Hits: 201

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2017 | June | Q#10

Hits: 201   Question Figure shows a sketch of part of the curve y = f(x), , where f(x) = (2x – 5)2(x + 3) a.   Given that                     i.       the curve with equation y = f(x) – k, , passes through the origin, find the value of the  constant k,                   ii.       the curve with equation y = f(x + c), […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2017 | June | Q#9

Hits: 662   Question a.   On separate axes sketch the graphs of                     i.       y = –3x + c, where c is a positive constant,                   ii.        On each sketch show the coordinates of any point at which the graph crosses the y-axis and the equation of any horizontal asymptote. Given that y = –3x + c, where c is a positive […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2017 | June | Q#8

Hits: 355   Question The straight line  , shown in Figure, has equation 5y = 4x + 10. The point P with x coordinate 5 lies on . The straight line  is perpendicular to  and passes through P. a.   Find an equation for  , writing your answer in the form ax + by + c = […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2017 | June | Q#7

Hits: 902 Question The curve C has equation y=f(x), x>0, where Given tht the point P(4,-8) lies on the curve C; a.   find the equation of the tangent to C at P, giving your answer in the form y = mx + c, where m and  c are constants. a.   find f(x), giving each term in […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2016 | June | Q#11

Hits: 110 Question The curve C has equation  , where k is a constant. a.   Find . The point P, where x=-2, lies on C. The tangent to C at the point P is parallel to the line with equation 2y – 17x – 1=0. Find b.  the value of k. c.  the value of y-coordinate of P. d.  the equation of […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2016 | June | Q#10

Hits: 139   Question The points P(0, 2) and Q(3, 7) lie on the line , as shown in Figure. The line  is perpendicular to , passes through Q and crosses the x-axis at the point R, as shown in Figure. Find a.   an equation for , giving your answer in the form ax + by + […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2016 | June | Q#8

Hits: 78 Question The straight line with equation y = 3x – 7 does not cross or touch the curve with equation y = 2px2 – 6px + 4p, where p is a constant. a.   Show that 4p2 – 20p + 9 < 0 b.   Hence find the set of possible values of p. Solution a.   […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2015 | June | Q#10

Hits: 148   Question A curve with equation y=f(x) passes through the point (4,9). Given that  , x > 0 a.   find f(x), giving each term in its simplest form. Point P lies on the curve. The normal to the curve at P is parallel to the line 2y + x = 0 b.   Find x […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2015 | June | Q#8

Hits: 465   Question a.   Factorise completely 9x – 4×3 b.   Sketch the curve C with equation y = 9x – 4×3 Show on your sketch the coordinates at which the curve meets the x-axis. The points A and B lie on C and have x coordinates of –2 and 1 respectively. c.   Show that the length of […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2015 | June | Q#6

Hits: 82   Question The curve C has equation  , a. Find  in its simplest form. b. Find an equation of the tangent to C at the point where x=-1. Give your answer in the form ax+by+c=0, where a, b and c are integers. Solution a.   We are given; We are required to find . Gradient (slope) of […]

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

Hits: 208   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 […]

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

Hits: 60   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.   […]

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

Hits: 1767   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 […]

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

Hits: 52   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 […]

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

Hits: 49   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 […]

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

Hits: 85 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 […]

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

Hits: 77   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 […]

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

Hits: 100   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 […]

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

Hits: 104   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 […]

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

Hits: 85   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  […]