Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2015 | June | Q#8

Question A curve has equation  and a line has equation  , where k is a  constant. a.   Show that the x-coordinate of any point of intersection of the curve and the line satisfies the equation b.   Given that the line and the curve do not intersect:.                    i.       Show that . […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2015 | June | Q#7

Question a.   Sketch the curve with equation . b.   The polynomial  is given by .                            i.       Find the remainder when  is divided by .                          ii.       Use the Factor Theorem to show that  is a factor of .                        iii.       Express  in the form , where B and c are integers.                         iv.       Hence show that the equation  has exactly one real root and state its value. Solution […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2015 | June | Q#5

Question a.   Express  in the form  , where p and q are rational numbers. b.   A curve has equation .                     i.       Use the result from part (a) to write down the coordinates of the vertex of the curve.                   ii.       State the equation of the line of symmetry of the curve. c.   The curve with equation  is translated by vector . Find the equation of […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2015 | June | Q#4

Question A circle with center C has the equation .  a.   Express this equation in the form b.                                i.       State the coordinates of C.                          ii.       Find the radius of the circle, giving your answer in the form  . c.                         i.       The point P with coordinates (4,k) lies on the circle. Find the possible values of k.                   ii.       The points […]