Coordinate Geometry (Straight Lines-AQA-MPC1-2011) Archives — O/A Level Solutions

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2011 | June | Q#4

  Question a.   Express  in the form  , where p and q are rational numbers. b.   A curve has equation .      i.   Find the coordinates of the vertex of the curve.     ii.   State the equation of the line of symmetry of the curve.    iii.   Sketch the curve, stating the value of the intercept on […]

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

  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 your answer […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2011 | June | Q#3

  Question The volume, V m3 , of water in a tank after time t seconds is given by a.   Find . b.                         i.       Find the rate of change of volume, in m3 s-1, when .                   ii.       Hence determine, with a reason, whether the volume is increasing or decreasing when . c.                         i.       Find the positive value of t […]

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

  Question The line AB has equation  . a.   Find the gradient of AB. b.   The point C has coordinates .                     i.       Find an equation of the line which passes through the point C and which is parallel to AB.                   ii.       The point  is the mid-point of AC . Find the coordinates of the point A.  c.   The line […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2011 | January | Q#7

  Question a.                         i.       Express  in the form .                   ii.       Hence write down the equation of the line of symmetry of the curve with equation  . b.   The curve C has equation  and the line L has equation , where k is a constant.                     i.       Show that the x-coordinates of any points of intersection of the curve C with the line L […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2011 | January | Q#6

  Question A circle has centre C(-3,1) and radius . a.                         i.       Express the equation of the circle in the form                   ii.       Hence find the equation of the circle in the form where m, n and p are integers. b.   The circle cuts the y-axis at the points A and B. Find the distance AB. c.                         i.       Verify that the […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2011 | January | Q#4

  Question The curve sketched below passes through the point A(-2,0) . The curve has equation and the point P(1,12) lies on the curve. a.                         i.       Find the gradient of the curve at the point P.                   ii.       Hence find the equation of the tangent to the curve at the point P, giving your answer in the  […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2011 | January | Q#3

  Question The line AB has equation  . The point C has coordinates (2,-7). a.                                i.       Find the gradient of AB.                          ii.       The line which passes through C and which is parallel to AB crosses the y-axis at the  point D. Find the y-coordinate of D. b.   The line with equation  intersects the line AB at the point A. Find    […]