Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2009 | June | Q#5

  Question A circle with center C has equation .  a.   Write down:                            i.       the coordinates of C;                          ii.       the radius of the circle b.   The point D has coordinates (7,-2).                            i.       Verify that the circle passes through the origin O.                          ii.       Given that the circle also passes through the points (10,0) and (0,p), sketch the circle  and find the value of p. […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2009 | January | Q#6

  Question a.  The polynomial  is given by .                     i.       Use the Factor Theorem to show that  is a factor of .                   ii.       Express  in the form  , where a and b are constants. b. The curve C with equation  , sketched below, crosses the x-axis at the point .                     i.       Find the gradient of the curve C at the point Q.                   ii.       Hence find an […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2009 | June | Q#3

  Question The curve with equation  passes through the point P, where  . a.   Find                          i.                                  ii.        b.   Verify that the point P is a stationary point of the curve. c.                                i.       Find the value of  at the point P.                           ii.       Hence, or otherwise, determine whether P is […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2009 | June | Q#1

  Question The line AB has equation . a.                        i.       Find the gradient of AB.                   ii.       The point A has coordinates (2,1) . Find an equation of the line which passes through the  point A and which is perpendicular to AB. b.  The line AB intersects the line with equation  at the point C. Find the            coordinates of C. Solution a.   […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2009 | January | Q#7

  Question A circle with center C has equation .  a.   Express this equation in the form b.   Write down:                            i.       the coordinates of C;                          ii.       the radius of the circle c.   The point D has coordinates (7,-2).                            i.       Verify that point D lies on the circle.                          ii.       Find an equation of the normal to the circle at the point D, giving […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2009 | January | Q#1

  Question The points A and B have coordinates (1,6) and (5,-2) respectively. The mid-point of AB is M. a.   Find the coordinates of M. b.   Find the gradient of AB, giving your answer in its simplest form. c.   A straight line passes through M and is perpendicular to AB.                     i.       Show that this line has equation  .                   ii.       Given […]