Hits: 75

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2006 | June | Q#11

Hits: 75   Question The line  passes through the points P(–1,2) and Q(11, 8). a.   Find an equation for  in the form y= mx + c, where m and c are constants. The line  passes through the point R(10, 0) and is perpendicular to . The lines  and  intersect at the point S. b.   Calculate the coordinates of S. […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2017 | June | Q#6

Hits: 115   Question A circle with centre C has .  a.   Express this equation in the form b.   Show that the circle touches the y-axis and crosses the x-axis in two distinct points. c.   A line has the equation , where  is a constant.                            i.       Show that the x-coordinates of any points of intersection of the circle and the line […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2016 | June | Q#5

Hits: 63   Question A circle with center C(5,-3) passes through the point A(-2,1). a.   Find the equation of the circle in the form b.   Given that AB is a diameter of the circle, find the coordinates of the point B. c.   Find an equation of the tangent to the circle at the point A, giving your answer […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2014 | June | Q#7

Hits: 221   Question A circle with center C has the equation . The point A(3,-2) lies on the  circle. a.   Express the equation of the circle in the form b.                                i.       Write down the coordinates of C.                          ii.       Show that the circle has radius , where n is an integer. c.                         i.       Find the equation of the tangent to […]

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

Hits: 84   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 […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2007 | June | Q#5

Hits: 103   Question A circle with centre C has equation  . a.   Write down:                            i.       the coordinates of C;                           ii.       the radius of the circle. b.                                i.       Verify that the point N(0,-2) lies on the circle.                           ii.       Sketch the circle.                         iii.       Find an equation of the normal to the circle at the point N. c.   The point P has coordinates (2, […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2013 | June | Q#3

Hits: 65   Question A circle C has the equation a.   Write the equation of C in the form Where a, b and k are integers. b.   Hence, for the circle C write down:                            i.       the coordinates of its center;                          ii.       its radius. c.                         i.       Sketch the circle C.                   ii.       Write down the coordinates of the point on C that […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2013 | January | Q#7

Hits: 50   Question A circle with centre C(-3,2) has equation a.   Find the y-coordinates of the points where the circle crosses the y-axis. b.   Find the radius of the circle.  c.   The point P(2,5) lies outside the circle.                     i.       Find the length of CP, giving your answer in the form  , where n is an integer.                   ii.       The point […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2012 | June | Q#6

Hits: 219   Question The circle with centre C(5,8) touches the y-axis, as shown in the diagram. a.   Express the equation of the circle in the form b.                         i.       Verify that the point A(2,12) lies on the circle.                   ii.       Find an equation of the tangent to the circle at the point A, giving your answer in the form    , […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2012 | January | Q#7

Hits: 69   Question A circle with centre C has . a.   Express the equation in the form b.   Write down:                            i.       the coordinates of C;                          ii.       the radius of the circle c.   Sketch the circle. d.   A line has the equation , where  is a constant.                            i.       Show that the x-coordinates of any points of intersection of the line and the […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2011 | June | Q#8

Hits: 88   Question A circle has centre C(3,-8) and radius 10 . a.   Express the equation of the circle in the form b.   Find the x-coordinates of the points where the circle crosses the x-axis. c.   The tangent to the circle at the point A has gradient . Find an equation of the line CA, giving […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2010 | June | Q#5

Hits: 69   Question A circle with centre  touches the y-axis, as shown in the diagram. a.   Find the equation of the circle in the form b.                          i.       Verify that the point  lies on the circle.                   ii.       Find an equation of the normal to the circle at the point P. […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2010 | January | Q#7

Hits: 166   Question A circle with centre C has . a.   Find:                            i.       the coordinates of C;                          ii.       the radius of the circle b.   Explain why the circle lies entirely below the x-axis. c.   The point P with coordinates  lies outside the circle.                            i.       Show that .                          ii.       Hence show that                        iii.       Find the possible values of k. Solution a.   […]

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

Hits: 41   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 […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2008 | June | Q#7

Hits: 137   Question The circle S has centre C(8,13) and touches the x-axis, as shown in the diagram. a.   Write down an equation for S, giving your answer in the form b.   The point P with coordinates (3,1) lies on the circle.                     i.       Find the gradient of the straight line passing through P and […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2008 | January | Q#4

Hits: 43   Question A circle with centre C has equation .  a.   By completing the square, express this equation in the form b.    Write down:                            i.       the coordinates of C;                          ii.       the radius of the circle, leaving your answer in surd form. c.   A line has equation .                            i.       Show that the x-coordinate of any point of […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2007 | January | Q#4

Hits: 58   Question A circle with centre C has equation  . a.  By completing the square, express this equation in the form b. Write down:                     i.       the coordinates of C;                   ii.       the radius of the circle. c.   Show that the circle does not intersect the x-axis. d.  The line with equation  intersects the circle at the points P and Q. […]

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

Hits: 76   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 […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2006 | January | Q#5

Hits: 36   Question A circle with centre C has equation   .  a.   By completing  the square, express this equation in the form b.   Write down:                            i.       the coordinates of ;                          ii.       the radius of the circle. c.   The point  has coordinates .                            i.       Find the length of  ;                          ii.       Hence determine whether the point  lies inside or outside the circle, giving a reason […]

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

Hits: 83   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 […]