# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2006 | June | Q#7

Question A circle has equation . a.   Find                            i.       the coordinates of the centre of the circle;                          ii.       the radius of the circle in the form , where  is an integer. b.   A chord of the circle has length 8. Find the perpendicular distance from the centre of the circle to  this chord. c.   A line has equation , where  is a constant.                            i.       Show […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2006 | June | Q#3

Question A curve has equation . a.   Find b.   Find an equation for the tangent to the curve at the point where . c.   Determine whether  is increasing or decreasing when . Solution a.   We have the equation; Rule for differentiation is of  is: Rule for differentiation is of  is: Rule for differentiation is of  is: b. […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2006 | June | Q#1

Question The point  has coordinates  and the point  has coordinates . a.                          i.    Find the gradient of the line .                    ii.    Hence, or otherwise, show that the line  has equation b.         The line  intersects the line with equation   at the point . Find the coordinates of  . c.           Find an equation of the line through which is perpendicular to  . Solution a. […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2006 | January | Q#8

Question The diagram shows the curve with equation  and the line  . The points  and  have coordinates  and  respectively. The curve touches the x-axis at  the origin  and crosses the x-axis at the point .  The line  cuts the curve at the point   where  and touches the curve at  where . a.   Find the area of the rectangle . b.                                i.      […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2006 | January | Q#3

Question a.                                i.       Express  in the form , where   and  are integers.                          ii.       Hence, or otherwise, describe the coordinates of the minimum point of the curve with                       equation . b.   The line  has equation  and the curve  has the equation .                             i.       Show that the x-coordinates of the points of […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2006 | January | Q#2

Question The point  has coordinates  and the point  has coordinates . The line  has equation . a.                                i.       Show that .                          ii.       Hence find the coordinates of the mid-point of . b.   Find the gradient of . c.   Line  is perpendicular to the line .                            i.       Find the gradient of .                          ii.       Hence find the equation of the line .                        iii.       Given that point […]