{"id":2291,"date":"2022-12-01T17:38:51","date_gmt":"2022-12-01T17:38:51","guid":{"rendered":"http:\/\/www.kaptest.com\/blog\/prep\/?p=2291"},"modified":"2022-12-05T21:35:23","modified_gmt":"2022-12-05T21:35:23","slug":"psat-math-quiz-exponents-roots-and-polynomials","status":"publish","type":"post","link":"https:\/\/wpapp.kaptest.com\/study\/psat\/psat-math-quiz-exponents-roots-and-polynomials\/","title":{"rendered":"PSAT Math Quiz: Exponents, Roots and Polynomials"},"content":{"rendered":"<p>Content Review:<\/p>\n<ul>\n<li><a title=\"PSAT Math: Exponents and Radicals\" href=\"https:\/\/www.kaptest.com\/blog\/prep\/psat\/psat-math-exponents-and-radicals\/\">PSAT Math: Exponents and Radicals<\/a><\/li>\n<li><a title=\"PSAT Math: Polynomials\" href=\"https:\/\/www.kaptest.com\/blog\/prep\/psat\/psat-math-polynomials\/\">PSAT Math:&nbsp;Polynomials<\/a><\/li>\n<li><a title=\"PSAT Math: Rational Expressions and Equations\" href=\"https:\/\/www.kaptest.com\/blog\/prep\/psat\/psat-math-rational-expressions-and-equations\/\">PSAT Math:&nbsp;Rational Expressions and Equations<\/a><\/li>\n<\/ul>\n<p>Test your <a title=\"psat math\" href=\"http:\/\/kaptest.com\/psat\">PSAT readiness<\/a>&nbsp;by taking this PSAT math quiz!<br \/>\n<div  class='avia-builder-widget-area clearfix  avia-builder-el-0  el_before_av_promobox  avia-builder-el-first '><div id=\"custom_html-32\" class=\"widget_text widget clearfix widget_custom_html\"><div class=\"textwidget custom-html-widget\"><div><div class='op-interactive' id='6389424f886d59597a873036' data-title='PSAT Math Quiz: Exponents, Roots, and Polynomials' data-url='https:\/\/kaplannorthamerica.outgrow.us\/6389424f886d59597a873036?vHeight=1' data-width='100%'><\/div><script src='\/\/dyv6f9ner1ir9.cloudfront.net\/assets\/js\/nloader.js'><\/script><script>initIframe('6389424f886d59597a873036');<\/script><\/div><\/div><\/div><\/div><br \/>\n\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>\n<strong>Question 1<\/strong><br \/>\nWhich of the following is equivalent to the expression:<br \/>\n(9\u2074 x 3\u00b2) \/ 9\u2075<br \/>\nA. 0<br \/>\nB. 1<br \/>\nC. 3<br \/>\nD. 9<\/p>\n<\/div><\/div><br \/>\n<div  class=\"togglecontainer   toggle_close_all  avia-builder-el-2  el_after_av_promobox  el_before_av_promobox \" >\n<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\"   ><div class=\"QuizQuestion-header\">\n<section id=\"questionFeedback\" class=\"QuizQuestion-feedback QuizQuestion-feedback-is-correct\">\n<article class=\"QuizQuestion-feedback-description\">\n<div class=\"QuizQuestion-feedback-description-body\"><strong>B:&nbsp;<\/strong>Raising 9 to the 4th and 5th powers is very time-consuming without a calculator. Instead, start by using exponent rules to simplify expressions written in the same base. Then raise any remaining numbers to the resulting powers. The power of 9 is larger in the denominator, so subtract the exponents there. Then, simplify further if possible:<br \/>\n(9\u2074 x 3\u00b2) \/ 9\u2075 = (3\u00b2) \/ 9\u2075\u207b\u2074 = 9\/9 = 1<\/div>\n<\/article>\n<\/section>\n<\/div>\n            <\/div>        <\/div>    <\/div><\/section>\n<\/div><br \/>\n\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>\n<strong>Question 2<\/strong><br \/>\nWhat is the resulting coefficient of&nbsp;<i>x<\/i>&nbsp;after multiplying \u2013<i>x<\/i>&nbsp;+ 4 by&nbsp;<i>x<\/i>&nbsp;\u2013 5 ?<br \/>\nA. -9<br \/>\nB. -1<br \/>\nC. 1<br \/>\nD. 9<\/p>\n<\/div><\/div><br \/>\n<div  class=\"togglecontainer   toggle_close_all  avia-builder-el-4  el_after_av_promobox  el_before_av_promobox \" >\n<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\"   ><div class=\"QuizQuestion-header\">\n<section id=\"questionFeedback\" class=\"QuizQuestion-feedback QuizQuestion-feedback-is-incorrect\">\n<article class=\"QuizQuestion-feedback-description\">\n<div class=\"QuizQuestion-feedback-description-body\"><strong>D:&nbsp;<\/strong>Distribute each term in the first factor to each term in the second factor, paying careful attention to the signs.<br \/>\n(\u2013<i>x<\/i>&nbsp;+ 4)(<i>x<\/i>&nbsp;\u2013 5)<br \/>\n=&nbsp;\u2013<i>x<\/i>(<i>x<\/i>&nbsp;\u2013 5) + 4(<i>x<\/i>&nbsp;\u2013 5)<br \/>\n=&nbsp;\u2013<i>x<\/i>\u00b2&nbsp;+ 5<i>x<\/i>&nbsp;+ 4<i>x<\/i>&nbsp;&#8211; 20<br \/>\n=&nbsp;\u2013<i>x<\/i>\u00b2 + 9<i>x<\/i>&nbsp;&#8211; 20<br \/>\nDon\u2019t let (B) fool you\u2014the question asks for the coefficient of&nbsp;<i>x<\/i>, not&nbsp;<i>x<\/i><sup>2<\/sup>, so the correct answer is (D).<\/div>\n<\/article>\n<\/section>\n<\/div>\n            <\/div>        <\/div>    <\/div><\/section>\n<\/div><br \/>\n\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>\n<strong>Question 3<\/strong><br \/>\nThe power generated by a windmill is related to the velocity of the wind by the equation shown, where&nbsp;<i>P<\/i>&nbsp;is the power in watts and&nbsp;<i>v<\/i>is the wind velocity in miles per hour. What is the wind velocity when the windmill is generating 160 watts of power?<br \/>\n<a href=\"http:\/\/www.kaptest.com\/blog\/prep\/wp-content\/uploads\/sites\/21\/2016\/08\/Screen-Shot-2019-08-02-at-10.18.02-PM.png\"><img loading=\"lazy\" class=\"alignnone size-medium wp-image-26039\" src=\"http:\/\/www.kaptest.com\/blog\/prep\/wp-content\/uploads\/sites\/21\/2016\/08\/Screen-Shot-2019-08-02-at-10.18.02-PM-300x180.png\" alt=\"psat math\" width=\"300\" height=\"180\"><\/a><br \/>\nA. 20 mph<br \/>\nB. 32 mph<br \/>\nC. 64 mph<br \/>\nD. 89 mph<\/p>\n<\/div><\/div><br \/>\n<div  class=\"togglecontainer   toggle_close_all  avia-builder-el-6  el_after_av_promobox  el_before_av_promobox \" >\n<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\"   ><div class=\"QuizQuestion-header\">\n<section id=\"questionFeedback\" class=\"QuizQuestion-feedback QuizQuestion-feedback-is-correct\">\n<article class=\"QuizQuestion-feedback-description\">\n<div class=\"QuizQuestion-feedback-description-body\"><strong>A:&nbsp;<\/strong>Substitute 160 for&nbsp;<i>P<\/i>&nbsp;and simplify using your calculator. Don\u2019t try to enter the entire expression into the calculator all at one time\u2014you\u2019re likely to miss a parenthesis somewhere. Instead, divide 160 by 0.02 to get 8,000. Then, take the cube root of 8,000 using the cube root function or by raising it to the one-third power. The result is 20, so the wind velocity is 20 miles per hour. Choice (A) is correct.<\/div>\n<\/article>\n<\/section>\n<\/div>\n            <\/div>        <\/div>    <\/div><\/section>\n<\/div><br \/>\n\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>\n<strong>Question 4<\/strong><\/p>\n<article class=\"QuizQuestion-info-description-container\">\n<div class=\"QuizQuestion-info-description\">The length of Box 2 (<i>y<\/i>) shown above is twice the length of Box 1 (<i>x<\/i>). Which expression shows the difference in the volumes of the two boxes?<\/div>\n<\/article>\n<p><a href=\"http:\/\/www.kaptest.com\/blog\/prep\/wp-content\/uploads\/sites\/21\/2016\/08\/Screen-Shot-2019-08-02-at-10.22.19-PM.png\"><img loading=\"lazy\" class=\"alignnone size-medium wp-image-26040\" src=\"http:\/\/www.kaptest.com\/blog\/prep\/wp-content\/uploads\/sites\/21\/2016\/08\/Screen-Shot-2019-08-02-at-10.22.19-PM-300x111.png\" alt=\"psat math\" width=\"300\" height=\"111\"><\/a><br \/>\nA.&nbsp;2x\u200a\u00b3 \u2013 2x<br \/>\nB.&nbsp;7x\u00b3\u200a \u2013 x<br \/>\nC.&nbsp;7x\u200a\u00b3 \u2013 2x<br \/>\nD.&nbsp;8\u200ax\u200a\u00b3 \u2013 2x<\/p>\n<div class=\"QuizQuestion-header\">\n<\/div><\/div><\/div>\n<div class=\"QuizQuestion-header\"><\/div>\n<div class=\"QuizQuestion-header\"><div  class=\"togglecontainer   toggle_close_all  avia-builder-el-8  el_after_av_promobox  el_before_av_promobox \" >\n<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>B:&nbsp;<\/strong>Find the volume of each box and then subtract.<br \/>\nBox 1:&nbsp;<i>V = x<\/i>(<i>x +<\/i>&nbsp;1)(<i>x<\/i>&nbsp;\u2013 1)&nbsp;<i>= x<\/i>(<i>x<\/i><sup>\u200a2<\/sup>&nbsp;<i>\u2013 1<\/i>)&nbsp;<i>= x<\/i><sup>\u200a3<\/sup>&nbsp;<i>\u2013 x<\/i><br \/>\nBox 2: Substitute 2<i>x<\/i>&nbsp;for&nbsp;<i>x<\/i>&nbsp;in the volume you already found:<br \/>\n(2<i>x<\/i>)<sup>3<\/sup>&nbsp;\u2013 2<i>x<\/i>&nbsp;= 2<sup>3<\/sup><i>x<\/i><sup>\u200a3<\/sup>&nbsp;\u2013 2<i>x<\/i>&nbsp;= 8<i>x<\/i><sup>\u200a3<\/sup>&nbsp;\u2013 2<i>x<\/i><br \/>\nDifference: (8<i>x<\/i><sup>\u200a3<\/sup>&nbsp;\u2013 2<i>x<\/i>) \u2013 (<i>x<\/i><sup>\u200a3<\/sup>&nbsp;\u2013&nbsp;<i>x<\/i>) = 8<i>x<\/i><sup>\u200a3<\/sup>&nbsp;\u2013&nbsp;<i>x<\/i><sup>\u200a3<\/sup>&nbsp;\u2013 2<i>x<\/i>&nbsp;+&nbsp;<i>x<\/i>&nbsp;= 7<i>x<\/i><sup>\u200a3<\/sup>&nbsp;\u2013&nbsp;<i>x<\/i>, (B).<\/p>\n            <\/div>        <\/div>    <\/div><\/section>\n<\/div><br \/>\n\t<div   class='av_promobox  avia-button-no   avia-builder-el-9  el_after_av_toggle_container  avia-builder-el-last '>\t\t<div class='avia-promocontent'><\/div><\/div><\/p>\n<\/div>\n<p>Previous: <a title=\"PSAT Math Quiz: Rates, Ratios, Proportions and Percents\" href=\"https:\/\/www.kaptest.com\/blog\/prep\/psat\/psat-math-quiz-rates-ratios-proportions-and-percents\/\">PSAT Math Quiz: Rates, Ratios, Proportions, and Percents<\/a><br \/>\nNext: <a title=\"PSAT Math Quiz: Functions\" href=\"https:\/\/www.kaptest.com\/blog\/prep\/psat\/psat-math-quiz-functions\/\">PSAT Math Quiz: Functions<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Content Review: PSAT Math: Exponents and Radicals PSAT Math:&nbsp;Polynomials PSAT Math:&nbsp;Rational Expressions and Equations Test your PSAT readiness&nbsp;by taking this PSAT math quiz! Previous: PSAT Math Quiz: Rates, Ratios, Proportions, and Percents Next: PSAT Math Quiz: Functions<\/p>\n","protected":false},"author":1,"featured_media":42029,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[240],"tags":[195,310,311],"_links":{"self":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/2291"}],"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=2291"}],"version-history":[{"count":5,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/2291\/revisions"}],"predecessor-version":[{"id":42031,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/2291\/revisions\/42031"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/media\/42029"}],"wp:attachment":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/media?parent=2291"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/categories?post=2291"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/tags?post=2291"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}