# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2007 | June | Q#6

Question a.   The polynomial f(x) is given by  .                                                i.    Use the Factor Theorem to show that (x-1) is a factor of f(x).                                               ii.    Express f(x) in the form  , where p and q are integers.                                             iii.    Hence show that the equation f(x)=0 has exactly one real root and state its value. b.   The curve with equation  is sketched below. The […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2007 | June | Q#7

Question The quadratic equation where k is a constant, has real roots. a.   Show that . b.                 i.               Factorise .          ii.               Hence, or otherwise, solve the quadratic inequality  Solution a.   We are given a quadratic equation as follows; We are also given that it has real roots. For a quadratic equation , […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2007 | June | Q#3

Question a.                           i.       Express  in the form  , where p and q are integers.                    ii.       Write down the coordinates of the vertex (minimum point) of the curve with equation                     iii.    […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2007 | January | Q#7

Question The quadratic equation  has real roots. i.       Show that .  ii.       Hence find the possible values of . Solution i.   We are given the equation It is a quadratic equation and we are also given that it has real roots. For a quadratic equation , the expression for solution is; Where  is called discriminant. If , the equation will have two […]