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

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), , has […]

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

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 constant, meets […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2016 | June | Q#4

Question Figure  shows a sketch of part of the curve with equation y = f(x). The curve has a maximum point A  at (–2, 4) and a minimum point B at (3, –8) and passes through the origin O.  On separate diagrams, sketch the curve with equation a.   y = 3f(x), b.   y = f(x) – 4 On each […]

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

Question Figure 1 shows a sketch of a curve with equation y = f(x). The curve crosses the y-axis at (0, 3) and has a minimum at P (4, 2). On separate diagrams, sketch the curve with equation a.   y = f(x + 4), b.    y = 2f(x). On each diagram show the coordinates of minimum point and […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01R) | Year 2013 | June | Q#9

Question Figure 1 shows a sketch of the curve C with equation y = f(x). The curve C passes through the point (-1,0) and touches the x-axis at the point (2,0). The curve C has a maximum at the point (0,4). a.   The equation of the curve C can be written in the form Where a, b […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2013 | June | Q#8

Question Figure 1 shows a sketch of the curve with equation y = f(x) where  , The curve crosses the x-axis at (1, 0), touches it at (–3, 0) and crosses the y-axis at (0, –9). a.   In the space below, sketch the curve C with equation y=f(x+2) and state the coordinates of the  points where the […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2013 | January | Q#6

Question Figure 1 shows a sketch of the curve with equation  , x ≠ 0. The curve C has equation , x ≠ 0, and the line  has equation y = 4x + 2. a.   Sketch and clearly label the graphs of C and  on a single diagram. On your diagram, show clearly the coordinates of the […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2012 | June | Q#10

Question Figure 1 shows a sketch of the curve C with equation y = f(x) where f (x) = x2(9 –2x) There is a minimum at the origin, a maximum at the point (3, 27) and C cuts the x-axis at the point  A. a.   Write down the coordinates of the point A. b.   On separate […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2012 | January | Q#8

Question The curve  has equation a.   Find . b.   Sketch , showing the coordinates of the points where C1 meets the x-axis. c.   Find the gradient of  at each point where C1 meets the x-axis. The curve  has equation where k is a constant and . d.   Sketch , showing the coordinates of the points where  meets the x […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2011 | June | Q#8

Question Figure 1 shows a sketch of the curve C with equation y = f (x). The curve C passes through the origin and through (6, 0). The curve C has a minimum at the point (3, –1). On separate diagrams, sketch the curve with equation a.   y=f(2x), b.   y=-f(x) c.   y=f(x+p), where p is a constant . On […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2011 | January | Q#10

Question a.   On the axes below, sketch the graphs of i.        ii.     showing clearly the coordinates of all the points where the curves cross the coordinate axes. b.   Using your sketch state, giving a reason, the number of real solutions to the equation Solution a.   i.   We are required to sketch; We need to expand it […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2011 | January | Q#5

Question Figure 1 shows a sketch of the curve with equation y = f (x) where  , The curve passes through the origin and has two asymptotes, with equations y=1 and x=2, as  shown in Figure. a.   In the space below, sketch the curve with equation y = f (x −1) and state the equations of the  […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2010 | June | Q#6

Question Figure 1 shows a sketch of the curve with equation y = f (x). The curve has a maximum  point A at  (–2, 3) and a minimum point B at (3, – 5). On separate diagrams sketch the curve with equation a.   y = f (x + 3) b.   y = 2f (x) On each diagram show […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2010 | January | Q#8

Question Figure 1 shows a sketch of part of the curve with equation y = f(x). The curve has a maximum point  (−2, 5) and an asymptote y = 1, as shown in Figure 1. On separate diagrams, sketch the curve with equation a.   y = f(x) + 2 b.   y = 4f(x) c.   y = […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2009 | June | Q#10

Question a)   Factorise completely x3 – 6×2 + 9x b)  Sketch the curve with equation y = x3 – 6×2 + 9x showing the coordinates of the points at which the curve meets the x-axis. Using your answer to part (b), or otherwise, c)   (c) sketch, on a separate diagram, the curve with equation y = (x […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2009 | January | Q#8

Question The point P (1, a) lies on the curve with equation y = (x + 1)2(2– x). a.   Find the value of a. b.   On the axes below sketch the curves with the following equations: i.       y = (x + 1)2(2– x) ii.        On your diagram show clearly the coordinates of any points at […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2009 | January | Q#5

Question Figure 1 shows a sketch of the curve C with equation y=f(x). There is a maximum at (0, 0), a  minimum at (2, –1) and C passes through (3, 0). On separate diagrams sketch the curve with equation a.   y = f(x + 3), b.   y = f(–x). On each diagram show clearly the coordinates of the […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2008 | June | Q#6

Question The curve C has equation  and the line  has equation y = 2x + 5. a.   On the axes below, sketch the graphs of C and , indicating clearly the coordinates of any intersections with the axes. b.   Find the coordinates of the points of intersection of C and . Solution a.   We are […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2008 | June | Q#3

Question Figure 1 shows a sketch of the curve with equation y = f(x). The curve passes through the point (0,7) and has a minimum point at (7, 0). On separate diagrams, sketch the curve with equation a.   y = f(x) + 3, b.   y = f(2x). On each diagram, show clearly the coordinates of the […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2008 | January | Q#6

Question Figure 1 shows a sketch of the curve with equation y= f(x). The curve crosses the x-axis at the  points (1, 0) and (4, 0). The maximum point on the curve is (2, 5). In separate diagrams sketch the curves with the following equations.  On each diagram show clearly the coordinates of the maximum point and of […]