Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2005 | January | Q#4

Question a.   The function f is defined for all values of  by  .                            i.       Find the remainder when  is divided by .                          ii.       Given that  and  , write down two linear factors of .                        iii.       Hence express  as the product of three linear factors. b.   The curve with equation  is sketched below.                            i.       The curve intersects the y-axis at the point . Find the […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2005 | June | Q#8

Question A line has equation   , where  is a constant. A curve has equation  . a.   Show that the x-coordinate of any point of intersection of the line and the curve satisfies the  equation b.   Find the values of  for which the equation   has equal roots. c.   Describe geometrically the situation when  takes either of the values found in part (b). Solution […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2005 | June | Q#4

Question The curve with equation  is sketched below. The curve touches the x-axis at the point  and cuts the x-axis at the point  . a.                               i.       Use the factor theorem to show that  is a factor  of                          ii.       Hence find the coordinates of B b. The point , shown on  the  diagram, is  a   minimum point  of  the  curve with equation                            i.       Find  . […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2005 | June | Q#3

Question A circle has center  and radius 5. The point  has coordinates . a.   Write down the equation of the circle. b.   Verify that point  lies on the circle. c.   Find the gradient of the line .   d.                                 i.  Find the gradient of the […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2005 | June | Q#2

Question a.   Express  in the form . b.   A curve has equation  .  Using your answer form part (a), or otherwise:                       i.       Find the coordinates of the vertex (minimum point) of the curve.                     ii.       Sketch the curve, indicating the value where the curve crosses the y-axis. c.   Describe geometrically the […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2005 | June | Q#1

Question The point  has coordinates  and the point  has coordinates . a.   Find the coordinates of mid-point of . b.   Show that  has length , where  is an integer. c.                                i.       Find the gradient of line .                          ii.       Hence, or otherwise, show that the line  has equation d.    The line  intersects the line with equation  at the point . Find the  coordinates of . Solution a. […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2005 | January | Q#3

Question A circle has equation .  a.   By completing  the square, express the equation in the form b.   Write down:                            i.       the coordinates of the center of the circle;                          ii.       the radius of the circle c.   The line with equation  intersects the circle at the points P and Q.                            i.       Show that the x-coordinates of P and Q satisfy the equation […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2005 | January | Q#2

Question A curve has equation   . a.   Find . b.   The point  on the curve has coordinates .                            i.       Show that the gradient of the curve at  is 5.                          ii.       Hence find an equation of the normal to the curve at P, expressing your answer in the form ax + by = c , where a, b and c are integers. […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2005 | January | Q#1

Question The point  has coordinates  and the point  has coordinates . a.                 i.    Find the gradient of .           ii.    Hence, or otherwise, show that the line  has equation . b.   The line with equation   intersects the line  at the point . Find the coordinates of . Solution a.   i.   Expression […]