# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2007 | June | Q#11

Question The line  has equation y=3x+2 and the line  has equation 3x+2y-8=0. a.   Find the gradient of line for . The point of intersection of  and  is P. b.   Find the coordinates of P. The lines  and  cross the line y=1 at the points A and B respectively. c.   Find the area of triangle ABP. Solution a. […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2007 | June | Q#10

Question The curve C has equation , . The points P and Q lie on C and have x-coordinates 1 and 2 respectively. a.   Show that the length of PQ is . b.   Show that the tangents to C at P and Q are parallel. c.   Find an equation for the normal to C at […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2007 | June | Q#9

Question The curve C has equation y= f(x) passes through the point (5,65). Given that; a.   Use integration to find f(x). b.   Hence show that c.   In the space provided on page 17, sketch C, showing the coordinates of the points where C crosses the x-axis. Solution a.   We are required to find f(x), when; […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2007 | June | Q#5

Question Figure 1 shows a sketch of the curve with equation  , x ≠0. a.   On a separate diagram, sketch the curve with equation , x≠−2, showing the coordinates of  any point at which the curve crosses a coordinate axis. b.   Write down the equations of the asymptotes of the curve in part (a). Solution a.   […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2007 | January | Q#10

Question a.   On the same axes sketch the graphs of the curves with equations i.       y=x2(x –2), ii.     y=x(6 –x), and indicate on your sketches the coordinates of all the points where the curves  cross the x-axis. b.   Use algebra to find the coordinates of the points where the graphs intersect. Solution a.         […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2007 | January | Q#8

Question The curve C has equation , x > 0. a.   Find an expression for . b.   Show that the point P (4, 8) lies on C. c.   Show that an equation of the normal to C at the point P is 3y=x + 20. The normal to C at P cuts the x-axis at […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2007 | January | Q#7

Question The curve C has equation y= f(x), x ≠ 0, and the point P(2,1) lies on C. Given that; a.   find f(x). b.   Find an equation for the tangent to C at the point P, giving your answer in the form  y =mx + c, where m and c are integers. Solution a.   We are required […]