# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2010 | January | Q#1

Question The polynomial  is given by  . a.   Use the Factor Theorem to show that  is a factor of . b.   Express  as the product of three linear factors. Solution a.   Factor theorem states that if  is a factor of   then; For the given case  is factor of . We can write the factor in standard form as; Here  and . […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2010 | January | Q#7

Question A circle with centre C has . a.   Find:                            i.       the coordinates of C;                          ii.       the radius of the circle b.   Explain why the circle lies entirely below the x-axis. c.   The point P with coordinates  lies outside the circle.                            i.       Show that .                          ii.       Hence show that                        iii.       Find the possible values of k. Solution a.   We are given […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2010 | January | Q#6

Question The curve with equation  is sketched below. a.                       i.       Find the gradient of the curve with equation  at the point A.                   ii.       Hence find the equation of the normal to the curve at the point A, giving your answer in the  form  , where p and q are integers.   b.                       i.       Find the value of                   ii.       Hence determine […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2010 | January | Q#5

Question a.   Express  in the form  , where p and q are integers. b.                        i.       Sketch the graph of  , stating the coordinates of the minimum point  and the point where the graph crosses the y-axis.                   ii.       Write down an equation of the tangent to the graph of  at its vertex. c.   […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2010 | January | Q#4

Question a.   Show that  is an integer and find its value. b.    Express  in the form  , where m and n are integers. Solution a.   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 […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2010 | January | Q#3

Question The depth of water, y metres, in a tank after time t hours is given by ,  a.   Find:                             i.                                  ii.        b.   Verify that y has a stationary value when  and determine whether it is a maximum value or a minimum value. c.                                 i.       Find the rate of change of the depth of water, in metres […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2010 | January | Q#2

Question The triangle ABC has vertices A(1,3), B(3,7) and C(-1,9). a.                         i.       Find the gradient of AB.                   ii.       Hence show that angle ABC is a right angle. b.                         i.       Find the coordinates of M, the mid-point of AC.                   ii.       Show that the lengths of AB and BC are equal.                  iii.       Hence find an equation of the line of symmetry of the […]