# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2006 | June | Q#11

Question The line  passes through the points P(–1,2) and Q(11, 8). a.   Find an equation for  in the form y= mx + c, where m and c are constants. The line  passes through the point R(10, 0) and is perpendicular to . The lines  and  intersect at the point S. b.   Calculate the coordinates of S. c.   Show […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2006 | June | Q#10

Question The curve C with equation y=f(x), x ≠ 0, passes through the point . Given that a.   find f(x). b.   Verify that f(–2) = 5. c.   Find an equation for the tangent to C at the point (–2, 5), giving your answer in the form ax + by +  c = 0, where a, b […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2006 | January | Q#9

Question Figure 2 shows part of the curve C with equation The curve cuts the x-axis at the points P, (1, 0) and Q, as shown in Figure 2. a.   Write down the x-coordinate of P, and the x-coordinate of Q. b.   Show that . c.   Show that y=x+7 is an equation of the tangent to […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2006 | January | Q#3

Question The line L has equation y=5 – 2x. a.   Show that the point P (3, –1) lies on L. b.   Find an equation of the line perpendicular to L, which passes through P. Give your answer in the form ax + by + c = 0, where a, b and c are integers. […]

# 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#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. […]

# 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#3

Question a.                                i.       Express  in the form , where   and  are integers.                          ii.       Hence, or otherwise, describe the coordinates of the minimum point of the curve with                       equation . b.   The line  has equation  and the curve  has the equation .                             i.       Show that the x-coordinates of the points of […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2006 | January | Q#2

Question The point  has coordinates  and the point  has coordinates . The line  has equation . a.                                i.       Show that .                          ii.       Hence find the coordinates of the mid-point of . b.   Find the gradient of . c.   Line  is perpendicular to the line .                            i.       Find the gradient of .                          ii.       Hence find the equation of the line .                        iii.       Given that point […]