# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2012 | June | Q#7

Question The gradient,  , of a curve C at the point (x,y) is given by a.                         i.       Show that y is increasing when .                   ii.       Solve the inequality . b.   The curve C passes through the point P(2,3).                     i.       Verify that the tangent to the curve at P is parallel to the x-axis.                   ii.       The point Q(3,-1) also lies on the […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2012 | June | Q#6

Question The circle with centre C(5,8) touches the y-axis, as shown in the diagram. a.   Express the equation of the circle in the form b.                         i.       Verify that the point A(2,12) lies on the circle.                   ii.       Find an equation of the tangent to the circle at the point A, giving your answer in the form    , where s, t […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2012 | June | Q#5

Question a.                         i.       Express  in the form .                   ii.       Hence write down the equation of the line of symmetry of the curve with equation . b.   The curve C with equation  and the straight line  intersect at the point  A(0,5) and at the point B, as shown in the diagram below. i.       Find the coordinates of the point B. ii.       Find iii.       Find […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2012 | June | Q#2

Question The line AB has equation  . a.                         i.       Find the gradient of AB.                   ii.       Find an equation of the straight line that is parallel to AB and which passes through the  point C(3,-5), giving your answer in the form , where p, q and r are integers. b.   The line AB intersects the line with equation  at […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2012 | January | Q#7

Question A circle with centre C has . a.   Express the equation in the form b.   Write down:                            i.       the coordinates of C;                          ii.       the radius of the circle c.   Sketch the circle. d.   A line has the equation , where  is a constant.                            i.       Show that the x-coordinates of any points of intersection of the line and the circle satisfy  […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2012 | January | Q#4

Question The curve with equation  is sketched below. The point O is at the origin and the  curve passes through the points A(-1,0) and B(1,4). a.   Given that  , find:                            i.       ;                          ii.        b.   Find an equation of the tangent to the curve at the point A(-1,0). c.   Verify that the point B, where  , is a minimum point […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2012 | January | Q#2

Question a.   Factorise . b.   Sketch the graph with equation  , stating the values where the curve crosses  the coordinate axes. c.                   i.       Express  in the form , where p and q are positive integers.               ii.       Hence find the minimum value of . d.   The curve with […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2012 | January | Q#1

Question The point A has coordinates (6,-4) and the point B has coordinates (-2,7). a.   Given that the point O has coordinates (0,0), show that the length of OA is less than the length of OB. b.                         i.       Find the gradient of AB.                   ii.       Find an equation of the line AB in the form  , where p, q and r are […]