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Students answer questions about limit existence, one-sided limits, vertical asymptotes, and removable discontinuities using algebraic reasoning and graph-based interpretation. The quiz also tests estimating instantaneous rate of change, applying continuity conditions, solving derivative-related expressions, and using Intermediate Value Theorem requirements. Explanations are provided for multiple-choice selections.",{"@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/ap-calculus-bc-unit-1-quiz-practice-questions/451860/",{"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-calculus-bc-unit-1-quiz-practice-questions/451860.png","ImageObject",300,407,{"name":92,"@type":93},"Jiven","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-19","2026-09-30",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",11,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How do I choose an interval to estimate the instantaneous rate of change for f(x)?","Question",{"text":113,"@type":114},"Use the interval from the choices that centers around the x-value where the instantaneous rate is requested (so the average rate of change best approximates the instantaneous rate).","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What condition(s) must be met for a function to be continuous at x = a?",{"text":118,"@type":114},"The function value f(a) must exist, the limit as x→a must exist, and the limit as x→a must equal f(a).",{"name":120,"@type":111,"acceptedAnswer":121},"How can I determine whether there is a zero between -3 and 3?",{"text":122,"@type":114},"Apply the Intermediate Value Theorem: if the function is continuous on [-3, 3] and f(-3) and f(3) have opposite signs, then a zero exists between them.","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},451860,1790884547,{"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},1099513958607,"https://ap-avatar.wpscdn.com/avatar/100002390cf8733938c?x-image-process=image/resize,m_fixed,w_180,h_180&k=1778829742770036399","AP Calculus BC Unit 1 Quiz  \n1. What is  \n?  \na. 13  \nb. Limit does not Exist  \nc. 43  \nd. 0  \n2. What is  \n?  \na. Limit Does not Exist  \nb. 3  \nc. 0  \nd. 3 sin x  \n3. What are the vertical asymptotes of: Y =  ?  \ni. x = 3  \nii. x = -3  \niii. x = -½  \na. I  \nb. II  \nc. I and III  \nd. I and II  \ne. I, II, III  \n4. If a student were to try and find the estimate the instantaneous rate of change off(x) = x3 − 4x2 + 7 at x = 2, which interval would be best to use to estimate the instantaneous rate of change?  \na. 3 ≤ x ≤ 4.5  \nb. 2.75 ≤ x ≤ 3.25  \nc. 2 ≤ x ≤ 3  \nd. 3 ≤ x ≤ 3.5  \n5. What is the limit as x goes to-1 of F(x) as seen on the graph?  \n6. What is the  \na. 0  \nb. Limit Does Not Exist  \nc. 2  \nd. 1  \n7. What is the limit as x goes to-3 from the left side?  \na. DNE  \nb. 6  \nc. 2  \nd. 7  \n8. What is the limit as x goes-5 of H(x)?  \na. -⅙  \nb. ⅙  \nc. -9  \nd. 5  \n9. What is the limit?  \na. 0/0  \nb. DNE  \nc. 12  \nd. Infinity  \n10. If the lim f(x) = 2 and lim g (x) = 4 , what is the lim f(x) + g (x) − 2 ?  \nx → c x → c x → c  \na. 6  \nb. DNE  \nc. 4  \nd. 14  \n11. Using the function  , for what values does there exist a removable discontinuity?  \nx=5  \na. x=7  \nb. x=2  \nc. NONE  \n12. Using the table, what is the lim 3sin(h(x))? x → 2  \na. 0  \nb. 3  \nc. DNE  \nd. -3  \n13. What is the lim f(x)? x → −1+  \na. DNE  \nb. 0  \nc. -1  \nd. 1  \n14. What is the lim f(x) ? x → 0  \na. 1  \nb. 0  \nc. -1  \nd. 3  \n15. What are the main requirements for a function to be considered continuous at a x value, x = a?  \ni. f(a) must be an actual, existing value  \nii. the lim equals f(a)  \nx → a  \niii.the lim exists  \nx → a  \na. I  \nb. III  \nc. I & III  \nd. I, II, III  \n16. What is the derivative of m(x), if m(x) = √1 − 5x ?  \na.  5  2√1−5x  \nb.  − 5  2√1−5x  \nc. 5/2  \nd. -½( √1 − 5x )  \n17. What is the lim 4xx8 ? x →∞  \na. DNE  \nb. 0  \nc. - ∞  \nd. ∞  \n18. What are the vertical asymptotes of f(x)= ~~((~~7x+22~~) )((~~x7x32~~))~~ ?  \na. x = -2  \nb. x-2/7  \nc. x = -2, x = -2/7  \nd. x = 0  \n19. Suppose we have a function, f(x), where f is continuous on [-3,3], f(-3) = 4 and f(3) = -2, is there a zero between-3 and 3?  \na. Yes, there is a zero.  \nb. Not enough information  \nc. No, there is no zero.  \nd. There is a zero at-3, but not between-3 and 3.  \n20. What are the parts of the Intermediate Value Theorem?  \ni. Function is continuous on domain [a, b] ii.f(a) and f(b) are not equal  \niii. Desired number is between f(a) and f(b)  \niv. Function is differentiable on 9a,b)  \na. I  \nb. II  \nc. III  \nd. I & IV  \ne. I, II, III, IV  \nf. I,II,III  \nExplanations  \n1. The answer is (A. 13). In order to find this limit, simply plug in 8, because the problem asks “as x goes to 8”. When 8 is plugged into the equation in the parenthesis, the answer is 13.  \n2. The answer is (C. 0). In this case, simply plug in 0, and since no indeterminant is found, we can continue and solve for the answer, which ends up being 0.  \n3. The answer is (A. I). The vertical asymptotes can be derived from the equation by setting the denominator to 0, or factoring the denominator. In this case, setting (x-3) equal to 0 gives us, X = 3; therefore A is the right answer.  \n4. The answer is B, because the value x = 3 lies directly in the middle of the interval in answer choice B, meaning that the average rate of change of that interval would be closest to the instantaneous rate of change at x = 3.  \n5. The answer is C, because at x = -1, there is a jump in the graph, meaning that the limit does not exist at this point, x = -1, because the limit as x approaches-1 from the left does not equal the limit as x approaches-1 from the right.  \n6. The answer is D. According to the rules of trig limits, the sin(x) in the numerator cancelsand the x in the denominator simplifies to 1. When 0 is plugged into cos (x) the answer is 1.  \n1 times 1 is 1.  \n7. The answer is B. This is because as x approaches the x-value-3 from the left, it approaches the y-value y = 6.  \n8. The answer is C, -9, because the number-5 is not ","cbCaiq1VBTIQK2DG","https://ap.wps.com/l/cbCaiq1VBTIQK2DG","pdf",1559823,"English","# AP Calculus BC Unit 1 Quiz\n## Limit, continuity, and asymptotes questions\n## Derivative and Instantaneous rate of change questions\n## Intermediate Value Theorem and continuity requirements","[{\"question\":\"How do I choose an interval to estimate the instantaneous rate of change for f(x)?\",\"answer\":\"Use the interval from the choices that centers around the x-value where the instantaneous rate is requested (so the average rate of change best approximates the instantaneous rate).\"},{\"question\":\"What condition(s) must be met for a function to be continuous at x = a?\",\"answer\":\"The function value f(a) must exist, the limit as x→a must exist, and the limit as x→a must equal f(a).\"},{\"question\":\"How can I determine whether there is a zero between -3 and 3?\",\"answer\":\"Apply the Intermediate Value Theorem: if the function is continuous on [-3, 3] and f(-3) and f(3) have opposite signs, then a zero exists between them.\"}]","AP Calculus BC Unit 1 Quiz - Practice Questions | PDF",1790736069]