1. 1.1
    Solve for x:
    1. 1.1.1
      x(x - 7) = 0
      (2)
      1. 1.1.2
        x2 - 6x + 2 = 0 (Correct to TWO decimal places)
        (3)
        1. 1.1.3
          x - 1 + 1 = x
          (5)
          1. 1.1.4
            3x + 3 - 3x + 2 = 486
            (4)
          2. 1.2
            Given f(x) = x2 + 3x - 4
            1. 1.2.1
              Solve for x if f(x) = 0
              (2)
              1. 1.2.2
                Solve for x if f(x) < 0
                (2)
                1. 1.2.3
                  Determine the values of x for which f`(x) ≥ 0
                  (2)
                2. 1.3
                  Solve for x and y: x = 2y and x2 - 5xy = -24
                  (4)
                  (24)
                  [{"prnt":"1.1","num":"1.1.1","answer":""},{"prnt":"1.1","num":"1.1.2","answer":""},{"prnt":"1.1","num":"1.1.3","answer":""},{"prnt":"1.1","num":"1.1.4","answer":""},{"prnt":"1.2","num":"1.2.1","answer":""},{"prnt":"1.2","num":"1.2.2","answer":""},{"prnt":"1.2","num":"1.2.3","answer":""},{"prnt":"1","num":"1.3","answer":""}]

                  Answers

                    1. 1.1
                      1. 1.1.1
                        x(x - 7) = 0
                        x = 0 or x = 7
                      2. 1.1.2
                        x2 - 6x + 2 = 0
                        x =
                        6 ± √(-6)2 - 4(1)(-2)
                        2(1)

                        =
                        6 ± √28
                        2

                        x = 0.35 or x = 5.65
                      3. 1.1.3
                        x - 1 + 1 = x
                        x - 1 = x -1
                        x - 1 = x2 - 2x + 1
                        x2 - 3x + 2 = 0
                        (x - 2)(x - 1) = 0
                        x = 2 or x = 1

                        Both answers are valid
                      4. 1.1.4
                        3x + 3 - 3x + 2 = 486
                        3x33 - 3x32 = 486
                        3x(33 - 32) = 486
                        3x = 27
                        3x = 33
                        x = 3
                    2. 1.2
                      1. 1.2.1
                        f(x) = x2 + 3x - 4
                        0 = (x + 4)(x - 1)
                        x = -4 or x = 1
                      2. 1.2.2
                        x2 + 3x - 4 < 0
                        (x + 4)(x - 1) < 0

                        Diagram

                        -4 < x < 1
                      3. 1.2.3
                        2x + 3 ≥ 0
                        x ≥ -32
                        f'(x) ≥ 0 when f is increasing

                        The turning point occurs at x =
                        -4 + 1
                        2

                        x ≥ -3/2
                    3. 1.3
                      x = 2y and x2 - 5xy = -24

                      (2y)2 - 5(2y)(y) = -24
                      4y2 - 10y2 = -24
                      -6y2 = -24
                      y2 = 4
                      y = -2 or y = 2
                      x = -4 or x = 4
                      Msaki, 26 Mar 2018 10:46
                      1. 1.1.1
                      2. 1.1.2
                      3. 1.1.3
                      4. 1.1.4
                      5. 1.2.1
                      6. 1.2.2
                      7. 1.2.3
                      8. 1.3
                    Loading...