(6,1)  \n15.The zeroes of the polynomial function f(x)=4x⁴(x-3)(x+1)are  \n(a){0,-3,1}(b){0,3,-1}  (c){4,0,1,-1}(d){0,1,-1}  \npcchm 4te(e)None of the above(d)(-3,-3)  \n4x⁴c×-3)(x+1)=0  \nct______   __        打.  VaoeTLe人Mo⁵     lNo  \nx4=C  \nmaxte amaximum (also CLsplaeQaAnswer:女m4 Same a tLe locA  nmaXIm认w  \nThevefonx=0  \n   \nAnswe:(b  \n   \n12.Find all of the x-intervals where the graph is increasing.  \n16.Given that the function f(x)=√x+3 is one-to-one,what is the range off-¹(x)?  \n(c)(-5,-1)U (3.6)  \n(a)(-3,4)U(-2.3)  \n(b)(3,6)  \n(a)Not enough information is given  \n(b)(一00,∞)  \n(c)(-3,c)  \n(e)None of the above.  \n(d)(-1,3)  \n(d)(0,c)  \n(e)(-3,∞)eSetdoma 0Range 0f f-'(x)  \nf-'(x)=Domaci of f(x)×+3≥0swer:  \nAnswer:  \n3 Chos th o)fontonhih on=to-n  \n(d)f(x)=e-³xGrne(a)psse→r  \n17.The range of f(x)=In(x-1)is  \n(a)(1,c)  \nAnswer:  \n(b)(7,∞)  \n(c)All real numbers  \n(d)(-∞0,1)  \n(e)None o the above  \nThe cyiterion     ×-1>0力…t YaQ       le f   chum     (一Answer:(c)of hefunchum一recome人asymptohc on way s一∞At×=1 ,tTeQn funchim  uodetunrod aom vacs asymte a=fr   \n七0L     东(,Gyaphs la.(5One-L-    oe hoo test,Gaph(d)passesfox te hoi²  \n14.Determine the vertex of f(x)=-2(x-1)²-2  \n(-1-2)  (b)(1.-2)  (c)(-2,-2)   (d)(-2,7)  \n(x-o-raolaofformf(×)=Vetex心1,(1,-2)Vetox  \ninto exponential form.  \nAnswer:Ln   (hkh=1,k=-2  \n(a)4¹/2=x  (b)x¹/2=4 (c)4ˣ=1/2 (d)x²=4log 4× =立 =fonmLoscrithmic fonm  \n(e)None of the abovelogb×=9(a)  \n23.  Find the midpoint between the two points(3,-5)and(1,7).All three points on the same grid toe two given points.  \n19.Find the exact value of the expression:e2n(3)  \n(b)eln(10)  \n(e)None of the above  \n(a)6(= 9  \n(c)16  \n(d)9  \ne24u(3)  \nAnswer:  \n24.Graphfx)=-√x-2(a)Labl at les two poins(b)What sthe domain5ofos an is range  \nlef  most powtら Wkem x-2=0Ranse-,0)CY×≥2×-2≥6  \n(b)Pom au uf(x)  \n468 io 12  \n20.If e-²is evaluated,the result is:  \n0  \n-1+  \n(a)Ln()  \n(2,∞)  \n(b)1.001  \n(c)negative  \n(d)positive  \n(e)  \n-21  \nNone of the above  \nAnswer:hawe ony po","cbCaibLKZrRLZhdP","https://ap.wps.com/l/cbCaibLKZrRLZhdP","pdf",6476340,"English","# Multiple Choice Section\n## Algebra and Coordinate Geometry\n## Inequalities, Intercepts, and Slopes\n## Functions, Maxima/Minima, and Graph Features\n## Circles, Logarithms, and Exponential/Quotient Tasks\n# Written Problems (Show All Steps)","[{\"question\":\"How do you solve the quadratic equation x² - x - 2 = 0 in this test?\",\"answer\":\"Set the equation to zero and factor the quadratic to find the roots. Select the option that matches the computed solutions.\"},{\"question\":\"What interval notation is used for the inequality |x| \\u003c 1/2 (as shown in the test context)?\",\"answer\":\"Convert the absolute value inequality into a compound inequality, then express the solution set as an open interval. Choose the option corresponding to that interval notation.\"},{\"question\":\"How is the midpoint of two points found in the problems?\",\"answer\":\"Use the midpoint formula by averaging the x-coordinates and averaging the y-coordinates. The answer is the point ( (x1+x2)/2, (y1+y2)/2 ).\"}]","MATH121 Practice Test Comprehensive Final for ALEKS students - SOLUTION 1 | PDF",1790460575]