{"id":18564,"date":"2025-03-03T13:00:23","date_gmt":"2025-03-03T13:00:23","guid":{"rendered":"http:\/\/www.kaptest.com\/blog\/prep\/?p=18564"},"modified":"2025-03-14T18:33:34","modified_gmt":"2025-03-14T18:33:34","slug":"ap-calculus-practice-questions","status":"publish","type":"post","link":"https:\/\/wpapp.kaptest.com\/study\/ap-calculus\/ap-calculus-practice-questions\/","title":{"rendered":"AP Calculus Practice Questions"},"content":{"rendered":"\n<p>Test your readiness for the AP Calculus exam with this quiz!<br><\/p>\n\n\n<div  class='avia-builder-widget-area clearfix  avia-builder-el-0  el_before_av_promobox  avia-builder-el-first '><div id=\"custom_html-14\" class=\"widget_text widget clearfix widget_custom_html\"><div class=\"textwidget custom-html-widget\"><div><div class='op-interactive' id='635828a32d2a0e31d4557600' data-title='AP Calculus Quiz' data-url='https:\/\/kaplannorthamerica.outgrow.us\/635828a32d2a0e31d4557600?vHeight=1' data-width='100%'><\/div><script src='\/\/dyv6f9ner1ir9.cloudfront.net\/assets\/js\/nloader.js'><\/script><script>initIframe('635828a32d2a0e31d4557600');<\/script><\/div><\/div><\/div><\/div>\n\n\n\n<div style=\"height:30px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<hr class=\"wp-block-separator is-style-wide\"\/>\n\n\n\n<div class=\"wp-block-columns\">\n<div class=\"wp-block-column\" style=\"flex-basis:66.66%\">\n<h4 class=\"has-text-color\" style=\"color:#ab0c78\"><strong>FREE PREMIUM CONTENT<\/strong><\/h4>\n\n\n\n<h4 class=\"has-col-240-f-6-e-color has-text-color\"><strong>AP Calculus Formulas &amp; Theorems Sheet<\/strong><\/h4>\n\n\n\n<p>Download a free list of formulas and theorems you should know for the AP Calc exam!<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column\" style=\"flex-basis:33.33%\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-col-ffffff-color has-col-AB0C78-background-color has-text-color has-background\" data-sumome-listbuilder-id=\"6b4676b0-93fb-4e26-9132-e784ca6e2d36\">Download<\/a><\/div>\n<\/div>\n<\/div>\n\n\n\n<hr class=\"wp-block-separator is-style-wide\"\/>\n\n\n<p><!-- \/wp:columns --><\/p>\n<p>\t<div   class='av_promobox  avia-button-no   avia-builder-el-1  el_after_av_sidebar  el_before_av_toggle_container '>\t\t<div class='avia-promocontent'><p><strong>AP Calculus Free Practice Question #1<\/strong><\/p>\n<p>A function f is defined by f(x)=|x+ 4|. For what values of x is the graph of f not differentiable?<br \/>A: x = -4<br \/>B: x = 0<br \/>C: x = 4<br \/>D: The function is differentiable over its entire domain.<\/p>\n<\/div><\/div><br \/><div  class=\"togglecontainer    avia-builder-el-2  el_after_av_promobox  el_before_av_promobox \" ><section class=\"av_toggle_section\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\"  >    <div role=\"tablist\" class=\"single_toggle\" data-tags=\"{All} \"  >        <p data-fake-id=\"#toggle-id-1\" class=\"toggler \"  itemprop=\"headline\"    role=\"tab\" tabindex=\"0\" aria-controls=\"toggle-id-1\">Answer 1<span class=\"toggle_icon\" >        <span class=\"vert_icon\"><\/span><span class=\"hor_icon\"><\/span><\/span><\/p>        <div id=\"toggle-id-1\" class=\"toggle_wrap \"  >            <div class=\"toggle_content invers-color \"  itemprop=\"text\"   ><p><strong>A<\/strong><b>:\u00a0<\/b>If the graph of a function has a sharp point, the function is not differentiable at that point. This is because the slopes directly to the left and right of the point do not approach the same value.<br \/>An absolute value function has a sharp point at its vertex. The graph off(x)=|x + 4| is a horizontal translation (to the left 4 units) of the standard absolute value function, y =|x|, which has vertex (0, 0). Thus, the vertex of fis (-4, 0), which means the function is not differentiable at x =-4. Choice (A) is correct.<\/p>\n            <\/div>        <\/div>    <\/div><\/section><\/div><br \/>\t<div   class='av_promobox  avia-button-no   avia-builder-el-3  el_after_av_toggle_container  el_before_av_toggle_container '>\t\t<div class='avia-promocontent'><p><strong>AP Calculus Free Practice Question #2<\/strong><\/p>\n<p>The function f has a removable discontinuity at:<br \/>A: x = -2 only<br \/>B: x = 0 only<br \/>C: x = -2 and x = 0<br \/>D: f(x) has no removable discontinuities<\/p>\n<\/div><\/div><br \/><div  class=\"togglecontainer    avia-builder-el-4  el_after_av_promobox  el_before_av_promobox \" ><section class=\"av_toggle_section\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\"  >    <div role=\"tablist\" class=\"single_toggle\" data-tags=\"{All} \"  >        <p data-fake-id=\"#toggle-id-2\" class=\"toggler \"  itemprop=\"headline\"    role=\"tab\" tabindex=\"0\" aria-controls=\"toggle-id-2\">Answer 2<span class=\"toggle_icon\" >        <span class=\"vert_icon\"><\/span><span class=\"hor_icon\"><\/span><\/span><\/p>        <div id=\"toggle-id-2\" class=\"toggle_wrap \"  >            <div class=\"toggle_content invers-color \"  itemprop=\"text\"   ><p><strong>D:<\/strong>\u00a0The only discontinuities that are removable are holes and holes with a point above or below\u2014this function has neither. The function has 2 jump discontinuities (gaps), at x=-2 and x= 0, but neither of these is removable.<\/p>\n            <\/div>        <\/div>    <\/div><\/section><\/div><br \/>\t<div   class='av_promobox  avia-button-no   avia-builder-el-5  el_after_av_toggle_container  el_before_av_toggle_container '>\t\t<div class='avia-promocontent'><p><strong>AP Calculus Free Practice Question #3<\/strong><\/p>\n<p>Using only the table of values shown in the quiz above, which of the following best describes f\u2032(x) and f\u2032\u2032(x) over the open interval (-1, 1)?<\/p>\n<p>A:\u00a0f\u2032(x) &lt; 0; f\u2032\u2032(x) &lt; 0<br \/>B:\u00a0f\u2032(x) &lt; 0; f\u2032\u2032(x) = 0<br \/>C:\u00a0f\u2032(x) &gt; 0; f\u2032\u2032(x) &lt; 0<br \/>D:\u00a0f\u2032(x) &gt; 0; f\u2032\u2032(x) = 0<\/p>\n<\/div><\/div><br \/><div  class=\"togglecontainer    avia-builder-el-6  el_after_av_promobox  el_before_av_promobox \" ><section class=\"av_toggle_section\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\"  >    <div role=\"tablist\" class=\"single_toggle\" data-tags=\"{All} \"  >        <p data-fake-id=\"#toggle-id-3\" class=\"toggler \"  itemprop=\"headline\"    role=\"tab\" tabindex=\"0\" aria-controls=\"toggle-id-3\">Answer 3<span class=\"toggle_icon\" >        <span class=\"vert_icon\"><\/span><span class=\"hor_icon\"><\/span><\/span><\/p>        <div id=\"toggle-id-3\" class=\"toggle_wrap \"  >            <div class=\"toggle_content invers-color \"  itemprop=\"text\"   ><p><strong>D:<\/strong>\u00a0Examine the values in the table: f(x) increases as x gets larger, which indicates that f\u2032(x), the slope of the function, is positive. This means f\u2032(x)&gt; 0, so eliminate (A) and (B).<br \/>To\u00a0choose between (C) and (D), take a closer look at the slopes. The slope between the first pair of points is 3, and the slope between the second pair of points is also 3, so f\u2032(x) is constant. This means f\u2032\u2032(x), which is the derivative of f\u2032(x), must be 0. Choice (D) is correct<\/p>\n            <\/div>        <\/div>    <\/div><\/section><\/div><br \/>\t<div   class='av_promobox  avia-button-no   avia-builder-el-7  el_after_av_toggle_container  el_before_av_toggle_container '>\t\t<div class='avia-promocontent'><p><strong>AP Calculus Free Practice Question #4<\/strong><br \/>Let f(x) be a differentiable function with f(-1)= 5 and f'(-1)= 2. Use the given information to find the local linear approximation of f(-0.9).<br \/>A: 4.9<br \/>B: 5.1<br \/>C: 5.2<br \/>D: 5.3<\/p>\n<\/div><\/div><br \/><div  class=\"togglecontainer    avia-builder-el-8  el_after_av_promobox  el_before_av_promobox \" ><section class=\"av_toggle_section\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\"  >    <div role=\"tablist\" class=\"single_toggle\" data-tags=\"{All} \"  >        <p data-fake-id=\"#toggle-id-4\" class=\"toggler \"  itemprop=\"headline\"    role=\"tab\" tabindex=\"0\" aria-controls=\"toggle-id-4\">Answer 4<span class=\"toggle_icon\" >        <span class=\"vert_icon\"><\/span><span class=\"hor_icon\"><\/span><\/span><\/p>        <div id=\"toggle-id-4\" class=\"toggle_wrap \"  >            <div class=\"toggle_content invers-color \"  itemprop=\"text\"   ><p><strong>C:<\/strong> To use a local linear approximation, you need to find the equation of the tangent line. You\u2019ve been given all the information you need in the question stem; you just need to piece it all together. The point on the function is given by f(-1)= 5, which translates to the point (-1, 5). The slope of the tangent line at x=-1 is given by f'(-1)= 2, so the slope is 2. Now the point-slope form of the tangent line is:<br \/>y-5 = 2(x-(-1))<br \/>y = 5+2(x+1)<br \/>Substituting x=-0.9 into the equation of the tangent line yields:<br \/>5+2(-0.9+1) = 5+2(0.1) = 5.2<br \/>That\u2019s (C).<\/p>\n            <\/div>        <\/div>    <\/div><\/section><\/div><br \/>\t<div   class='av_promobox  avia-button-no   avia-builder-el-9  el_after_av_toggle_container  el_before_av_toggle_container '>\t\t<div class='avia-promocontent'><p><strong>AP Calculus Free Practice Question #5<\/strong><\/p>\n<p>The graph of f(x) is shown above. Which of the following is the graph of f'(x) ? (Letters correspond with the image directly to their right)<\/p>\n<\/div><\/div><br \/><div  class=\"togglecontainer    avia-builder-el-10  el_after_av_promobox  avia-builder-el-last \" ><section class=\"av_toggle_section\"  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\"  >    <div role=\"tablist\" class=\"single_toggle\" data-tags=\"{All} \"  >        <p data-fake-id=\"#toggle-id-5\" class=\"toggler \"  itemprop=\"headline\"    role=\"tab\" tabindex=\"0\" aria-controls=\"toggle-id-5\">Answer 5<span class=\"toggle_icon\" >        <span class=\"vert_icon\"><\/span><span class=\"hor_icon\"><\/span><\/span><\/p>        <div id=\"toggle-id-5\" class=\"toggle_wrap \"  >            <div class=\"toggle_content invers-color \"  itemprop=\"text\"   ><p><strong>D:<\/strong>\u00a0A function has horizontal tangents where its first derivative is equal to 0. The graph of f(x) has horizontal tangents at the points where x=\u00b1 1. Of the choices for the graph f\u2032(x), only choice (D) has zeros at x=\u00b1 1.<\/p>\n            <\/div>        <\/div>    <\/div><\/section><\/div><\/p>","protected":false},"excerpt":{"rendered":"<p>Test your readiness for the AP Calculus exam with this quiz! FREE PREMIUM CONTENT AP Calculus Formulas &amp; Theorems Sheet Download a free list of formulas and theorems you should know for the AP Calc exam!<\/p>\n","protected":false},"author":1,"featured_media":27968,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[411],"tags":[408],"_links":{"self":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/18564"}],"collection":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/comments?post=18564"}],"version-history":[{"count":9,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/18564\/revisions"}],"predecessor-version":[{"id":48023,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/18564\/revisions\/48023"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/media\/27968"}],"wp:attachment":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/media?parent=18564"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/categories?post=18564"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/tags?post=18564"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}