{"id":2110,"date":"2019-09-19T13:50:14","date_gmt":"2019-09-19T17:50:14","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/?post_type=back-matter&p=2110"},"modified":"2019-11-19T17:17:28","modified_gmt":"2019-11-19T22:17:28","slug":"midterm-2-prep-answer-key","status":"publish","type":"back-matter","link":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/back-matter\/midterm-2-prep-answer-key\/","title":{"raw":"Midterm 2: Prep Answer Key","rendered":"Midterm 2: Prep Answer Key"},"content":{"raw":"[latexpage]\r\n

Midterm Two Review<\/h1>\r\n
    \r\n \t
  1. \r\n\r\n\r\n\r\n\r\n\r\n
    \\(x-2y=-4\\)<\/caption>\r\n
    \\(x\\)<\/th>\r\n\\(y\\)<\/th>\r\n<\/tr>\r\n
    \u22124<\/td>\r\n0<\/td>\r\n<\/tr>\r\n
    0<\/td>\r\n2<\/td>\r\n<\/tr>\r\n
    \u22122<\/td>\r\n1<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\r\n\r\n\r\n\r\n\r\n
    \\(x+y=5\\)<\/caption>\r\n
    \\(x\\)<\/th>\r\n\\(y\\)<\/th>\r\n<\/tr>\r\n
    0<\/td>\r\n5<\/td>\r\n<\/tr>\r\n
    5<\/td>\r\n0<\/td>\r\n<\/tr>\r\n
    2<\/td>\r\n3<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\"\"<\/li>\r\n \t
  2. \\(\\begin{array}{rrcrlrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n2x&-&y&=&0&\\Rightarrow &y=2x \\\\\r\n3x&+&4y&=&-22&& \\\\ \\\\\r\n\\therefore 3x&+&4(2x)&=&-22&& \\\\\r\n3x&+&8x&=&-22&& \\\\\r\n&&11x&=&-22&& \\\\\r\n&&x&=&-2&& \\\\ \\\\\r\n&&y&=&2x&& \\\\\r\n&&y&=&2(-2)&=&-4 \\\\\r\n\\end{array}\\)\r\n\\((-2,-4)\\)<\/li>\r\n \t
  3. \\(\\begin{array}{rrrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&(2x&-&5y&=&15)(2) \\\\\r\n&(3x&+&2y&=&13)(5) \\\\\r\n\\midrule\r\n&4x&-&10y&=&30 \\\\\r\n+&15x&+&10y&=&65 \\\\\r\n\\midrule\r\n&&&19x&=&95 \\\\\r\n&&&x&=&5 \\\\ \\\\\r\n&\\therefore 3(5)&+&2y&=&\\phantom{-}13 \\\\\r\n&15&+&2y&=&\\phantom{-}13 \\\\\r\n&-15&&&&-15 \\\\\r\n\\midrule\r\n&&&2y&=&-2 \\\\\r\n&&&y&=&-1\r\n\\end{array}\\)\r\n\\((5,-1)\\)<\/li>\r\n \t
  4. \\(\\begin{array}{rr}\r\n\\begin{array}{rrrrrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&&(5x&+&6z&=&-4)(-1) \\\\ \\\\\r\n&5x&+&y&+&6z&=&-2 \\\\\r\n+&-5x&&&-&6z&=&\\phantom{-}4 \\\\\r\n\\midrule\r\n&&&&&y&=&2 \\\\ \\\\\r\n&&&\\therefore 2y&-&3z&=&\\phantom{-}3 \\\\\r\n&&&2(2)&-&3z&=&\\phantom{-}3 \\\\\r\n&&&-4&&&&-4 \\\\\r\n\\midrule\r\n&&&&&-3z&=&-1 \\\\\r\n&&&&&z&=&\\dfrac{1}{3} \\\\\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n5x&+&6z&=&-4 \\\\\r\n5x&+&6\\left(\\dfrac{1}{3}\\right)&=&-4 \\\\\r\n5x&+&2&=&-4 \\\\\r\n&-&2&&-2 \\\\\r\n\\midrule\r\n&&5x&=&-6 \\\\\r\n&&x&=&-\\dfrac{6}{5}\r\n\\end{array}\r\n\\end{array}\\)\r\n\\(-\\dfrac{6}{5}, 2, \\dfrac{1}{3}\\)<\/li>\r\n \t
  5. \\(\\begin{array}{rrrrrr}\r\n\\\\ \\\\ \\\\\r\n&4a^2&-&9a&+&2 \\\\\r\n&-a^2&+&4a&+&5 \\\\\r\n+&3a^2&-&a&+&9 \\\\\r\n\\midrule\r\n&6a^2&-&6a&+&16\r\n\\end{array}\\)<\/li>\r\n \t
  6. \\(8x^4-12x^2y^2-15x^2y^2-3x^4\\Rightarrow 5x^4-27x^2y^2\\)<\/li>\r\n \t
  7. \\(\\begin{array}{l}\r\n\\\\ \\\\ \\\\\r\n6-2\\left[3x-20x+8-1\\right] \\\\\r\n6-2\\left[-17x+7\\right] \\\\\r\n6+34x-14 \\\\\r\n34x-8\r\n\\end{array}\\)<\/li>\r\n \t
  8. \\(25a^{-10}b^6\\text{ or } \\dfrac{25b^6}{a^{10}}\\)<\/li>\r\n \t
  9. \\(\\begin{array}{l}\r\n\\\\\r\n8a^2(a^2+10a+25) \\\\\r\n8a^4+80a^3+200a^2\r\n\\end{array}\\)<\/li>\r\n \t
  10. \\(\\begin{array}{l}\r\n\\\\\r\n4ab^2(a^2-4) \\\\\r\n4a^3b^2-16ab^2\r\n\\end{array}\\)<\/li>\r\n \t
  11. \\(\\begin{array}{rrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n&x^2&-&4x&+&7\\phantom{x}&& \\\\\r\n\\times &&&x&-&3\\phantom{x}&& \\\\\r\n\\midrule\r\n&x^3&-&4x^2&+&7x&& \\\\\r\n+&&-&3x^2&+&12x&-&21 \\\\\r\n\\midrule\r\n&x^3&-&7x^2&+&19x&-&21 \\\\\r\n\\end{array}\\)<\/li>\r\n \t
  12. \\(\\begin{array}{rrrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&2x^2&+&x&-&3\\phantom{x^2}&&&& \\\\\r\n\\times &2x^2&+&x&-&3\\phantom{x^2}&&&& \\\\\r\n\\midrule\r\n&4x^4&+&2x^3&-&6x^2&&&& \\\\\r\n&&&2x^3&+&x^2&-&3x&& \\\\\r\n+&&&&&-6x^2&-&3x&+&9 \\\\\r\n\\midrule\r\n&4x^4&+&4x^3&-&11x^2&-&6x&+&9\r\n\\end{array}\\)<\/li>\r\n \t
  13. \\(\\begin{array}{rrrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&x^2&+&5x&-&2\\phantom{x^2}&&&& \\\\\r\n\\times &2x^2&-&x&+&3\\phantom{x^2}&&&& \\\\\r\n\\midrule\r\n&2x^4&+&10x^3&-&4x^2&&&& \\\\\r\n&&&-x^3&-&5x^2&+&2x&& \\\\\r\n+&&&&&3x^2&+&15x&-&6 \\\\\r\n\\midrule\r\n&2x^4&+&9x^3&-&6x^2&+&17x&-&6\r\n\\end{array}\\)<\/li>\r\n \t
  14. \\(\\begin{array}{rrrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n(x+4)(x+4)&\\Rightarrow &&x^2&+&8x&+&16&&\u00a0 \\\\\r\n&&\\times&&&x&+&4&&\u00a0 \\\\\r\n\\midrule\r\n&&&x^3&+&8x^2&+&16x&&\u00a0 \\\\\r\n&&+&&&4x^2&+&32x&+&64\u00a0 \\\\\r\n\\midrule\r\n&&&x^3&+&12x^2&+&48x&+&64\r\n\\end{array}\\)<\/li>\r\n \t
  15. \\(r^{-4-3}s^{9+9}\\Rightarrow r^{-7}s^{18}\\Rightarrow \\dfrac{s^{18}}{r^7}\\)\r\n\\(\\dfrac{s^{18}}{r^7}\\)<\/li>\r\n \t
  16. \\(\\begin{array}{l}\r\n\\\\ \\\\\r\n(x^{-2--2}y^{-3-4})^{-1} \\\\\r\n(1\\cancel{x^0}y^{-7})^{-1} \\\\\r\ny^7\r\ny^7\r\n\\end{array}\\)<\/li>\r\n \t
  17. \\(\\polylongdiv{2x^3-7x^2+15}{x-2}\\)<\/li>\r\n \t
  18. \\(2^3\\cdot 11\\)<\/li>\r\n \t
  19. \\(2^5\\cdot 3\\cdot 7\r\n\\left\\{\r\n\\begin{array}{l}\r\n84=2^2\\cdot 3\\cdot 7 \\\\\r\n96=2^5\\cdot 3\r\n\\end{array}\\right.\\)<\/li>\r\n \t
  20. \\(x(5y+6z)-3(5y+6z)\\)\r\n\\((5y+6z)(x-3)\\)<\/li>\r\n \t
  21. \\(-12=4\\times -3\\)\r\n\\(1=4+-3 \\\\ \\)\r\n\\(x^2+4x-3x-12\\)\r\n\\(x(x+4)-3(x+4)\\)\r\n\\((x+4)(x-3)\\)<\/li>\r\n \t
  22. \\(x^2(x+1)-4(x+1)\\)\r\n\\((x+1)(x^2-4)\\)\r\n\\(x+1)(x-2)(x+2)<\/li>\r\n \t
  23. \\(x^3-(3y)^3\\)\r\n\\((x-3y)(x^2+3xy+9y^2)\\)<\/li>\r\n \t
  24. \\((x^2-36)(x^2+1)\\)\r\n\\((x-6)(x+6)(x^2+1)\\)<\/li>\r\n \t
  25. \\(\\begin{array}{lll}\r\n\\begin{array}{rrrrl}\r\n(A&+&B&=&70)(-4) \\\\\r\n4A&+&7B&=&430\r\n\\end{array}\r\n& \\Rightarrow \\hspace{0.25in}\r\n\\begin{array}{rrrrrl}\r\n\\\\ \\\\ \\\\ \\\\\r\n&-4A&-&4B&=&-280 \\\\\r\n+&4A&+&7B&=&\\phantom{-}430 \\\\\r\n\\midrule\r\n&&&3B&=&\\phantom{-}150 \\\\ \\\\\r\n&&&B&=&\\dfrac{150}{3}\\text{ or }50\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrrrr}\r\n\\\\ \\\\ \\\\\r\n\\therefore A&+&B&=&70 \\\\ \\\\\r\nA&+&50&=&70 \\\\\r\n&&-50&&-50 \\\\\r\n\\midrule\r\n&&A&=&20\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
  26. \\(\\begin{array}{rrcrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n5x&+&21(2)&=&11(x&+&2) \\\\ \\\\\r\n5x&+&42&=&11x&+&22 \\\\\r\n-5x&-&22&&-5x&-&22 \\\\\r\n\\midrule\r\n&&20&=&6x&& \\\\ \\\\\r\n&&x&=&\\dfrac{20}{6}&=&3\\dfrac{1}{3}\\text{ litres} \\\\\r\n\\end{array}\\)<\/li>\r\n \t
  27. \\(\\phantom{1}\\)\r\n\\(B+G=16\\Rightarrow B=16-G\\text{ or }G=16-B \\\\ \\)\r\n\\(\\begin{array}{ll}\r\n\\begin{array}{rrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\nG&-&4&=&3(B&-&4) \\\\\r\n16-B&-&4&=&3B&-&12 \\\\\r\n+B&+&12&&+B&+&12 \\\\\r\n\\midrule\r\n&&24&=&4B&& \\\\ \\\\\r\n&&B&=&\\dfrac{24}{4}&=&6\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrrrr}\r\n\\\\\r\n\\therefore G&=&16&-&B \\\\\r\nG&=&16&-&6 \\\\\r\nG&=&10&&\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n<\/ol>","rendered":"

    Midterm Two Review<\/h1>\n
      \n
    1. \n\n\n\n\n\n\n
      \"x-2y=-4\"<\/caption>\n
      \"x\"<\/th>\n\"y\"<\/th>\n<\/tr>\n
      \u22124<\/td>\n0<\/td>\n<\/tr>\n
      0<\/td>\n2<\/td>\n<\/tr>\n
      \u22122<\/td>\n1<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n\n\n
      \"x+y=5\"<\/caption>\n
      \"x\"<\/th>\n\"y\"<\/th>\n<\/tr>\n
      0<\/td>\n5<\/td>\n<\/tr>\n
      5<\/td>\n0<\/td>\n<\/tr>\n
      2<\/td>\n3<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      \"\"<\/li>\n

    2. \"\begin{array}{rrcrlrl}
      \n\"(-2,-4)\"<\/li>\n
    3. \"\begin{array}{rrrrrl}
      \n\"(5,-1)\"<\/li>\n
    4. \"\begin{array}{rr}
      \n\"-\dfrac{6}{5}, 2, \dfrac{1}{3}\"<\/li>\n
    5. \"\begin{array}{rrrrrr}<\/li>\n
    6. \"8x^4-12x^2y^2-15x^2y^2-3x^4\Rightarrow 5x^4-27x^2y^2\"<\/li>\n
    7. \"\begin{array}{l}<\/li>\n
    8. \"25a^{-10}b^6\text{ or } \dfrac{25b^6}{a^{10}}\"<\/li>\n
    9. \"\begin{array}{l}<\/li>\n
    10. \"\begin{array}{l}<\/li>\n
    11. \"\begin{array}{rrrrrrrr}<\/li>\n
    12. \"\begin{array}{rrrrrrrrrr}<\/li>\n
    13. \"\begin{array}{rrrrrrrrrr}<\/li>\n
    14. \"\begin{array}{rrrrrrrrrr}<\/li>\n
    15. \"r^{-4-3}s^{9+9}\Rightarrow r^{-7}s^{18}\Rightarrow \dfrac{s^{18}}{r^7}\"
      \n\"\dfrac{s^{18}}{r^7}\"<\/li>\n
    16. \"\begin{array}{l}<\/li>\n
    17. \"\polylongdiv{2x^3-7x^2+15}{x-2}\"<\/li>\n
    18. \"2^3\cdot 11\"<\/li>\n
    19. \"2^5\cdot 3\cdot 7<\/li>\n
    20. \"x(5y+6z)-3(5y+6z)\"
      \n\"(5y+6z)(x-3)\"<\/li>\n
    21. \"-12=4\times -3\"
      \n\"1=4+-3 \\\"
      \n\"x^2+4x-3x-12\"
      \n\"x(x+4)-3(x+4)\"
      \n\"(x+4)(x-3)\"<\/li>\n
    22. \"x^2(x+1)-4(x+1)\"
      \n\"(x+1)(x^2-4)\"
      \n\"x+1)(x-2)(x+2)</li>
      \n\"(x-3y)(x^2+3xy+9y^2)\"<\/li>\n
    23. \"(x^2-36)(x^2+1)\"
      \n\"(x-6)(x+6)(x^2+1)\"<\/li>\n
    24. \"\begin{array}{lll}<\/li>\n
    25. \"\begin{array}{rrcrrrl}<\/li>\n
    26. \"\phantom{1}\"
      \n\"B+G=16\Rightarrow B=16-G\text{ or }G=16-B \\\"
      \n\"\begin{array}{ll}<\/li>\n<\/ol>\n","protected":false},"author":727,"menu_order":63,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"back-matter-type":[],"contributor":[],"license":[],"class_list":["post-2110","back-matter","type-back-matter","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/2110","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/types\/back-matter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/users\/727"}],"version-history":[{"count":25,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/2110\/revisions"}],"predecessor-version":[{"id":3394,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/2110\/revisions\/3394"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/2110\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/media?parent=2110"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter-type?post=2110"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/contributor?post=2110"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/license?post=2110"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}