{"id":9011,"date":"2017-02-10t20:55:56","date_gmt":"2017-02-11t04:55:56","guid":{"rendered":"\/\/www.catharsisit.com\/hs\/?p=9011"},"modified":"2017-02-10t19:57:47","modified_gmt":"2017-02-11t03:57:47","slug":"ap-calculus-multiple-choice-practice-problems","status":"publish","type":"post","link":"\/\/www.catharsisit.com\/hs\/ap\/ap-calculus-multiple-choice-practice-problems\/","title":{"rendered":"ap calculus multiple choice practice problems"},"content":{"rendered":"<p>the best way to study for the ap calculus exam, whether that is calculus ab or calculus bc, is to do practice problems. they will give you an idea of the types of problems that you may encounter, reinforce what you already know, and learn how to approach problems that you have never seen before. the following is a handful of ap style multiple choice practice problems (for calc ab), with the full solutions given. this is certainly not an exhaustive list of all the topics and types of questions, but just some extra ap calculus multiple choice practice problems that can be used along with your textbook, ap calculus review books, and old ap exams.<\/p>\n<p>for the following practice problems, calculators are not permitted.<\/p>\n<h2>practice problems<\/h2>\n<p>1.<\/p>\n<p><img decoding=\"async\" class=\"alignnone size-full wp-image-9012\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/screen-shot-2017-02-09-at-5.19.43-pm.png\" alt=\"ap calculus multiple choice practice problems\" width=\"111\" height=\"61\" \/><\/p>\n<p>what is f(g(2))?<\/p>\n<p>a) -12<br \/>\nb) -8<br \/>\nc) -0<br \/>\nd) 8<br \/>\ne) 12<\/p>\n<p>2. calculate the following integral:<\/p>\n<p><img decoding=\"async\" class=\"alignnone size-full wp-image-9013\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/screen-shot-2017-02-09-at-5.19.46-pm.png\" alt=\"\" width=\"66\" height=\"57\" \/><\/p>\n<p>a) -1\/9<br \/>\nb) -1\/27<br \/>\nc) 0<br \/>\nd) 1\/27<br \/>\ne) 4\/ 9<\/p>\n<p>3. find the slope of the line tangent to the function f(x) at x = 2<\/p>\n<p><img decoding=\"async\" class=\"alignnone size-full wp-image-9014\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/screen-shot-2017-02-09-at-5.19.48-pm.png\" alt=\"\" width=\"138\" height=\"27\" \/><\/p>\n<p>a) 17\/16<br \/>\nb) 9\/8<br \/>\nc) -9\/8<br \/>\nd) 2<br \/>\ne) 1<\/p>\n<p>4.<\/p>\n<p><img decoding=\"async\" class=\"alignnone wp-image-9015\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/screen-shot-2017-02-09-at-5.19.57-pm.png\" alt=\"\" width=\"125\" height=\"38\" \/><\/p>\n<p>a) \u221e<br \/>\nb) -\u221e<br \/>\nc) 0<br \/>\nd) -1\/2<br \/>\ne) 1\/2<\/p>\n<p>5. compute the definite integral below:<\/p>\n<p><img decoding=\"async\" class=\"alignnone size-full wp-image-9016\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/screen-shot-2017-02-09-at-5.20.08-pm.png\" alt=\"\" width=\"98\" height=\"45\" \/><\/p>\n<p>a) -\/2<br \/>\nb) 0<br \/>\nc) \/4<br \/>\nd) \/2<br \/>\ne)<\/p>\n<p>6. find dy\/dx for f(x):<\/p>\n<p><img decoding=\"async\" class=\"alignnone size-full wp-image-9018\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/screen-shot-2017-02-09-at-5.20.48-pm.png\" alt=\"\" width=\"63\" height=\"46\" \/><\/p>\n<p>a)<img decoding=\"async\" class=\"alignnone size-full wp-image-9017\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/screen-shot-2017-02-09-at-5.20.12-pm.png\" alt=\"\" width=\"106\" height=\"55\" \/><br \/>\nb)<img decoding=\"async\" class=\"alignnone size-full wp-image-9019\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/screen-shot-2017-02-09-at-5.20.51-pm.png\" alt=\"\" width=\"57\" height=\"47\" \/><br \/>\nc)<img decoding=\"async\" class=\"alignnone size-full wp-image-9020\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/screen-shot-2017-02-09-at-5.20.55-pm.png\" alt=\"\" width=\"225\" height=\"52\" \/><br \/>\nd)<img decoding=\"async\" class=\"alignnone size-full wp-image-9021\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/screen-shot-2017-02-09-at-5.20.57-pm.png\" alt=\"\" width=\"51\" height=\"40\" \/><br \/>\ne)<img decoding=\"async\" class=\"alignnone size-full wp-image-9022\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/screen-shot-2017-02-09-at-5.21.00-pm.png\" alt=\"\" width=\"171\" height=\"48\" \/><\/p>\n<p>7.<img decoding=\"async\" class=\"alignnone size-full wp-image-9023\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/screen-shot-2017-02-09-at-5.21.13-pm.png\" alt=\"\" width=\"142\" height=\"60\" \/><\/p>\n<p>a) 0<br \/>\nb) -1\/5<br \/>\nc) 0<br \/>\nd) 1\/5<br \/>\ne) \u221e<\/p>\n<p>8. what is the area bounded between the graphs of<\/p>\n<p><img decoding=\"async\" class=\"alignnone size-full wp-image-9024\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/screen-shot-2017-02-09-at-5.21.16-pm.png\" alt=\"\" width=\"91\" height=\"42\" \/><\/p>\n<p>a) -4<br \/>\nb) 0<br \/>\nc) -32\/3<br \/>\nd) 32\/3<br \/>\ne) 32<\/p>\n<p>9. \u00a0<img decoding=\"async\" class=\"alignnone wp-image-9025\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/screen-shot-2017-02-09-at-5.21.24-pm.png\" alt=\"\" width=\"171\" height=\"37\" \/><\/p>\n<p>find dy\/dx<\/p>\n<p>a)<img decoding=\"async\" class=\"alignnone size-full wp-image-9026\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/screen-shot-2017-02-09-at-5.21.28-pm.png\" alt=\"\" width=\"57\" height=\"40\" \/><\/p>\n<p>b)<img decoding=\"async\" class=\"alignnone size-full wp-image-9027\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/screen-shot-2017-02-09-at-5.21.32-pm.png\" alt=\"\" width=\"56\" height=\"38\" \/><\/p>\n<p>c)<img decoding=\"async\" class=\"alignnone size-full wp-image-9030\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/screen-shot-2017-02-09-at-5.21.40-pm.png\" alt=\"\" width=\"99\" height=\"21\" \/><\/p>\n<p>d)<img decoding=\"async\" class=\"alignnone size-full wp-image-9029\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/screen-shot-2017-02-09-at-5.21.38-pm.png\" alt=\"\" width=\"101\" height=\"22\" \/><\/p>\n<p>e)<img decoding=\"async\" class=\"alignnone size-full wp-image-9028\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/screen-shot-2017-02-09-at-5.21.35-pm.png\" alt=\"\" width=\"88\" height=\"39\" \/><\/p>\n<p>10. where does the following function have a local maximum?<\/p>\n<p><img decoding=\"async\" class=\"alignnone size-full wp-image-9031\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/screen-shot-2017-02-09-at-5.21.43-pm.png\" alt=\"\" width=\"138\" height=\"29\" \/><\/p>\n<p>a) x = -3<br \/>\nb) x = 0<br \/>\nc) x = 3<br \/>\nd) x = 9<br \/>\ne) x = 27<\/p>\n<h2>solutions<\/h2>\n<p>1.first, we evaluate g(2) to get -2\/(4+1) = -2\/5<br \/>\nplugging this into f(x), we can evaluate f(-2\/5) = 5*(-2\/5)-10 = -12<\/p>\n<p>answer: a) \u201312<\/p>\n<p>2.this is a fairly straightforward integral that can be solved using the power rule. it\u2019s easier to think it as<\/p>\n<p><img decoding=\"async\" class=\"size-full wp-image-9032 alignnone\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/screen-shot-2017-02-09-at-5.21.57-pm.png\" alt=\"\" width=\"192\" height=\"32\" \/><\/p>\n<p><img decoding=\"async\" class=\"size-full wp-image-9055 alignnone\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/screen-shot-2017-02-09-at-5.31.49-pm.png\" alt=\"\" width=\"124\" height=\"42\" \/><\/p>\n<p>answer: e) 4\/9<\/p>\n<p>3. anytime we need to find the slope, our first thought should be \u2018find the derivative of the function.&#8217;<\/p>\n<p><img decoding=\"async\" class=\"alignnone size-full wp-image-9034\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/screen-shot-2017-02-09-at-5.22.03-pm.png\" alt=\"\" width=\"158\" height=\"29\" srcset=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/screen-shot-2017-02-09-at-5.22.03-pm.png 158w, \/\/www.catharsisit.com\/hs\/files\/2017\/02\/screen-shot-2017-02-09-at-5.22.03-pm-150x29.png 150w\" sizes=\"(max-width: 158px) 100vw, 158px\" \/><\/p>\n<p>plug in x = 2 to find the slope:<\/p>\n<p><img decoding=\"async\" class=\"alignnone size-full wp-image-9035\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/screen-shot-2017-02-09-at-5.22.05-pm.png\" alt=\"\" width=\"229\" height=\"46\" \/><\/p>\n<p>answer: a) 17\/16<\/p>\n<p>4. the solution to this question does not involve any calculation. anytime we are asked to evaluate a limit as x approaches infinity, look at the degree of the top and bottom equations. if they\u2019re different, our solution is already given. since in this case, the denominator has a larger degree equation, the limit approaches 0.<\/p>\n<p>answer: c) 0<\/p>\n<p>5. this is one of our common derivatives\/integrals which we should know.<\/p>\n<p><img decoding=\"async\" class=\"alignnone size-full wp-image-9036\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/screen-shot-2017-02-09-at-5.22.09-pm.png\" alt=\"\" width=\"157\" height=\"36\" \/><\/p>\n<p><img decoding=\"async\" class=\"alignnone size-full wp-image-9038\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/screen-shot-2017-02-09-at-5.22.30-pm.png\" alt=\"\" width=\"151\" height=\"53\" \/><\/p>\n<p>answer: c) <img decoding=\"async\" class=\"alignnone wp-image-9057\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/screen-shot-2017-02-09-at-5.34.39-pm.png\" alt=\"\" width=\"39\" height=\"28\" \/><\/p>\n<p>6. this is the <a href=\"\/\/www.catharsisit.com\/hs\/ap\/calculus-review-derivative-rules\/\">quotient rule<\/a>:<\/p>\n<p><img decoding=\"async\" class=\"size-full wp-image-9039 alignnone\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/screen-shot-2017-02-09-at-5.22.34-pm.png\" alt=\"\" width=\"98\" height=\"41\" \/><\/p>\n<p><img decoding=\"async\" class=\"alignnone size-full wp-image-9040\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/screen-shot-2017-02-09-at-5.22.39-pm.png\" alt=\"\" width=\"180\" height=\"40\" \/><\/p>\n<p>in our case:<\/p>\n<p><img decoding=\"async\" class=\"size-full wp-image-9041 alignnone\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/screen-shot-2017-02-09-at-5.22.42-pm.png\" alt=\"\" width=\"189\" height=\"42\" \/><br \/>\n<img decoding=\"async\" class=\"alignnone size-full wp-image-9043\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/screen-shot-2017-02-09-at-5.23.07-pm.png\" alt=\"\" width=\"220\" height=\"44\" \/><br \/>\nanswer: c)<img decoding=\"async\" class=\"alignnone size-full wp-image-9043\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/screen-shot-2017-02-09-at-5.23.07-pm.png\" alt=\"\" width=\"220\" height=\"44\" \/> (this can also be reduced to a simpler form.)<\/p>\n<p>7. in this case, the denominator and numerator both evaluate to 0. however, if we factor the top and bottom, we notice that a term cancels out<\/p>\n<p><img decoding=\"async\" class=\"alignnone size-full wp-image-9044 alignnone\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/screen-shot-2017-02-09-at-5.23.12-pm.png\" alt=\"\" width=\"224\" height=\"39\" \/><\/p>\n<p><img decoding=\"async\" class=\"alignnone size-full wp-image-9045 alignnone\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/screen-shot-2017-02-09-at-5.23.17-pm.png\" alt=\"\" width=\"100\" height=\"43\" \/><\/p>\n<p>answer: b) -1\/5<\/p>\n<p>8. when we see &#8216;area bounded by,&#8217; we need to take a definite integral between the points where the graphs intersect. in this case, in since the second equation is y = 0, our limits are the roots of our first equation, x = -2, or x = 2<br \/>\n<img decoding=\"async\" class=\"alignnone size-full wp-image-9046\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/screen-shot-2017-02-09-at-5.23.20-pm.png\" alt=\"\" width=\"195\" height=\"38\" \/><br \/>\n<img decoding=\"async\" class=\"alignnone size-full wp-image-9047\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/screen-shot-2017-02-09-at-5.23.24-pm.png\" alt=\"\" width=\"173\" height=\"38\" \/><br \/>\n<img decoding=\"async\" class=\"alignnone size-full wp-image-9048\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/screen-shot-2017-02-09-at-5.23.26-pm.png\" alt=\"\" width=\"193\" height=\"45\" \/><br \/>\nanswer: d) 32\/3<\/p>\n<p>9. this is an implicit differentiation problem.<\/p>\n<p><img decoding=\"async\" class=\"alignnone size-full wp-image-9049\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/screen-shot-2017-02-09-at-5.23.29-pm.png\" alt=\"\" width=\"189\" height=\"40\" \/><\/p>\n<p>solving for dy\/dx<\/p>\n<p><img decoding=\"async\" class=\"alignnone size-full wp-image-9050\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/screen-shot-2017-02-09-at-5.23.32-pm.png\" alt=\"\" width=\"113\" height=\"49\" \/><\/p>\n<p>we can reduce this to<\/p>\n<p><img decoding=\"async\" class=\"alignnone size-full wp-image-9051\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/screen-shot-2017-02-09-at-5.23.35-pm.png\" alt=\"\" width=\"99\" height=\"40\" \/><\/p>\n<p>answer: b)<img decoding=\"async\" class=\"alignnone size-full wp-image-9051\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/screen-shot-2017-02-09-at-5.23.35-pm.png\" alt=\"\" width=\"99\" height=\"40\" \/><\/p>\n<p>10. anytime we are looking for a local maximum, our first step is to take a look at the derivate.<\/p>\n<p><img decoding=\"async\" class=\"alignnone size-full wp-image-9053\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/screen-shot-2017-02-09-at-5.23.47-pm.png\" alt=\"\" width=\"98\" height=\"26\" \/><\/p>\n<p>solving for the root of this, we get<\/p>\n<p><img decoding=\"async\" class=\"alignnone size-full wp-image-9054\" src=\"\/\/www.catharsisit.com\/hs\/files\/2017\/02\/screen-shot-2017-02-09-at-5.23.51-pm.png\" alt=\"\" width=\"109\" height=\"51\" \/><\/p>\n<p>the equation has a min and a max at x = 3, and x = -3. you know the max is at x = -3, because if we plug x = -4 into the equation for f\u2019(x), we get a positive answer, so we know the function is increasing before that point.<\/p>\n<p>answer: c) x =3<\/p>\n","protected":false},"excerpt":{"rendered":"<p>this post has ap calculus multiple choice practice problems with full solutions. <\/p>\n","protected":false},"author":224,"featured_media":9013,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[240],"tags":[241],"ppma_author":[24930],"acf":[],"yoast_head":"<!-- this site is optimized with the yoast seo premium plugin v21.7 (yoast seo v21.7) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>ap calculus multiple choice practice problems - magoosh blog | high school<\/title>\n<meta name=\"description\" content=\"looking for ap calc preparation and review? click this post for ap calculus multiple choice practice problems 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