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Problems include computing average and instantaneous rates of change, using incremental approximations, and analyzing concavity, inflection points, and approximate zeros from function graphs. Additional questions cover classifying numbers (real, rational, irrational, complex), synthetic division, and factoring polynomials with multiplicities and complex roots.",{"@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/ap-precalculus-quiz-11-no-calculator/448631/",{"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/ap-precalculus-quiz-11-no-calculator/448631.png","ImageObject",300,407,{"name":92,"@type":93},"Dipper","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-19","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 kinds of problems are included in Quiz 1.1 (No Calculator)?","Question",{"text":112,"@type":113},"Quiz 1.1 includes function modeling from real-world situations, determining domain and range, and analyzing whether mappings or graphs represent functions. It also asks for increasing/decreasing intervals, concavity, inflection points, and approximate zeros from graphs.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How do the calculator-allowed exam questions define average vs. instantaneous rate of change?",{"text":117,"@type":113},"They first compute average rate of change over a given interval, then approximate the instantaneous rate at an endpoint using a small increment (k), and organize results in tables for verification.",{"name":119,"@type":110,"acceptedAnswer":120},"What topics appear in the no-calculator exams related to algebra and polynomials?",{"text":121,"@type":113},"They include classifying number types (natural, whole, integer, rational/irrational/real, complex), synthetic division, completing tables for factored forms and multiplicities, and factoring polynomials to find and classify all zeros, including complex ones.","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},448631,1790926276,{"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":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},1374404997633,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","AP Precalculus – Quiz 1.1 (No Calculator) Name   Pd.    \n1. For each situation, generate a function, describing the independent and dependent variable as well as possible units of measure.  \na. The cost of land is a function of its size.  \nb. The time to print a document is a function of how many pages it contains.  \nc. The sweetness of a cup of coffee is a function of how much sugar is added.  \n2. Determine the domain and range of these functions.  \na. f (x ) = 2 − 9x  \ne. f (x ) = 10x  \nb.  \nf.  \n2 y = −x  \nx + 3  \ny = ~~ ~~  \nx − 3  \nc. g(x ) = + 1  \ng. g(x ) = 0  \nd. y = 1 − x − 1  \nh. −5 − x + 4  \n3. In the following mappings, determine which are functions. If it fails to be a function, explain why.)  \na.  \nb.  \nc.  \nd.  \n4. Determine whether the following graphs are functions.  \n© [www.MasterMathMentor.com](www.MasterMathMentor.com) Illegal to post on Internet  \n5. For the following function graphs, determine approximate intervals of increasing, decreasing, concave up, concave down, and inflection points. Also find the approximate zeros ofthe function.  \na.  \nb.  \nc.  \nd.  \n6. You are given a function and an x-interval to view it. Determine intervals of increasing, decreasing, concave up and down, inflection points (approx.) as well as the zeros ofthe function.  \na. y = 1 − 2x3 −6, 6  b. y = x 3 + 8 −4, 4  c. y = 4x − x 4 −2, 2   \n© [www.MasterMathMentor.com](www.MasterMathMentor.com) Illegal to post on Internet  \nAP Precalculus – Exam 1.2 – 1.3 (Calculator Allowed) Name   Pd.    \n1. Find the average rate of change of the given function over the interval.  \na. f (x ) = 2x2 − 2x − 3 −2, 2  b. g(x ) = 1 − x − x 2 + x 3 −3, 1  \nc. g(x ) = 3~~ ~~8 −4, −2 d. h (x ) = x~~ ~~3x~~ ~~+x~~ ~~1 −1, 3  \n2. For the following functions, find the average rate of change on the interval [P, Q] given. Then approximate the instantaneous rate of change at P using P + k. Calculators allowed.  \na. f (x ) = 1− 8x 1, 4  , k = 0.1 Avg rate Instantaneous rate  \nd. f (x ) = 4x23 1, ~~ ~~287~~ ~~  , k = 0.01  \nAvg rate Instantaneous rate  \nb. f (x ) = 2x2 − 4x + 3 −3, 3 , k = 0.1 Avg rate Instantaneous rate  \nf. f (x ) = 2x − 2− x 0, 3 , k = 0.01  \nAvg rate Instantaneous rate  \n3. A turkey is placed into an oven and its temperature at time t is given by the equation T( t ) = 165 − 90( 2−0 .04t ) where t is measured in minutes. Determine whether the turkey’s temperature is rising quicker after 30 minutes or after an hour in the oven.  \n© [www.MasterMathMentor.com](www.MasterMathMentor.com) Illegal to post on Internet  \n4. Given the quadratic function, f (x ) and an increment and an interval, i) use the definition to find the average rate of change on that interval. Then ii) complete the table to find the average rate of change formula at any point x and iii) use the AROC formula to verify your answer in part i.  \na. f (x ) = x 2 + 5x − 4, increment = 1, 50, 51  \ni. AROC = ii.  \n\n| x | 0 | 1 | 2 |\n| --- | --- | --- | --- |\n| f (x ) |  |  |  |\n| AROC |  |  |  |\n\nb. f (x ) = − ~~ ~~12 x 2 − 6x, increment = 2, 35.5, 37.5  \ni. AROC = ii.  \n\n| x | 0 | 1 | 2 |\n| --- | --- | --- | --- |\n| f (x ) |  |  |  |\n| AROC |  |  |  |\n\n5. Determine whether the graph of the function is concave up or concave down in the interval containing the given x-value. Complete the table. and explain your reasoning.  \na. f (x ) = 3x2 − 4x − 1, x = 1  \n\n| x | 0.8 | 0.9 | 1 | 1.1 | 1.2 |\n| --- | --- | --- | --- | --- | --- |\n| f (x ) |  |  |  |  |  |\n| AROC |  |  |  |  |  |\n\n6. Show that the function has a point of inflection in the interval containing the x-value. Complete the table and explain your reasoning.  \nb. f (x ) = 10x3 + 30x2 , x = −1  \n\n| x | −1 .2 | −1 .1 | −1 | −0 .9 | −0 .8 |\n| --- | --- | --- | --- | --- | --- |\n| f (x ) |  |  |  |  |  |\n| AROC |  |  |  |  |  |\n\n© [www.MasterMathMentor.com](www.MasterMathMentor.com) Illegal to post on Internet  \nAP Precalculus – Exam 1.4, 1.5 (No Calculator) Name   Pd.    \n1. Classify the following numbers using the following: N – Na","cbCaiqTdX7MW7OE4","https://ap.wps.com/l/cbCaiqTdX7MW7OE4","pdf",5449141,28,"English","# Quiz 1.1 (No Calculator)\n## Function modeling, domains and ranges\n## Domain/range and function verification\n## Graph-based analysis: intervals and zeros\n## Function graph analysis with intervals\n# Exam 1.2 - 1.3 (Calculator Allowed)\n## Average rate of change and instantaneous rate\n## Temperature growth comparison\n## Average rate tables and AROC verification\n## Concavity and inflection point detection\n# Exam 1.4, 1.5 (No Calculator)\n## Number classification\n## Synthetic division\n## Factored form, multiplicity, and complex zeros\n## Degree and next values\n## Roots, rational root classification, and factoring","[{\"question\":\"What kinds of problems are included in Quiz 1.1 (No Calculator)?\",\"answer\":\"Quiz 1.1 includes function modeling from real-world situations, determining domain and range, and analyzing whether mappings or graphs represent functions. It also asks for increasing/decreasing intervals, concavity, inflection points, and approximate zeros from graphs.\"},{\"question\":\"How do the calculator-allowed exam questions define average vs. instantaneous rate of change?\",\"answer\":\"They first compute average rate of change over a given interval, then approximate the instantaneous rate at an endpoint using a small increment (k), and organize results in tables for verification.\"},{\"question\":\"What topics appear in the no-calculator exams related to algebra and polynomials?\",\"answer\":\"They include classifying number types (natural, whole, integer, rational/irrational/real, complex), synthetic division, completing tables for factored forms and multiplicities, and factoring polynomials to find and classify all zeros, including complex ones.\"}]","AP Precalculus - Quiz 1.1 - No Calculator | PDF",1790728173,71]