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The guide includes 15 representative questions covering trigonometry equations, rotational motion with wheel parameters, geometry with inscribed rectangles, inverse-trigonometric identities, complex number powers, continuity analysis from graphs, and average vs. instantaneous rates of change. Notes address calculator restrictions and key function definitions, with answer choices requiring careful scoring preparation.",{"@graph":14,"@context":65},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/mathematics-subtest-iii-sample-test-questions-for-cset-sample-questions-and-responses-and-scoring-information/394076/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/mathematics-subtest-iii-sample-test-questions-for-cset-sample-questions-and-responses-and-scoring-information/394076.png","ImageObject",300,407,{"name":42,"@type":43},"Stanley","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-04","2026-09-26",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",9,{"@type":57,"mainEntity":58},"FAQPage",[59],{"name":60,"@type":61,"acceptedAnswer":62},"How is log x defined in the Mathematics subtests?","Question",{"text":63,"@type":64},"The guide specifies that in CSET: Mathematics subtests, log x represents the base-10 logarithm of x.","Answer","https://schema.org",{"og:url":32,"og:type":67,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":69,"canonical":32},"index,follow",{"doc_id":71,"site_id":7},394076,1791083910,{"code":4,"msg":74,"data":75},"success",[76,80,84,87,92,97,102,107,111,114,118],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":77,"show_sort_weight":78,"slug":79},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":81,"show_sort_weight":82,"slug":83},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":85,"slug":86},70,"exam",{"id":88,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},5,"Comic",60,"comic",{"id":93,"doc_module":4,"doc_module_name":25,"category_name":94,"show_sort_weight":95,"slug":96},6,"Technology",50,"technology",{"id":98,"doc_module":4,"doc_module_name":25,"category_name":99,"show_sort_weight":100,"slug":101},7,"Healthcare",40,"healthcare",{"id":103,"doc_module":4,"doc_module_name":25,"category_name":104,"show_sort_weight":105,"slug":106},8,"Research & Report",30,"research-report",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":108,"show_sort_weight":109,"slug":110},"Religion & Spirituality",20,"religion-spirituality",{"id":109,"doc_module":4,"doc_module_name":25,"category_name":112,"show_sort_weight":109,"slug":113},"World Cup","world-cup",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":115,"slug":117},10,"Lifestyle","lifestyle",{"id":119,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":88,"slug":121},19,"General","general",{"code":4,"msg":74,"data":123},{"doc_id":71,"user_id":124,"nickname":42,"user_avatar":125,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":126,"file_id":127,"file_url":128,"file_type":129,"file_size":130,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":131,"language":132,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":133,"faqs":134,"seo_title":135,"seo_description":12,"update_tm":136,"read_time":137,"preview_page_count":4},2336477405376,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","| | California Subject Examinations for Teachers® |\n| --- | --- |\n| \u003Cbr>TEST GUIDE\u003Cbr>MATHEMATICS SUBTEST III\u003Cbr>Sample Questions and Responsesand Scoring Information |  |\n\nCopyright © 2014 Pearson Education, Inc. or its affiliate(s) . All rights reserved.  \nEvaluation Systems, Pearson, P.O. Box 226, Amherst, MA 01004  \nCalifornia Subject Examinations for Teachers, CSET, and the CSET logo are trademarks of the  \nCommission on Teacher Credentialing and Pearson Education, Inc. or its affiliate(s) . Pearson and its logo are trademarks, in the U.S. and/or other countries, of Pearson Education, Inc. or its affiliate(s) .  \nCS-TG-QR213X-01  \nSample Test Questions for CSET: Mathematics Subtest III  \nBelow is a set of multiple-choice questions and constructed-response questions that are similar to the questions you will see on Subtest III of CSET: Mathematics. Please note that, as on the actual test form, approximately one third of the multiple-choice questions in this test guide are more complex questions that require 2–3 minutes each to complete. You are encouraged to respond to the questions without looking at the responses provided in the next section. Record your responses on a sheet of paper and compare them with the provided responses.  \nNote: The use of calculators is not allowed for CSET: Mathematics Subtest III.  \nNote: In CSET: Mathematics subtests, log x represents the base-10 logarithm of x.  \n1. What are the solutions to tanx +  = 3 where 0 ≤ x ≤ 2π?  \nA. ~~ ~~11~~6~~π , 5π~~6~~  \nB. ~~ ~~5π~~3~~ , 2π~~3~~  \nC. ~~ ~~ , 4π~~3~~  \nD. ~~ ~~ , 7π~~6~~  \n2. Use the diagram below to answer the question that follows.  \ny  \nPoint P is on the edge of a wheel of radius of 1 that rotates counterclockwise around the origin at a speed of 15 revolutions per second. At t = 0, P has coordinates (–1, 0) . Which of the following functions could be used to describe the x-coordinate of P as a function of time, t, measured in seconds?  \nA. x(t) = sin(30πt)–1  \nB. x(t) = –sin21π5~~t~~ –1  \nC. x(t) = –cos(30πt)  \nD. x(t) = –cos21π5~~t~~  \n3. Use the diagram below to answer the question that follows.  \ny  \nThe diagram shows a rectangle inscribed in a circle of radius r. What is the area of the rectangle as a function of the angle θ?  \nA. 4r tan θ  \nB. r2 􀁾 cos θ sin θ􀁾  \nC. 4r2 tan2θ  \nD. 4r2 􀁾 cos θ sin θ􀁾  \n4. Which of the following expressions is equal to sinarccos x~~3~~?  \nA. ~~93~~–~~ ~~x2  \nB. ~~ ~~±~~ ~~~~93~~–~~ ~~x2  \nC.  9 + x2  \nx  \nD. ~~9􀁾 ~~~~􀁾 ~~x2  \n5. Given that z = cos 75° + i sin 75°, which of the following best represents z 3 in vector form?  \nA. B.  \nimaginary imaginary  \nreal  real  \nC. D.  \nimaginary imaginary  \nreal  real  \n6. Use the graph below to answer the question that follows.  \nLet f(x) be the function whose graph is shown above. Which of the following statements best describes why f(x) is discontinuous at x = c?  \nA. f(c) does not exist  \nB. c f(x) ≠ f(c)  \nC. c f(x) does not exist  \nD. f'(c) ≠ f'(c + ∆x)  \n7. Let f(x) and g(x) be functions such that c f(x) and c g(x) exist. If c [f(x) + g(x)] = 6 and c [2f(x)– g(x)] = 1, what is c f(x)?  \nA. ~~ ~~72 B. ~~ ~~7~~3 ~~C. ~~ ~~52 D. ~~ ~~5~~3~~  \n8. For which of the following values of k does lim sin x + sin x cos2x  \nx→k sin x cos x equal –2?  \nA. ~~ ~~π2  \nB. π  \nC. ~~ 3~~π2  \nD. 2π  \n9. Given the function g(x) = ~~3~~x22x–2~~9~~–x~~3~~–212 for x ≠ 4, define g(4) so that g(x) is continuous at x = 4.  \nA. g(4) = 0  \nB. g(4) = 2~~3~~  \nC. g(4) = ~~ ~~11~~6~~5  \nD. g(4) = ~~83~~  \n10. If f(x) is continuous on the interval [a , b], and N is any number strictly between f(a) and f(b), which of the following must be true?  \nA. The inverse of f(x) is defined on the interval [f(a), f(b)] .  \nB. There exists a number c in (a, b) such that f(c) = N.  \nC. f(x) is differentiable on the interval (a, b) .  \nD. There exists a number c in (a, b) such that f'(c) = 0.  \n11. An economist needs to approximate the function f(x) = 1x by a line tangent to f(x) at x = –1. Which of the foll","cbCaivRudIqcPm0U","https://ap.wps.com/l/cbCaivRudIqcPm0U","pdf",451952,27,"English","# Sample Test Questions for CSET: Mathematics Subtest III\n## Multiple-choice and constructed-response questions","[{\"question\":\"How is log x defined in the Mathematics subtests?\",\"answer\":\"The guide specifies that in CSET: Mathematics subtests, log x represents the base-10 logarithm of x.\"}]","MATHEMATICS SUBTEST III - Sample Test Questions for CSET - Sample Questions and Responses, and Scoring Information | PDF",1790398386,68]