Coordinate Geometry (AQA-MPC1-2013) Archives — O/A Level Solutions

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2013 | June | Q#6

  Question A curve has equation . The point P with coordinates (-1,6) lies on the curve.  a.   Find the equation of the tangent to the curve at the point P, giving your answer in the form   . b.   The point Q with coordinates (2,k) lies on the curve.                     i.       Find the value of k.                   ii.       Verify that Q also […]

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

  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 is furthest […]

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

  Question The line AB has equation . a.   The point with coordinates (p,p+2) lies on the line AB. Find the value of the constant p. b.   Find the gradient of AB. c.   The point A has coordinates (1,2). The point C(-5,k) is such that AC is perpendicular to AB. Find  the value of k. d.   The line AB […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2013 | January | Q#8

  Question A curve has equation  and a line has equation  , where k is a constant. a.   Show that the x-coordinate of any point of intersection of the curve and the line satisfies the  equation b.   The curve and the line intersect at two distinct points.                     i.       Show that .                   ii.       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 2013 | January | Q#7

  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 Q lies […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2013 | January | Q#6

  Question The gradient, , of a curve at the point (x,y) is given by The curve passes through the point P(1,4). a.   Find the equation of the tangent to the curve at the point P, giving your answer in the form . b.   Find the equation of the curve. Solution a.   We are required to find the […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2013 | January | Q#4

  Question a.                        i.       Express  in the form .                  ii.       Use the result from part (a)(i) to show that the equation  has no real  solutions. b.   A curve has equation .                            i.       Find the coordinates of the vertex of the curve.                          ii.       Sketch the curve, […]

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

  Question The point A has coordinates (-3,2) and the point B has coordinates (7,k). The line AB has equation . a.                         i.       Show that .                   ii.       Hence find the coordinates of the midpoint of AB. b.   Find the gradient of AB. c.   A line which passes through the point A is perpendicular to the line AB. Find an equation […]