# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2008 | January | Q#6

Question a.   The polynomial  is given by .                   i.       Use the Factor Theorem to show that  is a factor of  .                 ii.       Express  as the product of three linear factors. b.   The curve with equation  is sketched below. The curve cuts the x-axis at the point A and the points […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2008 | January | Q#5

Question a.   Factorise  . b.   Show that  can be written as  . c.   A curve has equation  .                            i.       Write down the equation of its line of symmetry.                          ii.       Find the coordinates of its vertex.                        iii.       Sketch the curve, indicating the values of the intercepts on the x-axis and  the y-axis. Solution a.   b.   c.                               i.   We are given […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2008 | January | Q#7

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

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2008 | January | Q#4

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 C;                          ii.       the radius of the circle, leaving your answer in surd form. c.   A line has equation .                            i.       Show that the x-coordinate of any point of intersection of […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2008 | January | Q#3

Question a.   Express  in the form  where  is an integer. b.   Express  in the form  , where   and  are an integers. Solution i.   We are given; ii.   We are given;   We have algebraic formulae;

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2008 | January | Q#2

Question The curve with equation  has a single stationary point, M. a.   Find b.   Hence find the x-coordinate of M. c.                         i.       Find                   ii.       Hence, or otherwise, determine whether M is a maximum or a minimum point.  d.    Determine whether the curve is increasing or decreasing at the point on the curve where . Solution a.   We are […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2008 | January | Q#1

Question The triangle ABC has vertices A(-2,3), B(4,1) and C(2,-5). a.   Find the coordinates of the mid-point of BC . b.                 i.  F ind the gradient of AB, in its simplest form.           ii.  Hence find an equation of the line AB , giving your answer in the form  , where q  and r are […]