Hits: 70

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2013 | June | Q#4

Hits: 70   Question a.   The polynomial f(x) is given by .                     i.       Use the Factor Theorem to show that x+3 is a factor of f(x).                   ii.       Express f(x) in the form  , where p and q are integers. b.   A curve has equation .                     i.       Find .                   ii.       Show that the x-coordinates of any stationary points of the curve satisfy the equation […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2013 | June | Q#7

Hits: 59   Question The quadratic equation  has real roots. (a)  Show that . (b)  Find the possible values of k. Solution a.    We are given the quadratic equation; For a quadratic equation , the expression for solution is; Where  is called discriminant. If , the equation will have two distinct roots. If , the equation will have […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2013 | June | Q#5

Hits: 35   Question a.                        i.       Express  in the form  , where p and q are rational numbers.                   ii.       Hence write down the minimum value of . b.   The point A has coordinates (-3,5) and the point B has coordinates (x,3x+9).                     i.       Show that .                   ii.       Use your result from part (a)(ii) to find […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2013 | June | Q#3

Hits: 60   Question A circle C has the equation a.   Write the equation of C in the form Where a, b and k are integers. b.   Hence, for the circle C write down:                            i.       the coordinates of its center;                          ii.       its radius. c.                         i.       Sketch the circle C.                   ii.       Write down the coordinates of the point on C that […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2013 | January | Q#8

Hits: 53   Question A curve has equation  and a line has equation  , where k is a constant. a.   Show that the x-coordinate of any point of intersection of the curve and the line satisfies the  equation b.   The curve and the line intersect at two distinct points.                     i.       Show that .                   ii.       Find the possible values of k. Solution […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2013 | January | Q#7

Hits: 44   Question A circle with centre C(-3,2) has equation a.   Find the y-coordinates of the points where the circle crosses the y-axis. b.   Find the radius of the circle.  c.   The point P(2,5) lies outside the circle.                     i.       Find the length of CP, giving your answer in the form  , where n is an integer.                   ii.       The point […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2013 | January | Q#4

Hits: 35   Question a.                        i.       Express  in the form .                  ii.       Use the result from part (a)(i) to show that the equation  has no real  solutions. b.   A curve has equation .                            i.       Find the coordinates of the vertex of the curve.                          ii.       Sketch […]