[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-453002-105":59,"doc-detail-453002-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","math-2412-precalculus-practice-exam-4","Math 2412 (Precalculus) - Practice Exam 4","","Practice Exam 4 for Math 2412 (Precalculus) focusing on topics from sections 11.5, 11.6, 11.7, 12.1, and 12.2. The exam includes 15 multiple-choice questions and 4 free-response problems requiring work shown for full credit on questions 16 to 19. Students must circle exactly one answer for each multiple-choice item and simplify expressions, especially logarithmic, exponential, and trigonometric forms, as well as evaluate limits using algebra or provided graphs. Instructions emphasize neat handwriting and scratch work not graded.",{"@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/math-2412-precalculus-practice-exam-4/453002/",{"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/math-2412-precalculus-practice-exam-4/453002.png","ImageObject",300,407,{"name":92,"@type":93},"jay","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-08","2026-09-30",true,{"@type":102,"interactionType":103,"userInteractionCount":39},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What are the grading rules for this practice exam?","Question",{"text":112,"@type":113},"Scratch paper will not be graded. For questions 16 to 19, full credit is given only if the necessary work is shown justifying the answer.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How should students answer the multiple-choice questions?",{"text":117,"@type":113},"Circle the correct answer for each question and circle one choice only.",{"name":119,"@type":110,"acceptedAnswer":120},"What is expected about simplifying answers?",{"text":121,"@type":113},"Simplify answers as much as possible; expressions like ln(1), e^0, sin((π/2)) and similar forms must be simplified for full credit.","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},453002,1790774695,{"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":39,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":29,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":144},3985747858866,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Name:  Student ID:  Section:  Instructor:   \nMath 2412 (Precalculus)  \nPractice Exam 4  \nInstructions:  \n􀀏 Work on scratch paper will not be graded.  \n􀀏 For questions 16 to 19, show all your work in the space provided. Full credit will be given only if the necessary work is shown justifying your answer.  \n􀀏 Please write neatly. If I cannot read your handwriting, you will not receive credit.  \n􀀏 Simplify your answers as much as possible. Expressions such as ln(1), e0 , sin(􀀙=2), etc. must be simpli􀀌ed for full credit.  \nFor Instructor use only.  \n\n| \\# | Possible | Earned |\n| --- | --- | --- |\n\n\n| MC | 60 |  |\n| --- | --- | --- |\n| 16 | 10 |  |\n| 17 | 10 |  |\n\n\n| Sub | 80 |  |\n| --- | --- | --- |\n|  |  |  |\n\n\n| \\# | Possible | Earned |\n| --- | --- | --- |\n\n\n| 18 | 10 |  |\n| --- | --- | --- |\n| 19 | 10 |  |\n|  |  |  |\n\n\n| Sub | 20 |  |\n| --- | --- | --- |\n| Total | 100 |  |\n\nMultiple Choice. Circle the correct answer for each question. Circle one choice only.  \n1. (Section 11.5) Find the number of subsets of the set of two-digit numbers with a 0 in the ones digit between 1 and 76 .  \na) 32 b) 64 c) 128  \nd) 256 e) 255 f) 76  \n2. (Section 11.5) Find the distinct number of arrangements of the letters in the word \\mirror.\"  \na) 120 b) 240 c) 360  \nd) 480 e) 720 f) 64  \n3. (Section 11.5) A family consisting of 2 parents and 4 children is to pose for a picture with 3 family members in the front and 3 in the back. How many arrangements are possible if the parents must sit in the front?  \na) 144 b) 192 c) 288  \nd) 384 e) 432 f) 720  \n4. (Section 11.6) Evaluate the binomial coe􀀎cient 􀀒 112􀀓 .  \na) 54 b) 55 c) 56  \nd) 60 e) 64 f) 66  \n5. (Section 11 .6) Find the fourth term of (x 􀀀 y)7 .  \na) 21x3 y4 b) 􀀀21x3 y4 c) 35x4 y 3  \nd) 􀀀35x4 y 3 e) 7x5 y 2 f) 􀀀7x5 y 2  \n6. (Section 11.6) Find the 􀀌fth term of 􀀒 y4 + 4x􀀓 6  \n240y4 240y2 360y4  \na) ~~ ~~ b) ~~ ~~ c) ~~ ~~  \nx2 x4 x2  \n360y2   480y4   480y2  \nd) x4 e) x2 f) x4  \n7. (Section 11.7) Four coins are tossed. Find the probability of tossing exactly two heads or at least one tail.  \n 1   11  3  \na) b) c)  \n16 16 4  \n13  7  15  \nd) e) f)  \n16 8 16  \n8. (Section 11.7) One card is drawn from a standard deck of 52 cards. Find the probability of drawing a two or a four.  \n 1   2   3   \na) b) c)  \n13 13 13  \n 4   5   6   \nd) e) f)  \n13 13 13  \n9. (Section 11.7) Two dice are rolled, and the results are summed. Find the probability of rolling a sum between 2 and 5, inclusive.  \n1  1  1  \na) b) c)  \n2 3 6  \n 5   7   11  \nd) e) f)  \n18 18 36  \n0 x2 􀀀 4x 􀀀 5  \n10. (Section 12.2) Find the ~~ ~~ limit lim ~~ ~~  \n0 x!􀀀 1 x + 1  \na) 􀀀4 b) 4  \nc) 􀀀6 d) 6  \ne) 0 f) Does not exist  \n11. (Section 12.2) Find the limit xl2 sin 􀀐 􀀙x􀀑  \na) 􀀀1 b) 0  \nc) 1 d) 􀀀2  \ne) 2 f) Does not exist  \n12. (Section 12.2) Find lim f (x) where  \nx!0 􀀀  \nf (x) = 􀀚 2x +3 2x + 5 if xif x  00  \na) 􀀀3 b) 3  \nc) 􀀀5 d) 5  \ne) 0 f) Does not exist  \n13. (Section 12.1) Use the given graph of the function y = f(x) in 􀀌gure 1 to 􀀌nd lim f (x) . x!8+  \nFigure 1: Figure for Question 13, 14 and 15  \na) 2 b) 3  \nc) 4 d) 8  \ne) Does not exist  \n14. (Section 12.1) Use the given graph of the function y = f(x) in 􀀌gure 1 to 􀀌nd lim f(x) . x!8  \na) 2 b) 3  \nc) 4 d) 8  \ne) Does not exist  \n15. (Section 12.1) Use the given graph of the function y = f(x) in 􀀌gure 1 to 􀀌nd f (8) .  \na) 2 b) 3  \nc) 4 d) 8  \ne) Does not exist  \nFree response: Show all work in the space provided. Full credit will be given only if the necessary work is shown justifying your answer. Please write neatly. Scratch work will not be graded.  \n16. (10 points) (Section 11.5)  \n(a) Use the Binomial Theorem to write the 􀀌rst three terms of the binomial (x5 􀀀py) 11 .  \n(b) Use the Binomial Theorem to 􀀌nd the coe􀀎cient of x in the expansion 􀀒 x + 1x2 􀀓 13 .  \n17. (10 points) (Section 11.7)  \n(a) Three coins are tossed. What is the sample space?  \n(b) Three coins are tossed. Find the probability of tossing exactly one head.  \n18. (10 points) of the following.  \n(a) (Section 11.7) A coi","cbCaiuX5UHc2y5NX","https://ap.wps.com/l/cbCaiuX5UHc2y5NX","pdf",136285,"English","# Multiple Choice\n## Questions 1-15\n# Free Response\n## Questions 16-19","[{\"question\":\"What are the grading rules for this practice exam?\",\"answer\":\"Scratch paper will not be graded. For questions 16 to 19, full credit is given only if the necessary work is shown justifying the answer.\"},{\"question\":\"How should students answer the multiple-choice questions?\",\"answer\":\"Circle the correct answer for each question and circle one choice only.\"},{\"question\":\"What is expected about simplifying answers?\",\"answer\":\"Simplify answers as much as possible; expressions like ln(1), e^0, sin((π/2)) and similar forms must be simplified for full credit.\"}]","Math 2412 (Precalculus) - Practice Exam 4 | PDF",1790738029,15]