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

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 of p. […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2009 | June | Q#4

Question a.  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.               iv.       The equation  has one root equal to -2. Show that equation has no other real roots. […]

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

Question The curve C has equation  , where k is a constant. The line L has equation . a.   Show that the x-coordinates of any points of intersection of the curve C with the line L satisfy the  equation b.   The curve C and the line L intersect in two distinct points.           […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2009 | June | Q#6

Question a.                       i.       Express  in the form  , where p and q are integers.                 ii.       Hence write down the minimum value of .               iii.       State the value of  for which the minimum value of  occurs.    b.   The point A has coordinates (5,4) and the point B has coordinates (x,7-x) .                            i.       Expand . […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2009 | June | Q#3

Question The curve with equation  passes through the point P, where  . a.   Find                          i.                                  ii.        b.   Verify that the point P is a stationary point of the curve. c.                                i.       Find the value of  at the point P.                           ii.       Hence, or otherwise, determine whether P is […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2009 | June | Q#2

Question a.   Express  in the form  , where m and n are integers. b.   The diagram shows a right-angled triangle. The hypotenuse has length  cm. The other two sides have lengths  cm and x cm. Find the  value of x. Solution a.   We are given the expression; We need to rationalize the denominator. If we need a rational number in […]

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

Question The line AB has equation . a.                        i.       Find the gradient of AB.                   ii.       The point A has coordinates (2,1) . Find an equation of the line which passes through the  point A and which is perpendicular to AB. b.  The line AB intersects the line with equation  at the point C. Find the            coordinates of C. Solution a.   […]