# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01R) | Year 2014 | June | Q#11

Question A sketch of part of the curve C with equation , x>0 is shown in Figure. Point A lies on C and has an x coordinate equal to 2 a.   Show that the equation of the normal to C at A is y = –2x + 7. The normal to C at A meets C […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01R) | Year 2014 | June | Q#9

Question The curve C has equation . The line L has equation y = 3x + k, where k is a positive constant. a.   Sketch C and L on separate diagrams, showing the coordinates of the points at which C and L cut the axes. Given that line L is a tangent to C, b.   find the […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01R) | Year 2014 | June | Q#7

Question Figure 2 shows a right angled triangle LMN. The points L and M have coordinates (–1, 2) and (7, –4) respectively. a.   Find an equation for the straight line passing through the points L and M. Give your answer in the  form ax + by + c = 0, where a, b and c are integers. Given […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2014 | June | Q#11

Question Given that f(x) = 2×2 + 8x + 3 a.   find the value of the discriminant of f(x). b.   Express f(x) in the form p(x + q)2 + r where p, q and r are integers to be found. The line y = 4x + c, where c is a constant, is a tangent […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2014 | June | Q#10

Question A curve with equation y=f(x) passes through the point (4,25). Given that a.   find f(x) simplifying each term. b.   Find an equation of the normal to the curve at the point (4, 25). Give your answer in the form ax + by + c = 0, where a, b and c are integers to […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2014 | June | Q#9

Question The line , shown in figure has equation 2x+3y = 26. The line  passes through the origin O and is perpendicular to . a.   Find an equation for the line . The line  intersects the line  at the point C. Line  crosses the y-axis at the point B as shown in Figure. b.   Find the area of triangle OBC. […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2014 | June | Q#4

Question Figure 1 shows a sketch of the curve C with equation  , x ≠ 0. The curve C crosses the x-axis at the point A. a.   State the x coordinate of the point A. The curve D has equation y = x2(x – 2), for all real values of x. b.   A copy of Figure 1 […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663A/01) | Year 2014 | January | Q#10

Question The curve C has equation . The point P, which lies on C, has coordinates (2, 1). a.   Show that an equation of the tangent to C at the point P is y = 3x – 5. The point Q also lies on C. Given that the tangent to C at Q is parallel to […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663A/01) | Year 2014 | January | Q#9

Question A curve with equation y=f(x) passes through the point (3,6). Given that a.   use integration to find f(x). Give your answer as a polynomial in its simplest form. b.   Show that , where p is a positive constant. State the value of p. c.   Sketch the graph of y = f(x), showing the coordinates of […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663A/01) | Year 2014 | January | Q#6

Question The straight line  has equation 2y = 3x + 7. The line  crosses the y-axis at the point A as shown in Figure. a.                         i.       State the gradient of .                   ii.       Write down the coordinates of the point A. Another straight line  intersects  at the point B (1, 5) and crosses the x-axis at the point C, as  shown in […]