# 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#5

Question The polynomial  is given by  , where c and d are constants. a.   When  is divided by x+2, the remainder is -150. Show that b.  Given that x-3 is a factor of , find another equation involving c and d.  c.   By solving these two equations, find the value of c and the value of d. Solution a.   Remainder […]

# 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#3

Question a.                               i.       Simplify .                          ii.       Show that  is an integer and find its value.                        iii.       Simplify  , giving your answer as an integer. b.   Express  in the form , where m and n are integers. Solution a.                               i.   We are given; ii.   We are given; As […]

# 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 […]