# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2006 | June | Q#5

Question The curve with equation  is sketched below. The curve crosses the x-axis at the origin  and the point  lies on the curve.  a.                                i.       Find                          ii.       Hence show that the curve has a stationary  point when  and find the x-coordinate  of the other stationary point. b.                                 […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2006 | June | Q#3

Question A curve has equation . a.   Find b.   Find an equation for the tangent to the curve at the point where . c.   Determine whether  is increasing or decreasing when . Solution a.   We have the equation; Rule for differentiation is of  is: Rule for differentiation is of  is: Rule for differentiation is of  is: b. […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2006 | January | Q#8

Question The diagram shows the curve with equation  and the line  . The points  and  have coordinates  and  respectively. The curve touches the x-axis at  the origin  and crosses the x-axis at the point .  The line  cuts the curve at the point   where  and touches the curve at  where . a.   Find the area of the rectangle . b.                                i.      […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2006 | January | Q#7

Question The volume, , of water in a tank at time  seconds is given by; , for  a.   Find:                            i.                                  ii.        b.   Find the rate of change of the volume of water in the tank, in , when . c.                                 i.       Verify that   has a stationary value when .                           ii.       Determine whether this is a maximum or minimum value. Solution […]