{"id":1568,"date":"2021-12-02T19:38:32","date_gmt":"2021-12-03T00:38:32","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/chapter\/final-exam-version-a\/"},"modified":"2023-08-31T19:43:03","modified_gmt":"2023-08-31T23:43:03","slug":"final-exam-version-a","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/chapter\/final-exam-version-a\/","title":{"raw":"Final Exam: Version A","rendered":"Final Exam: Version A"},"content":{"raw":"

Questions from Chapters 1 to 3<\/h1>\r\n
    \r\n \t
  1. Evaluate [latex]-b-\\sqrt{b^2-4ac}[\/latex] if [latex]a=4,[\/latex] [latex]b=6[\/latex] and [latex]c=2[\/latex].<\/li>\r\n<\/ol>\r\nFor problems 2 and 3, solve for [latex]x[\/latex].\r\n
      \r\n \t
    1. [latex]6(x + 4) = 5(7 - x) - 4( 2 - 3x)[\/latex]<\/li>\r\n \t
    2. [latex]\\dfrac{x+4}{2}-\\dfrac{1}{2}=\\dfrac{x+2}{4}[\/latex]<\/li>\r\n \t
    3. Write an equation of the vertical line that passes through the point (\u22122, \u22123).<\/li>\r\n \t
    4. Find the distance between the points (\u22124, \u22122) and (2, 6).<\/li>\r\n \t
    5. Graph the relation [latex]2x - 3y = 6[\/latex].<\/li>\r\n<\/ol>\r\nFor problems 7 and 8, find the solution set and graph it.\r\n
        \r\n \t
      1. [latex]x - 2 ( x - 5 ) \\le 3 ( 6 + x )[\/latex]<\/li>\r\n \t
      2. [latex]\\left|\\dfrac{3x-2}{7}\\right|<1[\/latex]<\/li>\r\n<\/ol>\r\nIn problems 9 and 10, set up each problem algebraically and solve. Be sure to state what your variables represent.\r\n
          \r\n \t
        1. The time [latex](t)[\/latex] required to empty a tank varies inversely to the rate of pumping [latex](r).[\/latex] If a pump can empty a tank in 45 minutes at the rate of 600 kL\/min, how much time will it take the pump to empty the same tank at the rate of 1000 kL\/min?<\/li>\r\n \t
        2. Find two consecutive odd integers such that their sum is 12 less than four times the first integer.<\/li>\r\n<\/ol>\r\n

          Questions from Chapters 4 to 6<\/h1>\r\nFor problems 1\u20133, find the solution set of each system by any convenient method.\r\n
            \r\n \t
          1. [latex]\\left\\{\r\n\\begin{array}{l}\r\n2x + 5y = -18 \\\\\r\n\\phantom{2}y - 6\\phantom{y} = \\phantom{-}2x\r\n\\end{array}\\right.[\/latex]<\/li>\r\n \t
          2. [latex]\\left\\{\r\n\\begin{array}{l}\r\n8x+7y=51 \\\\\r\n5x+2y=20\r\n\\end{array}\\right.[\/latex]<\/li>\r\n \t
          3. [latex]\\left\\{\r\n\\begin{array}{l}\r\n\\phantom{2}x+y+6z=5 \\\\\r\n2x\\phantom{+3y}-3z=4 \\\\\r\n\\phantom{2x+}3y+4z=9\r\n\\end{array}\\right.[\/latex]<\/li>\r\n<\/ol>\r\nFor problems 4\u20136, perform the indicated operations and simplify.\r\n
              \r\n \t
            1. [latex]24 + \\{-3x - {[6x - 3(5 - 2x)]}^{0}\\} + 3x[\/latex]<\/li>\r\n \t
            2. [latex]2ab^3 (a - 4)(a + 4)[\/latex]<\/li>\r\n \t
            3. [latex]\\left(\\dfrac{xy^{-3}}{x^{-2}y^4}\\right)^{-1}[\/latex]<\/li>\r\n<\/ol>\r\nFor problems 7 and 8, factor each expression completely.\r\n
                \r\n \t
              1. [latex]3x^2 +11x + 8[\/latex]<\/li>\r\n \t
              2. [latex]64x^3 - y^3[\/latex]<\/li>\r\n \t
              3. A 50 kg mixture of two different grades of coffee costs [latex]\\$191.25.[\/latex] If grade A is worth [latex]\\$3.95[\/latex] per kg and grade B is worth [latex]\\$3.70[\/latex] per kg, how many kg of each type were used?<\/li>\r\n \t
              4. Kyra gave her brother Mark a logic question to solve: If she has 16 coins in her pocket worth [latex]\\$2.35,[\/latex] and if the coins are only dimes and quarters, how many of each kind of coin does she have?<\/li>\r\n<\/ol>\r\n

                Questions from Chapters 7 to 9<\/h1>\r\nIn problems 1\u20133, perform the indicated operations and simplify.\r\n
                  \r\n \t
                1. [latex]\\dfrac{15s^3}{3t^2}\\div \\dfrac{5t}{17s^3}\\div \\dfrac{34s^4}{3t^3}[\/latex]<\/li>\r\n \t
                2. [latex]\\dfrac{2x}{x-2}-\\dfrac{4x}{x-2}+\\dfrac{20}{x^2-4}[\/latex]<\/li>\r\n \t
                3. [latex]\\dfrac{\\dfrac{x^2}{y^2}-9}{\\dfrac{x+3y}{y^3}}[\/latex]<\/li>\r\n<\/ol>\r\nFor questions 4\u20136, simplify each expression.\r\n
                    \r\n \t
                  1. [latex]3\\sqrt{25x}-2\\sqrt{72x}-\\sqrt{16x^3}[\/latex]<\/li>\r\n \t
                  2. [latex]\\dfrac{\\sqrt{m^6n}}{\\sqrt{3n}}[\/latex]<\/li>\r\n \t
                  3. [latex]\\left(\\dfrac{a^0b^4}{c^8d^{-12}}\\right)^{\\frac{1}{4}}[\/latex]<\/li>\r\n<\/ol>\r\nFor questions 7 and 8, solve [latex]x[\/latex] by any convenient method.\r\n
                      \r\n \t
                    1. [latex]x^2 - 4x - 5 = 0[\/latex]<\/li>\r\n \t
                    2. [latex]\\dfrac{x-3}{x}=\\dfrac{x}{x-3}[\/latex]<\/li>\r\n<\/ol>\r\nIn problems 9 and 10, find the solution set of each system by any convenient method.\r\n
                        \r\n \t
                      1. The base of a right triangle is 6 cm longer than its height. If the area of this triangle is 20 cm2<\/sup>, find the length of both the base and the height.<\/li>\r\n \t
                      2. Find three consecutive even integers such that the product of the first two is 8 more than six times the third number.<\/li>\r\n<\/ol>\r\nFinal Exam: Version A Answer Key<\/a>","rendered":"

                        Questions from Chapters 1 to 3<\/h1>\n
                          \n
                        1. Evaluate [latex]-b-\\sqrt{b^2-4ac}[\/latex] if [latex]a=4,[\/latex] [latex]b=6[\/latex] and [latex]c=2[\/latex].<\/li>\n<\/ol>\n

                          For problems 2 and 3, solve for [latex]x[\/latex].<\/p>\n

                            \n
                          1. [latex]6(x + 4) = 5(7 - x) - 4( 2 - 3x)[\/latex]<\/li>\n
                          2. [latex]\\dfrac{x+4}{2}-\\dfrac{1}{2}=\\dfrac{x+2}{4}[\/latex]<\/li>\n
                          3. Write an equation of the vertical line that passes through the point (\u22122, \u22123).<\/li>\n
                          4. Find the distance between the points (\u22124, \u22122) and (2, 6).<\/li>\n
                          5. Graph the relation [latex]2x - 3y = 6[\/latex].<\/li>\n<\/ol>\n

                            For problems 7 and 8, find the solution set and graph it.<\/p>\n

                              \n
                            1. [latex]x - 2 ( x - 5 ) \\le 3 ( 6 + x )[\/latex]<\/li>\n
                            2. [latex]\\left|\\dfrac{3x-2}{7}\\right|<1[\/latex]<\/li>\n<\/ol>\n

                              In problems 9 and 10, set up each problem algebraically and solve. Be sure to state what your variables represent.<\/p>\n

                                \n
                              1. The time [latex](t)[\/latex] required to empty a tank varies inversely to the rate of pumping [latex](r).[\/latex] If a pump can empty a tank in 45 minutes at the rate of 600 kL\/min, how much time will it take the pump to empty the same tank at the rate of 1000 kL\/min?<\/li>\n
                              2. Find two consecutive odd integers such that their sum is 12 less than four times the first integer.<\/li>\n<\/ol>\n

                                Questions from Chapters 4 to 6<\/h1>\n

                                For problems 1\u20133, find the solution set of each system by any convenient method.<\/p>\n

                                  \n
                                1. [latex]\\left\\{ \\begin{array}{l} 2x + 5y = -18 \\\\ \\phantom{2}y - 6\\phantom{y} = \\phantom{-}2x \\end{array}\\right.[\/latex]<\/li>\n
                                2. [latex]\\left\\{ \\begin{array}{l} 8x+7y=51 \\\\ 5x+2y=20 \\end{array}\\right.[\/latex]<\/li>\n
                                3. [latex]\\left\\{ \\begin{array}{l} \\phantom{2}x+y+6z=5 \\\\ 2x\\phantom{+3y}-3z=4 \\\\ \\phantom{2x+}3y+4z=9 \\end{array}\\right.[\/latex]<\/li>\n<\/ol>\n

                                  For problems 4\u20136, perform the indicated operations and simplify.<\/p>\n

                                    \n
                                  1. [latex]24 + \\{-3x - {[6x - 3(5 - 2x)]}^{0}\\} + 3x[\/latex]<\/li>\n
                                  2. [latex]2ab^3 (a - 4)(a + 4)[\/latex]<\/li>\n
                                  3. [latex]\\left(\\dfrac{xy^{-3}}{x^{-2}y^4}\\right)^{-1}[\/latex]<\/li>\n<\/ol>\n

                                    For problems 7 and 8, factor each expression completely.<\/p>\n

                                      \n
                                    1. [latex]3x^2 +11x + 8[\/latex]<\/li>\n
                                    2. [latex]64x^3 - y^3[\/latex]<\/li>\n
                                    3. A 50 kg mixture of two different grades of coffee costs [latex]\\$191.25.[\/latex] If grade A is worth [latex]\\$3.95[\/latex] per kg and grade B is worth [latex]\\$3.70[\/latex] per kg, how many kg of each type were used?<\/li>\n
                                    4. Kyra gave her brother Mark a logic question to solve: If she has 16 coins in her pocket worth [latex]\\$2.35,[\/latex] and if the coins are only dimes and quarters, how many of each kind of coin does she have?<\/li>\n<\/ol>\n

                                      Questions from Chapters 7 to 9<\/h1>\n

                                      In problems 1\u20133, perform the indicated operations and simplify.<\/p>\n

                                        \n
                                      1. [latex]\\dfrac{15s^3}{3t^2}\\div \\dfrac{5t}{17s^3}\\div \\dfrac{34s^4}{3t^3}[\/latex]<\/li>\n
                                      2. [latex]\\dfrac{2x}{x-2}-\\dfrac{4x}{x-2}+\\dfrac{20}{x^2-4}[\/latex]<\/li>\n
                                      3. [latex]\\dfrac{\\dfrac{x^2}{y^2}-9}{\\dfrac{x+3y}{y^3}}[\/latex]<\/li>\n<\/ol>\n

                                        For questions 4\u20136, simplify each expression.<\/p>\n

                                          \n
                                        1. [latex]3\\sqrt{25x}-2\\sqrt{72x}-\\sqrt{16x^3}[\/latex]<\/li>\n
                                        2. [latex]\\dfrac{\\sqrt{m^6n}}{\\sqrt{3n}}[\/latex]<\/li>\n
                                        3. [latex]\\left(\\dfrac{a^0b^4}{c^8d^{-12}}\\right)^{\\frac{1}{4}}[\/latex]<\/li>\n<\/ol>\n

                                          For questions 7 and 8, solve [latex]x[\/latex] by any convenient method.<\/p>\n

                                            \n
                                          1. [latex]x^2 - 4x - 5 = 0[\/latex]<\/li>\n
                                          2. [latex]\\dfrac{x-3}{x}=\\dfrac{x}{x-3}[\/latex]<\/li>\n<\/ol>\n

                                            In problems 9 and 10, find the solution set of each system by any convenient method.<\/p>\n

                                              \n
                                            1. The base of a right triangle is 6 cm longer than its height. If the area of this triangle is 20 cm2<\/sup>, find the length of both the base and the height.<\/li>\n
                                            2. Find three consecutive even integers such that the product of the first two is 8 more than six times the third number.<\/li>\n<\/ol>\n

                                              Final Exam: Version A Answer Key<\/a><\/p>\n","protected":false},"author":90,"menu_order":1,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":"cc-by-nc-sa"},"chapter-type":[],"contributor":[],"license":[56],"class_list":["post-1568","chapter","type-chapter","status-publish","hentry","license-cc-by-nc-sa"],"part":1566,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/chapters\/1568","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/users\/90"}],"version-history":[{"count":3,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/chapters\/1568\/revisions"}],"predecessor-version":[{"id":2184,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/chapters\/1568\/revisions\/2184"}],"part":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/parts\/1566"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/chapters\/1568\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1568"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/chapter-type?post=1568"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1568"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1568"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}