{"id":3207,"date":"2019-11-19T13:41:31","date_gmt":"2019-11-19T18:41:31","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/?post_type=back-matter&p=3207"},"modified":"2020-01-04T14:27:00","modified_gmt":"2020-01-04T19:27:00","slug":"midterm-one-version-a-answer-key","status":"publish","type":"back-matter","link":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/back-matter\/midterm-one-version-a-answer-key\/","title":{"raw":"Midterm 1: Version A Answer Key","rendered":"Midterm 1: Version A Answer Key"},"content":{"raw":"[latexpage]\r\n
    \r\n \t
  1. \\(\\begin{array}{l}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n-(-3)-\\sqrt{(-3)^2-4(4)(-1)} \\\\ \\\\\r\n3-\\sqrt{9+16} \\\\ \\\\\r\n3-\\sqrt{25} \\\\ \\\\\r\n3-5 \\\\ \\\\\r\n-2\r\n\\end{array}\\)<\/li>\r\n \t
  2. \\(\\begin{array}{rrrrrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&2x&-&10&-&85&=&3&-&9x&-&54 \\\\\r\n+&9x&+&10&+&85&&&+&9x&+&3 \\\\\r\n&&&&&&&&&&+&85 \\\\\r\n&&&&&&&&&&+&10 \\\\\r\n\\midrule\r\n&&&&&\\dfrac{11x}{11}&=&\\dfrac{44}{11}&&&& \\\\ \\\\\r\n&&&&&x&=&4&&&&\r\n\\end{array}\\)<\/li>\r\n \t
  3. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\nA(B-b)&=&h \\\\ \\\\\r\nB-b&=&\\dfrac{h}{A} \\\\ \\\\\r\n-b&=&\\dfrac{h}{A}-B\r\n\\end{array}\\)<\/li>\r\n \t
  4. \\(\\phantom{1}\\)\r\n\\(\\left(\\dfrac{x+1}{4}-\\dfrac{5}{8}=\\dfrac{x-1}{8}\\right)(8) \\\\ \\)\r\n\\(\\begin{array}{rrrrrrrrr}\r\n2(x&+&1)&-&5&=&x&-&1 \\\\\r\n2x&+&2&-&5&=&x&-&1 \\\\\r\n-x&-&2&+&5&&-x&+&5 \\\\\r\n&&&&&&&-&2 \\\\\r\n\\midrule\r\n&&&&x&=&2&&\r\n\\end{array}\\)<\/li>\r\n \t
  5. \"Line\r\n\\(x=-2\\)<\/li>\r\n \t
  6. \\(\\begin{array}{ll}\r\n\\\\ \\\\ \\\\\r\n\\begin{array}{rrl}\r\nm&=&\\dfrac{\\Delta y}{\\Delta x} \\\\ \\\\\r\n\\dfrac{2}{5}&=&\\dfrac{y--2}{x--1}\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrrrrrrrl}\r\n\\\\ \\\\ \\\\\r\n&&2(x&+&1)&=&5(y&+&2) \\\\\r\n&&2x&+&2&=&5y&+&10 \\\\\r\n&&-5y&-&10&&-5y&-&10 \\\\\r\n\\midrule\r\n2x&-&5y&-&8&=&0&& \\\\\r\n&&&&0&=&2x&-&5y-8 \\\\ \\\\\r\n&&&&y&=&\\dfrac{2}{5}x&-&\\dfrac{8}{5}\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
  7. \\(\\begin{array}{ll}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\begin{array}{rrl}\r\n\\text{1st slope} && \\\\\r\nm&=&\\dfrac{\\Delta y}{\\Delta x} \\\\ \\\\\r\nm&=&\\dfrac{4-0}{6--2} \\\\ \\\\\r\nm&=&\\dfrac{4}{8}\\text{ or }\\dfrac{1}{2}\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\\r\n\\text{Now:} && \\\\\r\nm&=&\\dfrac{\\Delta y}{\\Delta x} \\\\ \\\\\r\n\\dfrac{1}{2}&=&\\dfrac{y-0}{x--2} \\\\ \\\\\r\n1(x+2) &=&2(y-0) \\\\\r\nx+2&=&2y \\\\ \\\\\r\n\\therefore y&=&\\dfrac{1}{2}+1 \\\\ \\\\\r\n\\text{or }x-2y+2&=&0\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
  8. \"Line<\/li>\r\n \t
  9. \\(\\begin{array}{rrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n6x&-&5&-&30x&>&67 \\\\\r\n&+&5&&&&+5 \\\\\r\n\\midrule\r\n&&&&\\dfrac{-24x}{-24}&>&\\dfrac{72}{-24} \\\\ \\\\\r\n&&&&x&<&-3\r\n\\end{array}\\)\r\n\"x<\/li>\r\n \t
  10. \\(\\begin{array}{rrrcrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n-10&\\le &4x&-&2&\\le &14 \\\\\r\n+2&&&+&2&&+2 \\\\\r\n\\midrule\r\n\\dfrac{-8}{4}&\\le &&\\dfrac{4x}{4}&&\\le &\\dfrac{16}{4} \\\\ \\\\\r\n-2&\\le &&x&&\\le &4\r\n\\end{array}\\)\r\n\"x<\/li>\r\n \t
  11. \\(\\begin{array}{ll}\r\n\\begin{array}{rrl}\r\n\\dfrac{3x+2}{5}&=& 2 \\\\ \\\\\r\n3x+2&=&10 \\\\\r\n-2&&-2 \\\\\r\n\\midrule\r\n\\dfrac{3x}{3}&=&\\dfrac{8}{3} \\\\ \\\\\r\nx&=&\\dfrac{8}{3}\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrl}\r\n\\dfrac{3x+2}{5}&=& -2 \\\\ \\\\\r\n3x+2 &=&-10 \\\\\r\n-2&&-2 \\\\\r\n\\midrule\r\n\\dfrac{3x}{3}&=&\\dfrac{-12}{3} \\\\ \\\\\r\nx&=&-4\r\n\\end{array}\r\n\\end{array}\\)\r\n\"x<\/li>\r\n \t
  12. \r\n\r\n\r\n\r\n\r\n\r\n\r\n
    \\(5x+2y<15\\)<\/caption>\r\n
    \\(x\\)<\/th>\r\n\\(y\\)<\/th>\r\n<\/tr>\r\n
    0<\/td>\r\n7.5<\/td>\r\n<\/tr>\r\n
    3<\/td>\r\n0<\/td>\r\n<\/tr>\r\n
    1<\/td>\r\n5<\/td>\r\n<\/tr>\r\n
    5<\/td>\r\n\u22125<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\"Line<\/li>\r\n \t
  13. \\(\\begin{array}{rrrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&(5L&+&3S&=&47)(2) \\\\\r\n&(4L&-&2S&=&20)(3) \\\\ \\\\\r\n&10L&+&6S&=&94 \\\\\r\n+&12L&-&6S&=&60 \\\\\r\n\\midrule\r\n&&&\\dfrac{22L}{22}&=&\\dfrac{154}{22} \\\\ \\\\\r\n&&&L&=&7 \\\\ \\\\\r\n\\therefore &4L&-&2S&=&\\phantom{-}20 \\\\\r\n&4(7)&-&2S&=&\\phantom{-}20 \\\\\r\n&28&-&2S&=&\\phantom{-}20 \\\\\r\n-&28&&&&-28 \\\\\r\n\\midrule\r\n&&&\\dfrac{-2S}{-2}&=&\\dfrac{-8}{-2} \\\\ \\\\\r\n&&&S&=&4\r\n\\end{array}\\)<\/li>\r\n \t
  14. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n36\\text{ cm}&=&5x+x \\\\\r\n36\\text{ cm}&=&6x \\\\ \\\\\r\nx&=&\\dfrac{36\\text{ cm}}{6} \\\\ \\\\\r\nx&=&6\\text{ cm} \\\\\r\n5x&=&5(6)=30 \\text{ cm}\r\n\\end{array}\\)<\/li>\r\n \t
  15. \\(\\begin{array}{ll}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\text{\\underline{1st}}&& \\\\\r\ny&=&\\dfrac{kmn}{d^2} \\\\ \\\\\r\n\\text{\\underline{2nd}}&& \\\\\r\ny&=&3 \\\\\r\nk&=&\\text{find} \\\\\r\nm&=&2 \\\\\r\nn&=&8 \\\\\r\nd&=&4 \\\\ \\\\\r\ny&=&\\dfrac{kmn}{d^2} \\\\ \\\\\r\n3&=&\\dfrac{k(2)(8)}{(4)^2} \\\\ \\\\\r\nk&=&\\dfrac{3\\cdot (4)^2}{2\\cdot 8} \\\\ \\\\\r\nk&=& 3\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\\r\n\\text{\\underline{3rd}}&& \\\\\r\ny&=&\\text{find} \\\\\r\nk&=&3 \\\\\r\nm&=&15 \\\\\r\nn&=&10 \\\\\r\nd&=& 5 \\\\ \\\\\r\ny&=&\\dfrac{kmn}{d^2} \\\\ \\\\\r\ny&=&\\dfrac{(3)(15)(10)}{(5)^2} \\\\ \\\\\r\ny&=&18\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n<\/ol>\r\n\r\n

    <\/h1>","rendered":"
      \n
    1. \"\begin{array}{l}<\/li>\n
    2. \"\begin{array}{rrrrrrrrrrrr}<\/li>\n
    3. \"\begin{array}{rrl}<\/li>\n
    4. \"\phantom{1}\"
      \n\"\left(\dfrac{x+1}{4}-\dfrac{5}{8}=\dfrac{x-1}{8}\right)(8) \\\"
      \n\"\begin{array}{rrrrrrrrr}<\/li>\n
    5. \"Line
      \n\"x=-2\"<\/li>\n
    6. \"\begin{array}{ll}<\/li>\n
    7. \"\begin{array}{ll}<\/li>\n
    8. \"Line<\/li>\n
    9. \"\begin{array}{rrrrrrr}
      \n\"x<\/li>\n
    10. \"\begin{array}{rrrcrrr}
      \n\"x<\/li>\n
    11. \"\begin{array}{ll}
      \n\"x<\/li>\n
    12. \n\n\n\n\n\n\n\n
      \"5x+2y<15\"<\/caption>\n
      \"x\"<\/th>\n\"y\"<\/th>\n<\/tr>\n
      0<\/td>\n7.5<\/td>\n<\/tr>\n
      3<\/td>\n0<\/td>\n<\/tr>\n
      1<\/td>\n5<\/td>\n<\/tr>\n
      5<\/td>\n\u22125<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      \"Line<\/li>\n

    13. \"\begin{array}{rrrrrl}<\/li>\n
    14. \"\begin{array}{rrl}<\/li>\n
    15. \"\begin{array}{ll}<\/li>\n<\/ol>\n

      <\/p>\n

      <\/h1>\n","protected":false},"author":14,"menu_order":32,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"back-matter-type":[],"contributor":[],"license":[],"class_list":["post-3207","back-matter","type-back-matter","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/3207","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\/14"}],"version-history":[{"count":6,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/3207\/revisions"}],"predecessor-version":[{"id":3733,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/3207\/revisions\/3733"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/3207\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/media?parent=3207"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter-type?post=3207"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/contributor?post=3207"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/license?post=3207"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}