Year 2013 January (6360-MPC1) Archives — O/A Level Solutions

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2013 | January | Q#5

  Question The polynomial  is given by a.   Use the Remainder Theorem to find the remainder when  is divided by x+1. b.                         i.       Use the Factor Theorem to show that x-3 is a factor of .                   ii.       Express  as a product of linear factors. c.   Sketch the curve with equation  , stating the values of where the curve meets the […]

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#3

  Question a.                               i.       Express  in the form , where k is an integer.                          ii.       Simplify  . b.   Express  in the form , where m and n are integers. Solution a.   i.   We are given; Since ; ii.   Since ; Since ; b.   If we […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2013 | January | Q#2

  Question A bird flies from a tree. At time t seconds, the bird’s height, y metres, above the horizontal ground is given by ,   a.   Find . b.                 i.       Find the rate of change of height of the bird in metres per second when .          ii.       Determine, with a […]

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 […]