# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2006 | June | Q#6

Question The polynomial  is given by  . a.   Use the Factor Theorem to show that  is a factor of  . b.   Express as the product of three linear factors. c.                 i.  Use the Remainder Theorem to find the remainder, , when is divided by .             ii. Using algebraic division, or otherwise,  express  in […]

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

Question A circle has equation . a.   Find                            i.       the coordinates of the centre of the circle;                          ii.       the radius of the circle in the form , where  is an integer. b.   A chord of the circle has length 8. Find the perpendicular distance from the centre of the circle to  this chord. c.   A line has equation , where  is a constant.                            i.       Show […]

# 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#4

Question a.   Express  in the form , where  and  are integers. b.   Show that Express  is an integer and find its value. Solution a.    We are given; We can do simple algebraic multiplication; b.   Since ; Since ;

# 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 | June | Q#2

Question a.   Express  in the form , where  and  are integers. b.   Hence, or otherwise, show that the equation  has no real solutions. c.   Sketch the graph of , stating the coordinates of the minimum  point and the point where the graph crosses the y-axis. d.   Describe geometrically the transformation that maps the graph of  onto the graph of Solution a. […]

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

Question The point  has coordinates  and the point  has coordinates . a.                          i.    Find the gradient of the line .                    ii.    Hence, or otherwise, show that the line  has equation b.         The line  intersects the line with equation   at the point . Find the coordinates of  . c.           Find an equation of the line through which is perpendicular to  . Solution a. […]