# 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 2017 | June | Q#8

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 = 0 where […]

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

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 its simplest […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2017 | June | Q#6

Question a.   Given y = 2x, show that can be written in the form b.   Hence solve Solution a)     We have the equation; We are given that y = 2x; b)    We are required to solve; As demonstrated in (a) this can be written as; Now we have two options. For these values of y, we can find corresponding values […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2017 | June | Q#5

Question f(x) = x2 – 8x + 19 a.   (a) Express f(x) in the form (x + a)2 + b, where a and b are constants. The curve C with equation y = f(x) crosses the y-axis at the point P and has a minimum point at the  point Q. b.   Sketch the graph of C showing the […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2017 | June | Q#4

Question A company, which is making 140 bicycles each week, plans to increase its production. The number of bicycles produced is to be increased by d each week, starting from 140 in week 1, to 140 + d in week 2, to 140 + 2d in week 3 and so on, until the company is producing  206 in week […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2017 | June | Q#3

Question A sequence  is defined by  ,  , Where k is a positive constant. a)   Write down expressions for  and  in terms of k, giving your answers in their simplest form. Given that , b)  Find an exact value for k. Solution a.     We are given that sequence  is defined by We are required to find  and  in terms of […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2017 | June | Q#2

Question Given , find the value of   when x=8, writing your answer in the form  where a is a rational number. Solution We are given; We are required to find . Gradient (slope) of the curve is the derivative of equation of the curve. Hence gradient of curve  with respect to  is: Therefore; Rule for differentiation is of […]

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

Question Find giving each term in its simplest form. Solution We are given; Rule for integration of  is: Rule for integration of  is: Rule for integration of  is:

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2016 | June | Q#2

Question Express  in the form , giving y in the form ax + b, where a and b are constants. Solution We are given; Hence; Therefore;