# 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 | January | Q#6

Question The diagram below shows a rectangular sheet of metal 24 cm by 9 cm. A square of side x cm is cut from each corner and the metal is then folded along the broken lines to  make an open box with a rectangular base and height x cm. a.   Show that the volume,  cm3, of liquid the […]

# 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. […]