{"id":401,"date":"2016-04-14T11:21:03","date_gmt":"2016-04-14T18:21:03","guid":{"rendered":"https:\/\/magoosh.com\/praxis\/?p=401"},"modified":"2019-01-30T20:16:42","modified_gmt":"2019-01-31T04:16:42","slug":"praxis-core-math-algebra-practice-questions","status":"publish","type":"post","link":"https:\/\/magoosh.com\/praxis\/praxis-core-math-algebra-practice-questions\/","title":{"rendered":"Praxis Core Math: Algebra Practice Questions"},"content":{"rendered":"<p>Algebra dominates Praxis Core Math. Even questions related to geometry, statistics, and numbers\/quantity may have an algebraic component. So it\u2019s good to know exactly what to expect when it comes to Praxis Core algebra.<\/p>\n<p>There are three types of algebra questions on the Praxis Core math exam. The most complex algebra question type is the story problem. In Core Math algebra story problems, you\u2019ll need to read about a situation involving numbers, come up with an algebra equation that works, and calculate the answer.<\/p>\n<p>The other two categories of algebra questions are somewhat simpler. You can expect to see problems related to equivalent expressions and solving algebraic equations for a single variable. In both cases, the equation that you start with is provided, and you must carry out the correct algebraic steps to arrive at the correct answer.<\/p>\n<p>Below is a practice set of Praxis Core Math algebra problems that can help you prepare for the exam. An answer key appears at the very bottom of this post. Once you finish the problems, check the answer key and see how you did.<\/p>\n<h2>Practice algebraic story problem<\/h2>\n<p><a href=\"https:\/\/magoosh.com\/praxis\/wp-content\/blogs.dir\/14\/files\/2016\/04\/PraxisCoreMathAlgebraGraphic.jpg\" rel=\"attachment wp-att-402\"><img decoding=\"async\" class=\"alignnone wp-image-402\" src=\"https:\/\/magoosh.com\/praxis\/wp-content\/blogs.dir\/14\/files\/2016\/04\/PraxisCoreMathAlgebraGraphic-1024x666.jpg\" alt=\"PraxisCoreMathAlgebraGraphic\" width=\"386\" height=\"251\" srcset=\"https:\/\/magoosh.com\/praxis\/files\/2016\/04\/PraxisCoreMathAlgebraGraphic-1024x666.jpg 1024w, https:\/\/magoosh.com\/praxis\/files\/2016\/04\/PraxisCoreMathAlgebraGraphic-300x195.jpg 300w, https:\/\/magoosh.com\/praxis\/files\/2016\/04\/PraxisCoreMathAlgebraGraphic-768x500.jpg 768w, https:\/\/magoosh.com\/praxis\/files\/2016\/04\/PraxisCoreMathAlgebraGraphic.jpg 1870w\" sizes=\"(max-width: 386px) 100vw, 386px\" \/><\/a><\/p>\n<p>The pictograph above shows the number of new textbooks a local public school must purchase for their fifth grade classes before the next school year begins. Math books cost $25 each, English books cost $15 each, and the total cost of the textbooks is $5700. If each history book costs <em>c<\/em> dollars, what is the value of <em>c<\/em>?<\/p>\n<ul>A) 35<\/ul>\n<ul>B) 30<\/ul>\n<ul>C) 25<\/ul>\n<ul>D) 20<\/ul>\n<ul>E) 15<\/ul>\n<p>&nbsp;<\/p>\n<h2>Practice equivalent expressions problem<\/h2>\n<p>Which of the following expressions is equivalent to 19-3<em>x<\/em> for all values of <em>x<\/em>?<\/p>\n<ul>\n<p>A) 3 \u2013 2(8 \u2013<em>x<\/em>)<\/p>\n<p>B) 22 \u2013 (3 \u2013 3<em>x<\/em>)<\/p>\n<p>C) 4 + 3(5 \u2013<em>x<\/em>)<\/p>\n<p>D) 3(2 \u2013<em>x<\/em>) -13<\/p>\n<p>E) 19(1 \u2013<em>x) \u2013 16x<\/em><\/ul>\n<p>&nbsp;<\/p>\n<h2>Practice algebra equation problem<\/h2>\n<p>If 14(2<em>x<\/em> + 1) = 7(x + 9) + 1, what is the value of <em>x<\/em>? Give your answer as a fraction.<\/p>\n<p><a href=\"https:\/\/magoosh.com\/praxis\/wp-content\/blogs.dir\/14\/files\/2016\/04\/fraction-answer.png\" rel=\"attachment wp-att-403\"><img decoding=\"async\" class=\"alignnone wp-image-403\" src=\"https:\/\/magoosh.com\/praxis\/wp-content\/blogs.dir\/14\/files\/2016\/04\/fraction-answer.png\" alt=\"fraction-answer\" width=\"173\" height=\"105\" srcset=\"https:\/\/magoosh.com\/praxis\/files\/2016\/04\/fraction-answer.png 334w, https:\/\/magoosh.com\/praxis\/files\/2016\/04\/fraction-answer-300x182.png 300w\" sizes=\"(max-width: 173px) 100vw, 173px\" \/><\/a><\/p>\n<p><em>(Note: This question is in one of the Praxis Core\u2019s <\/em><a href=\"https:\/\/magoosh.com\/praxis\/praxis-math-alternate-question-formats\/\"><em>alternative question formats<\/em><\/a><em>\u00a0 for Math.)<\/em><\/p>\n<p>&nbsp;<\/p>\n<h2>Answer Key:<\/h2>\n<ul>1) B<\/ul>\n<ul>2) C<\/ul>\n<ul>3)\u00a050\/21<\/ul>\n<p>&nbsp;<\/p>\n<h2>Notes about the answers:<\/h2>\n<p><em><strong>Story problem:<\/strong><\/em>The correct starting equation uses the three variables <em>Math<\/em>, <em>English<\/em>, and <em>History<\/em>. These variables can be expressed respectively as <em>M<\/em>, <em>E<\/em>, and <em>H<\/em>. The equation you start with will multiply the number of each type of book (20 times the number of icons on the chart) with its unit price, to equal a total of $5700. From there, you plug in the numbers you have to solve for unknown variable <em>d<\/em>, the cost of an individual history textbook. The steps look like this:<\/p>\n<ul>\n1) 20*25*<em>M<\/em>+ 20*15*<em>E<\/em>+ 20*<em>d<\/em>*<em>H\u00a0<\/em>= 5700<\/p>\n<p>2) 20*25*3 + 20*15*2 + 20*<em>d<\/em>*6 = 5700<\/p>\n<p>3) 1500 + 600 + 120<em>d<\/em>= 5700<\/p>\n<p>4) 2100 +120<em>d\u00a0<\/em>= 5700<\/p>\n<p>5) 2100 + 120<em>d<\/em>\u2013 2100 = 5700 &#8211; 2100<\/p>\n<p>6) 120<em>d<\/em>= 3600<\/p>\n<p>7) (120<em>d<\/em>)\/120 = 3600\/120<\/p>\n<p>8)\u00a0<em>d<\/em>= 3600\/120<\/p>\n<p>9)\u00a0<em>d<\/em>= 30<\/ul>\n<p><em><strong>Equivalent expressions problem:<\/strong><\/em> To solve this, use the commutative property of multiplication to \u201cfactor out\u201d everything in the parentheses in each answer choice. From there, rewrite each answer choice in its simplest form. You\u2019ll see that only answer C becomes 19-3<em>x<\/em> after being factored out and simplified.<\/p>\n<p><em><strong>Algebra equation problem<\/strong><\/em>: Starting with the given equation, the steps are as follows:<\/p>\n<ul>\n1) 14(2<em>x<\/em>+ 1) = 7(<em>x<\/em>+ 9) + 1<\/p>\n<p>2) 28<em>x<\/em>+ 14 = 7<em>x<\/em>+ 63 +1<\/p>\n<p>3) 28<em>x<\/em>+ 14 = 7<em>x<\/em>+ 64<\/p>\n<p>4) 28<em>x<\/em>+ 14 \u2013 14 = 7<em>x<\/em>+ 64 \u2013 14<\/p>\n<p>5) 28<em>x<\/em>= 7<em>x<\/em>+ 50<\/p>\n<p>6) 28<em>x<\/em>\u2013 7<em>x<\/em>= 7<em>x<\/em>+ 50 \u2013 7<em>x<\/em><\/p>\n<p>7) 21<em>x<\/em>= 50<\/p>\n<p>8) 21<em>x<\/em>\/21 = 50\/21<\/p>\n<p>9)\u00a0<em>x\u00a0<\/em>= 50\/21<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Algebra dominates Praxis Core Math. Even questions related to geometry, statistics and numbers\/quantity may have an algebraic component. <\/p>\n","protected":false},"author":80,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"om_disable_all_campaigns":false,"footnotes":""},"categories":[2435],"tags":[],"ppma_author":[4914],"class_list":["post-401","post","type-post","status-publish","format-standard","hentry","category-praxis-math-practice"],"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>Praxis Core Math: Algebra Practice Questions<\/title>\n<meta name=\"description\" content=\"Algebra dominates Praxis Core Math. 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Additionally, he's helped students with TOEIC, PET, FCE, BULATS, Eiken, SAT, ACT, GRE, and GMAT. David has a BS and MA from the University of Wisconsin-Eau Claire and an MA from the University of Wisconsin-River Falls.","sameAs":["https:\/\/www.facebook.com\/MagooshEnglishLearning","https:\/\/www.linkedin.com\/in\/david-recine\/","https:\/\/www.youtube.com\/channel\/UCra3KQoJlOP7RYwaCyH2qew"],"knowsAbout":["TOEFL","IELTS","TOEIC","PET","FCE","BULATS","Eiken","SAT","ACT","GRE","GMAT"],"knowsLanguage":["English","Italian"],"jobTitle":"Content Creator","worksFor":"Magoosh","url":"https:\/\/magoosh.com\/praxis\/author\/davidr\/"}]}},"authors":[{"term_id":4914,"user_id":80,"is_guest":0,"slug":"davidr","display_name":"David Recine","avatar_url":"https:\/\/secure.gravatar.com\/avatar\/b70c17ee6f3ef87dc4cc5dbdebda911d6dd30dfe15845e4b1d459a3e1b33ef98?s=96&d=mm&r=g","user_url":"","last_name":"Recine","first_name":"David","description":"David is a Test Prep Expert for Magoosh TOEFL and IELTS. Additionally, he's helped students with TOEIC, PET, FCE, BULATS, Eiken, SAT, ACT, GRE, and GMAT.\r\n\r\nDavid has a BS from the University of Wisconsin-Eau Claire and an MA from the University of Wisconsin-River Falls. His work at Magoosh has been cited in<a href=\"https:\/\/scholar.google.com\/scholar?hl=en&amp;as_sdt=0%2C50&amp;q=Recine+magoosh&amp;btnG=\" rel=\"noopener noreferrer\"> many scholarly articles<\/a>,<a href=\"https:\/\/minds.wisconsin.edu\/handle\/1793\/65479\" rel=\"noopener noreferrer\"> his Master's Thesis<\/a> is featured on the<a href=\"https:\/\/www.readingwithpictures.org\/2013\/09\/research-highlight-teaching-english-language-learners-with-comics\/\" rel=\"noopener noreferrer\"> Reading with Pictures<\/a> website, and he's presented at the<a href=\"https:\/\/www.witesol.com\/wp-content\/uploads\/2014\/11\/2014-WITESOL-Program-FINAL-10-28-14.pdf\" rel=\"noopener noreferrer\"> WITESOL (link to PDF)<\/a> and<a href=\"https:\/\/issuu.com\/interoff\/docs\/nafsaregionv_2014conference\" rel=\"noopener noreferrer\"> NAFSA<\/a> conferences. David has taught K-12 ESL in South Korea as well as undergraduate English and MBA-level business English at American universities. 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