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Instructions require all calculations and formulas, including units where appropriate, clear final answers, and no diagrams drawn to scale. The exam includes sequence and series, factoring and rational expressions, quadratic functions in vertex form with range/direction/axis/intercepts and sketching, and equation solving for quadratic and rational equations, with marks specified per question.",{"@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/grade-11-pre-calculus-mathematics-final-practice-exam/453889/",{"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/grade-11-pre-calculus-mathematics-final-practice-exam/453889.png","ImageObject",300,407,{"name":92,"@type":93},"404brain","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-26","2026-09-30",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",12,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How is the final exam weighted and how long is the exam time?","Question",{"text":113,"@type":114},"Modules 1–8 are weighted to 100% total, and the allotted time is 2.5 hours.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What rules must students follow for work presentation and diagrams?",{"text":118,"@type":114},"Show all calculations and formulas with units where appropriate, clearly state the final answer, and diagrams may not be drawn to scale.",{"name":120,"@type":111,"acceptedAnswer":121},"What topics are covered in Modules 1–4?",{"text":122,"@type":114},"Module 1 covers sequences and series, Module 2 covers factoring and rational expressions, Module 3 focuses on quadratic functions in vertex form, and Module 4 covers solving rational and quadratic equations.","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},453889,1791166884,{"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":140,"language":141,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":67,"update_tm":145,"read_time":146},1099529839291,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","G r a d e 1 1 P r e-C a l C u l u s M a t h e M a t i C s ( 3 0 s )  \nFinal Practice Exam  \nG r a d e 1 1 P r e-C a l C u l u s M a t h e M a t i C s  \nFinal Practice Exam  \nName:    \nStudent Number:    \nAttending q Non-Attending q  \nPhone Number:    \nAddress:  \n_________________________________  \n__________________________________________  \n__________________________________________  \nFor Marker’s Use Only  \nDate:   Final Mark:   /100 =   %  \nComments:  \nInstructions  \nThe final examination will be weighted as follows:  \nModules 1–8 100%  \nThe format of the examination will be as follows:  \nModule 1: 5 marks Module 5: 19 marks  \nModule 2: 5 marks Module 6: 19 marks  \nModule 3: 5 marks Module 7: 23 marks  \nModule 4: 5 marks Module 8: 19 marks  \nTime allowed: 2.5 hours  \nNote: You are allowed to bring the following to the exam: pencils (2 or 3 of each), blank paper, a ruler, a scientific or graphing calculator, and your Final Exam Resource Sheet. Your Final Exam Resource Sheet must be handed in with the exam.  \nShow all calculations and formulas used. Include units where appropriate. Clearly state your final answer. Diagrams may not be drawn to scale.  \n4 of 32  \n G r a d e 1 1 P r e-C a l c u l u s M a t h e m a t i c s  \nName:    \nAnswer all questions to the best of your ability. Show all your work.  \nModule 1: Sequences and Series (5 marks)  \n1. Write the defining linear function of the following arithmetic sequence. (2 marks) 99, 103, 107,    \n2. Use a formula to find the value of ∑8k=2 81 􀀟􀀞􀀝 13􀀜􀀛􀀚 k−1 . (3 marks)  \n F i n a l P r a c t i c e E x a m   5 of 32    \nModule 2: Factoring and Rational Expressions (5 marks)  \n1. Simplify. Identify all non-permissible values. (5 marks)  \n5x2 + 14x − 19 􀀜 3x − 12 2x − 2 􀀙  \n 2x2 + 5x + 3  ÷ 􀀚􀀛  x 2 − 2x − 8 + x 2 + 4x − 5 􀀘􀀗  \nName:    \nModule 3: Quadratic Functions (5 marks)  \n1. Given the following parabola in vertex form, complete the following questions. (1 mark each, for a total of 5 marks)  \ny = ~~ ~~12 (x−3)2 + 2  \na) Identify the range.  \nb) Identify the direction of the opening.  \nc) Identify the axis of symmetry.  \nd) Identify the y-intercept.  \ne) Sketch the graph of the parabola.  \n\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n\n8 of 32  \n G r a d e 1 1 P r e-C a l c u l u s M a t h e m a t i c s  \nName:    \nModule 4: Solving Rational and Quadratic Equations (5 marks)  \n1. Solve the following quadratic equation using any method you wish. Explain why you chose the method you used. (2 marks)  \n2x2 + 25 = 15x  \n F i n a l P r a c t i c e E x a m   9 of 32    \n2. Solve the following rational equation. Identify any non-permissible values. (3 marks)  \n3x + 1 x   \n=−  \nx x + 1","cbCainy1j8aHP1E4","https://ap.wps.com/l/cbCainy1j8aHP1E4","pdf",602054,32,"English","# Instructions\n# Module 1: Sequences and Series\n# Module 2: Factoring and Rational Expressions\n# Module 3: Quadratic Functions\n# Module 4: Solving Rational and Quadratic Equations","[{\"question\":\"How is the final exam weighted and how long is the exam time?\",\"answer\":\"Modules 1–8 are weighted to 100% total, and the allotted time is 2.5 hours.\"},{\"question\":\"What rules must students follow for work presentation and diagrams?\",\"answer\":\"Show all calculations and formulas with units where appropriate, clearly state the final answer, and diagrams may not be drawn to scale.\"},{\"question\":\"What topics are covered in Modules 1–4?\",\"answer\":\"Module 1 covers sequences and series, Module 2 covers factoring and rational expressions, Module 3 focuses on quadratic functions in vertex form, and Module 4 covers solving rational and quadratic equations.\"}]","Grade 11 Pre-Calculus Mathematics - Final Practice Exam | PDF",1790739777,81]