# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2006 | January | Q#6

Question The polynomial  is given by a.                                i.       Using the factor theorem, show that  is a factor  of .                          ii.       Hence express  as the product of three linear factors.   b.       Sketch the curve with equation  , showing the coordinates of the points  where the curve cuts the axes. (You are not required to calculate the coordinates of […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2006 | January | Q#8

Question The diagram shows the curve with equation  and the line  . The points  and  have coordinates  and  respectively. The curve touches the x-axis at  the origin  and crosses the x-axis at the point .  The line  cuts the curve at the point   where  and touches the curve at  where . a.   Find the area of the rectangle . b.                                i.      […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2006 | January | Q#7

Question The volume, , of water in a tank at time  seconds is given by; , for  a.   Find:                            i.                                  ii.        b.   Find the rate of change of the volume of water in the tank, in , when . c.                                 i.       Verify that   has a stationary value when .                           ii.       Determine whether this is a maximum or minimum value. Solution […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2006 | January | Q#5

Question A circle with centre C has equation   .  a.   By completing  the square, express this equation in the form b.   Write down:                            i.       the coordinates of ;                          ii.       the radius of the circle. c.   The point  has coordinates .                            i.       Find the length of  ;                          ii.       Hence determine whether the point  lies inside or outside the circle, giving a reason for    […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2006 | January | Q#4

Question The quadratic equation , where  is a constant,  has equal roots.  a.   Show that . b.   Hence find the possible values of . Solution a.   For a quadratic equation , the expression for solution is; Where  is called discriminant. If , the equation will have two roots. If , the equation will have two identical/repeated […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2006 | January | Q#3

Question a.                                i.       Express  in the form , where   and  are integers.                          ii.       Hence, or otherwise, describe the coordinates of the minimum point of the curve with                       equation . b.   The line  has equation  and the curve  has the equation .                             i.       Show that the x-coordinates of the points of […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2006 | January | Q#2

Question The point  has coordinates  and the point  has coordinates . The line  has equation . a.                                i.       Show that .                          ii.       Hence find the coordinates of the mid-point of . b.   Find the gradient of . c.   Line  is perpendicular to the line .                            i.       Find the gradient of .                          ii.       Hence find the equation of the line .                        iii.       Given that point […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2006 | January | Q#1

Question a.   Simplify . b.   Express  in the form  , where  is an integer. Solution a.   We have algebraic formula; For the given case; b.   Since ; Since ; Comparing with  gives us;