# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2015 | June | Q#8

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.   Given that the line and the curve do not intersect:.                    i.       Show that . […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2015 | June | Q#7

Question a.   Sketch the curve with equation . b.   The polynomial  is given by .                            i.       Find the remainder when  is divided by .                          ii.       Use the Factor Theorem to show that  is a factor of .                        iii.       Express  in the form , where B and c are integers.                         iv.       Hence show that the equation  has exactly one real root and state its value. Solution […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2015 | June | Q#6

Question The diagram shows a cylindrical container of radius r cm and height h cm. The container has an  open top and a circular base. The external surface area of the container’s curved surface and base is 48 cm2. When the radius of the base is r cm, the volume of the container is V cm3. a. i.Find an […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2015 | June | Q#5

Question a.   Express  in the form  , where p and q are rational numbers. b.   A curve has equation .                     i.       Use the result from part (a) to write down the coordinates of the vertex of the curve.                   ii.       State the equation of the line of symmetry of the curve. c.   The curve with equation  is translated by vector . Find the equation of […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2015 | June | Q#4

Question A circle with center C has the equation .  a.   Express this equation in the form b.                                i.       State the coordinates of C.                          ii.       Find the radius of the circle, giving your answer in the form  . c.                         i.       The point P with coordinates (4,k) lies on the circle. Find the possible values of k.                   ii.       The points […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2015 | June | Q#3

Question The diagram shows a sketch of a curve and a line. The curve has equation  . The points A(-1,6) and B(2,30) lie on the curve. a.   Find an equation of the tangent to the curve at the point A. b.                 i.       Find           ii.       Calculate the area of the shaded region bounded by the curve and the line AB. […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2015 | June | Q#2

Question The point P has coordinates  and the point Q has coordinates . Show that the  gradient of PQ can be expressed as , stating the value of the integer n. Solution Expression for slope (gradient) of a line joining points  and ; We are given coordinates of points  and . Therefore; If we need a rational number […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2015 | June | Q#1

Question The line AB has equation . a.               i.       Find the gradient of AB.           ii.       Find an equation of the line that is perpendicular to the line AB and which passes through the  point (-2,-3) . Express your answer in the form , where p, q and r are […]