{"id":1392,"date":"2021-12-02T19:37:48","date_gmt":"2021-12-03T00:37:48","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/part\/midterm-two-preparation\/"},"modified":"2022-11-02T10:35:08","modified_gmt":"2022-11-02T14:35:08","slug":"midterm-two-preparation","status":"publish","type":"part","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/part\/midterm-two-preparation\/","title":{"raw":"Midterm 2 Preparation","rendered":"Midterm 2 Preparation"},"content":{"raw":"The second midterm will be composed of fifteen questions covering chapters 5 to 7.\n\nTwelve questions will be algebra questions, and three questions will be word problems.\n<ul>\n \t<li><b>Questions 1\u20134 will be drawn from Chapter 5: Systems of Equations<\/b>\n<ul>\n \t<li>5.1 Graphed Solutions<\/li>\n \t<li>5.2 Substitution Solutions<\/li>\n \t<li>5.3 Addition and Subtraction Solutions<\/li>\n \t<li>5.4 Solving for Three Variables<\/li>\n<\/ul>\n<\/li>\n \t<li><b>Questions 5\u20136 will be drawn from Chapter 6: Polynomials<\/b>\n<ul>\n \t<li>6.1 Working with Exponents<\/li>\n \t<li>6.2 Negative Exponents<\/li>\n \t<li>6.3 Scientific Notation<\/li>\n \t<li>6.4 Basic Operations Using Polynomials<\/li>\n \t<li>6.5 Multiplication of Polynomials<\/li>\n \t<li>6.6 Special Products<\/li>\n \t<li>6.7 Dividing Polynomials<\/li>\n<\/ul>\n<\/li>\n \t<li><b>Questions 9\u201312 will be drawn from Chapter 7: Factoring<\/b>\n<ul>\n \t<li>7.1 Greatest Common Factor<\/li>\n \t<li>7.2 Factoring by Grouping<\/li>\n \t<li>7.3 Factoring Trinomials where a = 1<\/li>\n \t<li>7.4 Factoring Trinomials where a \u2260 1<\/li>\n \t<li>7.5 Factoring Special Products<\/li>\n \t<li>7.6 Factoring Quadratics of Increasing Difficulty<\/li>\n \t<li>7.7 Choosing the Correct Factoring Strategy<\/li>\n \t<li>7.8 Solving Quadratic Equations by Factoring<\/li>\n<\/ul>\n<\/li>\n \t<li><b>Questions 13\u201315 will be drawn from:<\/b>\n<ul>\n \t<li>5.5 Monetary Word Problems<\/li>\n \t<li>6.8 Mixture and Solution Word Problems<\/li>\n \t<li>7.9 Age Word Problems<\/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>Midterm Two Review<\/h1>\n<h2>Chapter 4: Systems of Equations (Exam Type Questions)<\/h2>\nFind the solution set of the system of equations below graphically.\n<ol>\n \t<li>[latex]\\left\\{\n\\begin{array}{llrllll}\nx&amp;-&amp;2y&amp;+&amp;4&amp;=&amp;3 \\\\\nx&amp;+&amp;y&amp;-&amp;5&amp;=&amp;0\n\\end{array}\\right.[\/latex]<\/li>\n<\/ol>\nFor problems 2\u20134, find the solution set of each system by any convenient method.\n<ol start=\"2\">\n \t<li>[latex]\\left\\{\n\\begin{array}{rrrrr}\n2x&amp;-&amp;y&amp;=&amp; 0 \\\\\n3x&amp;+&amp;4y&amp;=&amp;-22\n\\end{array}\\right.[\/latex]<\/li>\n \t<li>[latex]\\left\\{\n\\begin{array}{rrrrr}\n2x&amp;-&amp;5y&amp;=&amp;15 \\\\\n3x&amp;+&amp;2y&amp;=&amp;13\n\\end{array}\\right.[\/latex]<\/li>\n \t<li>[latex]\\left\\{\n\\begin{array}{rrrrrrr}\n5x&amp;+&amp;y&amp;+&amp;6z&amp;=&amp;-2 \\\\\n&amp;&amp;2y&amp;-&amp;3z&amp;=&amp;3 \\\\\n5x&amp;&amp;&amp;+&amp;6z&amp;=&amp;-4\n\\end{array}\\right.[\/latex]<\/li>\n<\/ol>\n<h2>Chapter 5: Polynomials (Exam Type Questions)<\/h2>\nSimplify.\n<ol start=\"5\">\n \t<li>[latex](4a^2-9a+2)-(a^2-4a-5)+(9-a+3a^2)[\/latex]<\/li>\n \t<li>[latex]2x^2(4x^2-6y^2)-3x(5xy^2+x^3)[\/latex]<\/li>\n \t<li>[latex]6 - 2[3x - 4(5x - 2) - (1 - 7x)^0][\/latex]<\/li>\n \t<li>[latex](5a^{-5}b^3)^2[\/latex]<\/li>\n \t<li>[latex]8a^2(a+5)^2[\/latex]<\/li>\n \t<li>[latex]4ab^2(a-2)(a+2)[\/latex]<\/li>\n \t<li>[latex](x^2-4x+7)(x-3)[\/latex]<\/li>\n \t<li>[latex](2x^2+x-3)^2[\/latex]<\/li>\n \t<li>[latex](x^2+5x-2)(2x^2-x+3)[\/latex]<\/li>\n \t<li>[latex](x+4)^3[\/latex]<\/li>\n \t<li>[latex]\\dfrac{(r^{-4}s^9)}{(r^3s^{-9})}[\/latex]<\/li>\n<\/ol>\nDivide using long division.\n<ol start=\"17\">\n \t<li>[latex](2x^3-7x^2+15)\\div (x-2)[\/latex]<\/li>\n<\/ol>\n<h2>Chapter 6: Factoring\u00a0(Exam Type Questions)<\/h2>\n<strong>Questions 18\u201319 are for review only and will not show up on exams.<\/strong>\n<ol start=\"18\">\n \t<li>Find the prime factorization of 88.<\/li>\n \t<li>Find the LCM of 84 and 96.<\/li>\n<\/ol>\n<b>Questions similar to 20\u201327 will show up on exams.<\/b>\n\nFactor each expression completely.\n<ol start=\"20\">\n \t<li>[latex]5xy+6xz-15y-18z[\/latex]<\/li>\n \t<li>[latex]x^2+x-12[\/latex]<\/li>\n \t<li>[latex]x^3+x^2-4x-4[\/latex]<\/li>\n \t<li>[latex]x^3-27y^3[\/latex]<\/li>\n \t<li>[latex]x^4-35x^2-36[\/latex]<\/li>\n<\/ol>\n<h2>Chapter 4\u20136 Word Problems (Exam Type Questions)<\/h2>\n<ol start=\"25\">\n \t<li>A 70 kg mixture of two different types of nuts costs [latex]\\$430.[\/latex] If type A costs [latex]\\$4[\/latex] per kg and type B costs [latex]\\$7[\/latex] per kg, how many kg of each type were used?<\/li>\n \t<li>A wedding reception bartender is faced with a problem: how many litres of a 5% rum drink must be mixed with 2 litres of a 21% flavoured rum to make a rum punch of 11% strength?<\/li>\n \t<li>The sum of the ages of a boy and a girl is 16 years. Four years ago, the girl was three times the age of the boy. Find the present age of each child.<\/li>\n<\/ol>\n<a class=\"internal\" href=\"\/\/back-matter\/midterm-2-prep-answer-key\/\">Mid Term 2 Prep Answer Key<\/a>","rendered":"<p>The second midterm will be composed of fifteen questions covering chapters 5 to 7.<\/p>\n<p>Twelve questions will be algebra questions, and three questions will be word problems.<\/p>\n<ul>\n<li><b>Questions 1\u20134 will be drawn from Chapter 5: Systems of Equations<\/b>\n<ul>\n<li>5.1 Graphed Solutions<\/li>\n<li>5.2 Substitution Solutions<\/li>\n<li>5.3 Addition and Subtraction Solutions<\/li>\n<li>5.4 Solving for Three Variables<\/li>\n<\/ul>\n<\/li>\n<li><b>Questions 5\u20136 will be drawn from Chapter 6: Polynomials<\/b>\n<ul>\n<li>6.1 Working with Exponents<\/li>\n<li>6.2 Negative Exponents<\/li>\n<li>6.3 Scientific Notation<\/li>\n<li>6.4 Basic Operations Using Polynomials<\/li>\n<li>6.5 Multiplication of Polynomials<\/li>\n<li>6.6 Special Products<\/li>\n<li>6.7 Dividing Polynomials<\/li>\n<\/ul>\n<\/li>\n<li><b>Questions 9\u201312 will be drawn from Chapter 7: Factoring<\/b>\n<ul>\n<li>7.1 Greatest Common Factor<\/li>\n<li>7.2 Factoring by Grouping<\/li>\n<li>7.3 Factoring Trinomials where a = 1<\/li>\n<li>7.4 Factoring Trinomials where a \u2260 1<\/li>\n<li>7.5 Factoring Special Products<\/li>\n<li>7.6 Factoring Quadratics of Increasing Difficulty<\/li>\n<li>7.7 Choosing the Correct Factoring Strategy<\/li>\n<li>7.8 Solving Quadratic Equations by Factoring<\/li>\n<\/ul>\n<\/li>\n<li><b>Questions 13\u201315 will be drawn from:<\/b>\n<ul>\n<li>5.5 Monetary Word Problems<\/li>\n<li>6.8 Mixture and Solution Word Problems<\/li>\n<li>7.9 Age Word Problems<\/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>Midterm Two Review<\/h1>\n<h2>Chapter 4: Systems of Equations (Exam Type Questions)<\/h2>\n<p>Find the solution set of the system of equations below graphically.<\/p>\n<ol>\n<li>[latex]\\left\\{ \\begin{array}{llrllll} x&-&2y&+&4&=&3 \\\\ x&+&y&-&5&=&0 \\end{array}\\right.[\/latex]<\/li>\n<\/ol>\n<p>For problems 2\u20134, find the solution set of each system by any convenient method.<\/p>\n<ol start=\"2\">\n<li>[latex]\\left\\{ \\begin{array}{rrrrr} 2x&-&y&=& 0 \\\\ 3x&+&4y&=&-22 \\end{array}\\right.[\/latex]<\/li>\n<li>[latex]\\left\\{ \\begin{array}{rrrrr} 2x&-&5y&=&15 \\\\ 3x&+&2y&=&13 \\end{array}\\right.[\/latex]<\/li>\n<li>[latex]\\left\\{ \\begin{array}{rrrrrrr} 5x&+&y&+&6z&=&-2 \\\\ &&2y&-&3z&=&3 \\\\ 5x&&&+&6z&=&-4 \\end{array}\\right.[\/latex]<\/li>\n<\/ol>\n<h2>Chapter 5: Polynomials (Exam Type Questions)<\/h2>\n<p>Simplify.<\/p>\n<ol start=\"5\">\n<li>[latex](4a^2-9a+2)-(a^2-4a-5)+(9-a+3a^2)[\/latex]<\/li>\n<li>[latex]2x^2(4x^2-6y^2)-3x(5xy^2+x^3)[\/latex]<\/li>\n<li>[latex]6 - 2[3x - 4(5x - 2) - (1 - 7x)^0][\/latex]<\/li>\n<li>[latex](5a^{-5}b^3)^2[\/latex]<\/li>\n<li>[latex]8a^2(a+5)^2[\/latex]<\/li>\n<li>[latex]4ab^2(a-2)(a+2)[\/latex]<\/li>\n<li>[latex](x^2-4x+7)(x-3)[\/latex]<\/li>\n<li>[latex](2x^2+x-3)^2[\/latex]<\/li>\n<li>[latex](x^2+5x-2)(2x^2-x+3)[\/latex]<\/li>\n<li>[latex](x+4)^3[\/latex]<\/li>\n<li>[latex]\\dfrac{(r^{-4}s^9)}{(r^3s^{-9})}[\/latex]<\/li>\n<\/ol>\n<p>Divide using long division.<\/p>\n<ol start=\"17\">\n<li>[latex](2x^3-7x^2+15)\\div (x-2)[\/latex]<\/li>\n<\/ol>\n<h2>Chapter 6: Factoring\u00a0(Exam Type Questions)<\/h2>\n<p><strong>Questions 18\u201319 are for review only and will not show up on exams.<\/strong><\/p>\n<ol start=\"18\">\n<li>Find the prime factorization of 88.<\/li>\n<li>Find the LCM of 84 and 96.<\/li>\n<\/ol>\n<p><b>Questions similar to 20\u201327 will show up on exams.<\/b><\/p>\n<p>Factor each expression completely.<\/p>\n<ol start=\"20\">\n<li>[latex]5xy+6xz-15y-18z[\/latex]<\/li>\n<li>[latex]x^2+x-12[\/latex]<\/li>\n<li>[latex]x^3+x^2-4x-4[\/latex]<\/li>\n<li>[latex]x^3-27y^3[\/latex]<\/li>\n<li>[latex]x^4-35x^2-36[\/latex]<\/li>\n<\/ol>\n<h2>Chapter 4\u20136 Word Problems (Exam Type Questions)<\/h2>\n<ol start=\"25\">\n<li>A 70 kg mixture of two different types of nuts costs [latex]\\$430.[\/latex] If type A costs [latex]\\$4[\/latex] per kg and type B costs [latex]\\$7[\/latex] per kg, how many kg of each type were used?<\/li>\n<li>A wedding reception bartender is faced with a problem: how many litres of a 5% rum drink must be mixed with 2 litres of a 21% flavoured rum to make a rum punch of 11% strength?<\/li>\n<li>The sum of the ages of a boy and a girl is 16 years. Four years ago, the girl was three times the age of the boy. Find the present age of each child.<\/li>\n<\/ol>\n<p><a class=\"internal\" href=\"\/\/back-matter\/midterm-2-prep-answer-key\/\">Mid Term 2 Prep Answer Key<\/a><\/p>\n","protected":false},"parent":0,"menu_order":11,"template":"","meta":{"pb_part_invisible":false,"pb_part_invisible_string":""},"contributor":[],"license":[],"class_list":["post-1392","part","type-part","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/parts\/1392","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\/1392\/revisions"}],"predecessor-version":[{"id":1393,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/parts\/1392\/revisions\/1393"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1392"}],"wp:term":[{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1392"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1392"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}