# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2011 | January | Q#5

Question a.                         i.       Sketch the curve with equation         ii.       Show that the equation  can be expressed as b.   The polynomial  is given by  .                     i.       Find the remainder when  is divided by .                   ii.       Use the Factor Theorem to show that  is a factor of .                  iii.       Express  in the form  , where b and c are integers. c.   Hence show that […]

# 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    […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2011 | January | Q#2

Question a.   Simplify . b.    Express  in the form Solution a.   We are given; b.   We are given the expression; If we need a rational number in the denominator of a fraction, we need to follow procedure of  “denominator rationalization” as given below. ü If the denominator is of the form  then multiply both numerator and denominator by […]

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

Question The curve with equation  passes through the point P where . a.   Find .  b.    Show that the point P is a stationary point of the curve and find the other value of x where the  curve has a stationary point. c.                             […]