{"id":1479,"date":"2021-12-02T19:38:12","date_gmt":"2021-12-03T00:38:12","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/part\/midterm-three-preparation\/"},"modified":"2022-11-02T10:35:58","modified_gmt":"2022-11-02T14:35:58","slug":"midterm-three-preparation","status":"publish","type":"part","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/part\/midterm-three-preparation\/","title":{"raw":"Midterm 3 Preparation and Sample Questions","rendered":"Midterm 3 Preparation and Sample Questions"},"content":{"raw":"This chapter contains several sections that will help prepare for the midterm exam:\n<table class=\"aligncenter\" style=\"border-collapse: collapse; width: 69.6947%; height: 142px;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 80%;\"><a href=\"#composition\">Midterm 3 Composition<\/a>\n<a href=\"#reviewquestions\">Midterm 3 Review<\/a>\n<a href=\"#midterma\">Midterm Sample A<\/a>\n<a href=\"#midtermb\">Midterm Sample B<\/a>\n<a href=\"#midtermc\">Midterm Sample C<\/a>\n<a href=\"#midtermd\">Midterm Sample D<\/a>\n<a href=\"#midterme\">Midterm Sample E<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1 id=\"composition\">Midterm Three Composition<\/h1>\nThe third midterm will be composed of fifteen questions covering chapters 7 to 9. Twelve questions will be algebra questions, and three questions will be word problems.\n<ul>\n \t<li><strong>Questions 1\u20134 will be drawn from Chapter 8: Rational Expressions<\/strong>\n<ul>\n \t<li>8.1 Reducing Rational Expressions<\/li>\n \t<li>8.2 Multiplication and Division of Rational Expressions<\/li>\n \t<li>8.3 Least Common Denominators<\/li>\n \t<li>8.4 Addition and Subtraction of Rational Expressions<\/li>\n \t<li>8.5 Reducing Complex Fractions<\/li>\n \t<li>8.6 Solving Complex Fractions<\/li>\n \t<li>8.7 Solving Rational Equations<\/li>\n<\/ul>\n<\/li>\n \t<li><strong>Questions 5\u20138 will be drawn from Chapter 9: Radicals<\/strong>\n<ul>\n \t<li>9.1 Reducing Square Roots<\/li>\n \t<li>9.2 Reducing Higher Power Roots<\/li>\n \t<li>9.3 Adding and Subtracting Radicals<\/li>\n \t<li>9.4 Multiplication and Division of Radicals<\/li>\n \t<li>9.5 Rationalizing Denominators<\/li>\n \t<li>9.6 Radicals and Rational Exponents<\/li>\n \t<li>9.8 Radicals of Mixed Index<\/li>\n \t<li>9.9 Complex Numbers (Optional)<\/li>\n<\/ul>\n<\/li>\n \t<li><strong>Questions 9\u201312 will be drawn from Chapter 10: Quadratics<\/strong>\n<ul>\n \t<li>10.1 Solving Radical Equations<\/li>\n \t<li>10.2 Solving Exponential Equations<\/li>\n \t<li>10.3 Completing the Square<\/li>\n \t<li>10.4 The Quadratic Equation<\/li>\n \t<li>10.5 Solving Quadratic Equations Using Substitution<\/li>\n \t<li>\u00a010.6 Graphing Quadratic Equations\u2014Vertex and Intercept Method<\/li>\n \t<li>10.7 Quadratic Word Problems: Age and Numbers<\/li>\n \t<li>10.8 Construct a Quadratic Equation from its Roots<\/li>\n<\/ul>\n<\/li>\n \t<li>Questions 13\u201315 will be three word problems drawn from:\n<ul>\n \t<li>8.8 Rate Word Problems: Speed, Distance and Time<\/li>\n \t<li>9.10 Rate Word Problems: Work and Time<\/li>\n \t<li>10.7 Quadratic Word Problems: Age and Numbers<\/li>\n<\/ul>\n<\/li>\n<\/ul>\nStudents will be allowed to use MATQ 1099 Data Booklets &amp; Glossaries for both Midterms and the Final Exam.\n<h1 id=\"reviewquestions\">Midterm Three Review<\/h1>\n<h2>Chapter 7: Rational Expressions (Exam Type Questions)<\/h2>\nIn the problems below, perform the indicated operations and simplify.\n<ol>\n \t<li>[latex]\\dfrac{6a-6b}{a^3+b^3}\\div \\dfrac{a^2-b^2}{a^2-ab+b^2}[\/latex]<\/li>\n \t<li>[latex]\\dfrac{x}{x^2-25} - \\dfrac{2}{x^2-6x+5}[\/latex]<\/li>\n \t<li>[latex]\\dfrac{1-\\dfrac{6}{x}}{\\dfrac{4}{x}-\\dfrac{24}{x^2}}[\/latex]<\/li>\n<\/ol>\nSolve for [latex]x[\/latex].\n<ol start=\"4\">\n \t<li>[latex]\\dfrac{4}{x+4}-\\dfrac{5}{x-2}=5[\/latex]<\/li>\n<\/ol>\n<h2>Chapter 8: Radicals\u00a0(Exam Type Questions)<\/h2>\nQuestions 5\u20136 are for review only and will not show up on exams.\n<ol start=\"5\">\n \t<li>[latex]\\sqrt[3]{-64}=-4 \\text{ (true or false)}[\/latex]<\/li>\n \t<li>[latex]\\sqrt[6]{-64}=-2\\text{ (true or false)}[\/latex]<\/li>\n<\/ol>\nQuestions similar to 7\u201313 will show up on exams.\n\nFor questions 7\u201310, simplify each expression.\n<ol start=\"7\">\n \t<li>[latex]4\\sqrt{36}+3\\sqrt{72}+\\sqrt{16}[\/latex]<\/li>\n \t<li>[latex]\\dfrac{\\sqrt{300a^5b^2}}{3ab^2}[\/latex]<\/li>\n \t<li>[latex]\\dfrac{12}{3-\\sqrt{6}}[\/latex]<\/li>\n \t<li>[latex]\\left(\\dfrac{a^0b^3}{c^6d^{-12}}\\right)^{\\frac{1}{3}}[\/latex]<\/li>\n<\/ol>\nFor questions 11\u201313, solve for [latex]x[\/latex].\n<ol start=\"11\">\n \t<li>[latex]\\sqrt{5x-6}=x[\/latex]<\/li>\n \t<li>[latex]\\sqrt{2x+9}+3=x[\/latex]<\/li>\n \t<li>[latex]\\sqrt{x-3}=\\sqrt{2x-5}[\/latex]<\/li>\n<\/ol>\n<h2>Chapter 9: Quadratics\u00a0(Exam Type Questions)<\/h2>\nUse the quadratic discriminant to determine the nature of the roots of each equation.\n<ol start=\"14\">\n \t<li>[latex]\\phantom{1}[\/latex]\n<ol type=\"a\">\n \t<li>[latex]2x^2 + 4x + 3 = 0[\/latex]<\/li>\n \t<li>[latex]3x^2-2x-8=0[\/latex]<\/li>\n<\/ol>\n<\/li>\n<\/ol>\nFor the questions below, find the solution set by any convenient method.\n<ol start=\"15\">\n \t<li>[latex]\\phantom{1}[\/latex]\n<ol type=\"a\">\n \t<li>[latex]3x^2 = 27[\/latex]<\/li>\n \t<li>[latex]2x^2=16x[\/latex]<\/li>\n<\/ol>\n<\/li>\n \t<li>[latex]\\phantom{1}[\/latex]\n<ol type=\"a\">\n \t<li>[latex]x^2-x-12=0[\/latex]<\/li>\n \t<li>[latex]x^2+9x=-8[\/latex]<\/li>\n<\/ol>\n<\/li>\n \t<li>[latex]\\dfrac{x-3}{2}+\\dfrac{6}{x+3}=1[\/latex]<\/li>\n \t<li>[latex]\\dfrac{x-2}{x}=\\dfrac{x}{x+4}[\/latex]<\/li>\n<\/ol>\n<h2>Chapter 7\u20139 Word Problems (Exam Type Questions)<\/h2>\n<ol start=\"19\">\n \t<li>The length of a rectangle is 3 cm longer than twice the width. If the area of the rectangle is 65 cm<sup>2<\/sup>, find its length and width.<\/li>\n \t<li>Find three consecutive even integers such that the product of the first and the second is 68 more than the third integer.<\/li>\n \t<li>A boat cruises upriver for 8 hours and returns to its starting point in 6 hours. If the speed of the river is 4 km\/h, find the speed of this boat in still water.<\/li>\n \t<li>The base of a right triangle is 8 m longer than its height. If the area of the triangle is 330 m<sup>2<\/sup>, what are its base and height measurements?<\/li>\n<\/ol>\n<a class=\"internal\" href=\"\/\/back-matter\/midterm-3-prep-answer-key\/\">Midterm 3: Prep Questions Answer Key<\/a>","rendered":"<p>This chapter contains several sections that will help prepare for the midterm exam:<\/p>\n<table class=\"aligncenter\" style=\"border-collapse: collapse; width: 69.6947%; height: 142px;\">\n<tbody>\n<tr>\n<td style=\"width: 80%;\"><a href=\"#composition\">Midterm 3 Composition<\/a><br \/>\n<a href=\"#reviewquestions\">Midterm 3 Review<\/a><br \/>\n<a href=\"#midterma\">Midterm Sample A<\/a><br \/>\n<a href=\"#midtermb\">Midterm Sample B<\/a><br \/>\n<a href=\"#midtermc\">Midterm Sample C<\/a><br \/>\n<a href=\"#midtermd\">Midterm Sample D<\/a><br \/>\n<a href=\"#midterme\">Midterm Sample E<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1 id=\"composition\">Midterm Three Composition<\/h1>\n<p>The third midterm will be composed of fifteen questions covering chapters 7 to 9. Twelve questions will be algebra questions, and three questions will be word problems.<\/p>\n<ul>\n<li><strong>Questions 1\u20134 will be drawn from Chapter 8: Rational Expressions<\/strong>\n<ul>\n<li>8.1 Reducing Rational Expressions<\/li>\n<li>8.2 Multiplication and Division of Rational Expressions<\/li>\n<li>8.3 Least Common Denominators<\/li>\n<li>8.4 Addition and Subtraction of Rational Expressions<\/li>\n<li>8.5 Reducing Complex Fractions<\/li>\n<li>8.6 Solving Complex Fractions<\/li>\n<li>8.7 Solving Rational Equations<\/li>\n<\/ul>\n<\/li>\n<li><strong>Questions 5\u20138 will be drawn from Chapter 9: Radicals<\/strong>\n<ul>\n<li>9.1 Reducing Square Roots<\/li>\n<li>9.2 Reducing Higher Power Roots<\/li>\n<li>9.3 Adding and Subtracting Radicals<\/li>\n<li>9.4 Multiplication and Division of Radicals<\/li>\n<li>9.5 Rationalizing Denominators<\/li>\n<li>9.6 Radicals and Rational Exponents<\/li>\n<li>9.8 Radicals of Mixed Index<\/li>\n<li>9.9 Complex Numbers (Optional)<\/li>\n<\/ul>\n<\/li>\n<li><strong>Questions 9\u201312 will be drawn from Chapter 10: Quadratics<\/strong>\n<ul>\n<li>10.1 Solving Radical Equations<\/li>\n<li>10.2 Solving Exponential Equations<\/li>\n<li>10.3 Completing the Square<\/li>\n<li>10.4 The Quadratic Equation<\/li>\n<li>10.5 Solving Quadratic Equations Using Substitution<\/li>\n<li>\u00a010.6 Graphing Quadratic Equations\u2014Vertex and Intercept Method<\/li>\n<li>10.7 Quadratic Word Problems: Age and Numbers<\/li>\n<li>10.8 Construct a Quadratic Equation from its Roots<\/li>\n<\/ul>\n<\/li>\n<li>Questions 13\u201315 will be three word problems drawn from:\n<ul>\n<li>8.8 Rate Word Problems: Speed, Distance and Time<\/li>\n<li>9.10 Rate Word Problems: Work and Time<\/li>\n<li>10.7 Quadratic Word Problems: Age and Numbers<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>Students will be allowed to use MATQ 1099 Data Booklets &amp; Glossaries for both Midterms and the Final Exam.<\/p>\n<h1 id=\"reviewquestions\">Midterm Three Review<\/h1>\n<h2>Chapter 7: Rational Expressions (Exam Type Questions)<\/h2>\n<p>In the problems below, perform the indicated operations and simplify.<\/p>\n<ol>\n<li>[latex]\\dfrac{6a-6b}{a^3+b^3}\\div \\dfrac{a^2-b^2}{a^2-ab+b^2}[\/latex]<\/li>\n<li>[latex]\\dfrac{x}{x^2-25} - \\dfrac{2}{x^2-6x+5}[\/latex]<\/li>\n<li>[latex]\\dfrac{1-\\dfrac{6}{x}}{\\dfrac{4}{x}-\\dfrac{24}{x^2}}[\/latex]<\/li>\n<\/ol>\n<p>Solve for [latex]x[\/latex].<\/p>\n<ol start=\"4\">\n<li>[latex]\\dfrac{4}{x+4}-\\dfrac{5}{x-2}=5[\/latex]<\/li>\n<\/ol>\n<h2>Chapter 8: Radicals\u00a0(Exam Type Questions)<\/h2>\n<p>Questions 5\u20136 are for review only and will not show up on exams.<\/p>\n<ol start=\"5\">\n<li>[latex]\\sqrt[3]{-64}=-4 \\text{ (true or false)}[\/latex]<\/li>\n<li>[latex]\\sqrt[6]{-64}=-2\\text{ (true or false)}[\/latex]<\/li>\n<\/ol>\n<p>Questions similar to 7\u201313 will show up on exams.<\/p>\n<p>For questions 7\u201310, simplify each expression.<\/p>\n<ol start=\"7\">\n<li>[latex]4\\sqrt{36}+3\\sqrt{72}+\\sqrt{16}[\/latex]<\/li>\n<li>[latex]\\dfrac{\\sqrt{300a^5b^2}}{3ab^2}[\/latex]<\/li>\n<li>[latex]\\dfrac{12}{3-\\sqrt{6}}[\/latex]<\/li>\n<li>[latex]\\left(\\dfrac{a^0b^3}{c^6d^{-12}}\\right)^{\\frac{1}{3}}[\/latex]<\/li>\n<\/ol>\n<p>For questions 11\u201313, solve for [latex]x[\/latex].<\/p>\n<ol start=\"11\">\n<li>[latex]\\sqrt{5x-6}=x[\/latex]<\/li>\n<li>[latex]\\sqrt{2x+9}+3=x[\/latex]<\/li>\n<li>[latex]\\sqrt{x-3}=\\sqrt{2x-5}[\/latex]<\/li>\n<\/ol>\n<h2>Chapter 9: Quadratics\u00a0(Exam Type Questions)<\/h2>\n<p>Use the quadratic discriminant to determine the nature of the roots of each equation.<\/p>\n<ol start=\"14\">\n<li>[latex]\\phantom{1}[\/latex]\n<ol type=\"a\">\n<li>[latex]2x^2 + 4x + 3 = 0[\/latex]<\/li>\n<li>[latex]3x^2-2x-8=0[\/latex]<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<p>For the questions below, find the solution set by any convenient method.<\/p>\n<ol start=\"15\">\n<li>[latex]\\phantom{1}[\/latex]\n<ol type=\"a\">\n<li>[latex]3x^2 = 27[\/latex]<\/li>\n<li>[latex]2x^2=16x[\/latex]<\/li>\n<\/ol>\n<\/li>\n<li>[latex]\\phantom{1}[\/latex]\n<ol type=\"a\">\n<li>[latex]x^2-x-12=0[\/latex]<\/li>\n<li>[latex]x^2+9x=-8[\/latex]<\/li>\n<\/ol>\n<\/li>\n<li>[latex]\\dfrac{x-3}{2}+\\dfrac{6}{x+3}=1[\/latex]<\/li>\n<li>[latex]\\dfrac{x-2}{x}=\\dfrac{x}{x+4}[\/latex]<\/li>\n<\/ol>\n<h2>Chapter 7\u20139 Word Problems (Exam Type Questions)<\/h2>\n<ol start=\"19\">\n<li>The length of a rectangle is 3 cm longer than twice the width. If the area of the rectangle is 65 cm<sup>2<\/sup>, find its length and width.<\/li>\n<li>Find three consecutive even integers such that the product of the first and the second is 68 more than the third integer.<\/li>\n<li>A boat cruises upriver for 8 hours and returns to its starting point in 6 hours. If the speed of the river is 4 km\/h, find the speed of this boat in still water.<\/li>\n<li>The base of a right triangle is 8 m longer than its height. If the area of the triangle is 330 m<sup>2<\/sup>, what are its base and height measurements?<\/li>\n<\/ol>\n<p><a class=\"internal\" href=\"\/\/back-matter\/midterm-3-prep-answer-key\/\">Midterm 3: Prep Questions Answer Key<\/a><\/p>\n","protected":false},"parent":0,"menu_order":15,"template":"","meta":{"pb_part_invisible":false,"pb_part_invisible_string":""},"contributor":[],"license":[],"class_list":["post-1479","part","type-part","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/parts\/1479","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/parts"}],"about":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/types\/part"}],"version-history":[{"count":1,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/parts\/1479\/revisions"}],"predecessor-version":[{"id":1480,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/parts\/1479\/revisions\/1480"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1479"}],"wp:term":[{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1479"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1479"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}