# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2005 | June | Q#8

Question A line has equation   , where  is a constant. A curve has equation  . a.   Show that the x-coordinate of any point of intersection of the line and the curve satisfies the  equation b.   Find the values of  for which the equation   has equal roots. c.   Describe geometrically the situation when  takes either of the values found in part (b). Solution […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2005 | June | Q#7

Question Solve each of the following inequalities: a.   b.   Solution a.   We are given; b.   We are given; First we find the critical values for this inequality. Therefore; Now we have two options. Standard form of quadratic equation is; The graph of quadratic equation is a parabola. If  (‘a’ is positive) then parabola opens upwards  and its vertex […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2005 | June | Q#6

Question The cubic polynomial  is given by . a.   Show that  can be written in the form  , where   and   are constants  whose values are to be found. b.   Use the Remainder Theorem to find the remainder when    is divided by  . c.   Prove that the equation  has only one real root and state its value. Solution a.   […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2005 | June | Q#5

Question Express each of the following in the form  where  and  are an integers. a.    . b.   . Solution a.   We have algebraic formula; For the given case; b.   To express   in the form  , we need to rationalize the denominator. If we need a rational number in the denominator of a fraction, we need to follow procedure of  […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2005 | June | Q#4

Question The curve with equation  is sketched below. The curve touches the x-axis at the point  and cuts the x-axis at the point  . a.                               i.       Use the factor theorem to show that  is a factor  of                          ii.       Hence find the coordinates of B b. The point , shown on  the  diagram, is  a   minimum point  of  the  curve with equation                            i.       Find  . […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2005 | June | Q#3

Question A circle has center  and radius 5. The point  has coordinates . a.   Write down the equation of the circle. b.   Verify that point  lies on the circle. c.   Find the gradient of the line .   d.                                 i.  Find the gradient of the […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2005 | June | Q#2

Question a.   Express  in the form . b.   A curve has equation  .  Using your answer form part (a), or otherwise:                       i.       Find the coordinates of the vertex (minimum point) of the curve.                     ii.       Sketch the curve, indicating the value where the curve crosses the y-axis. c.   Describe geometrically the […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2005 | June | Q#1

Question The point  has coordinates  and the point  has coordinates . a.   Find the coordinates of mid-point of . b.   Show that  has length , where  is an integer. c.                                i.       Find the gradient of line .                          ii.       Hence, or otherwise, show that the line  has equation d.    The line  intersects the line with equation  at the point . Find the  coordinates of . Solution a. […]