# 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#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#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 2015 | June | Q#10

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 coordinate of […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2015 | June | Q#3

Question Given that , ,  , find in their simplest form, a.   b.   . Solution a.   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  is: Rule for differentiation is […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01R) | Year 2014 | June | Q#8

Question  , Given that y=37 at x=4, find y in terms of x, giving each term in its simplest form. Solution We are given that; We are given coordinates of appoint that is y=37 at x=4 ie  (4,37). We are required to find the equation of y in terms of x. We can find equation of the curve […]

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

Question Given that , ,  , find in their simplest form, a.   b.   . Solution a.   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  is: Rule for differentiation is […]

# 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#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 (C1-6663A/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 (C1-6663/01R) | Year 2013 | June | Q#10

Question A curve has equation y=f(x). The point P with coordinates (9,0) lies on the curve. Given that  , a.   Find f(x). b.   Find the x-coordinates of two points on y=f(x) where the gradient of the curve is equal to 10. Solution a.   We are given; We are given coordinates of a point on the […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01R) | Year 2013 | June | Q#3

Question Find giving each term in its simplest form. Solution We are given; 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 2013 | June | Q#9

Question  , a.   Show that Where A and B are constants to be found. b.   Find Given that the point (-3,10) lies on the curve with equation y=f(x), c.   Find f(x). Solution a.   We are given; Therefore; b.   We are given; We are required to find . Second derivative is the derivative of the derivative. […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2013 | June | Q#2

Question Find giving each term in its simplest form. Solution We are given; 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 2013 | January | Q#8

Question  , Given that y=7 at x=1, find y in terms of x, giving each term in its simplest form. Solution We are given that; We are given coordinates of appoint that is y=7 at x=1 ie  (1,7). We are required to find the equation of y in terms of x. We can find equation of the curve […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2012 | June | Q#7

Question The point P(4,–1) lies on the curve C with equation y = f(x), x > 0, and a.   Find the equation of the tangent to C at the point P, giving your answer in the form y = mx + c,  where m and c are integers. b.   Find f(x). Solution a.   We are required to […]

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

Question Find Giving each term in its simplest form. Solution a.   We are required to find; 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 2012 | January | Q#7

Question A curve with equation y = f (x) passes through the point (2,10). Given that f ′(x) = 3×2 − 3x + 5 find the value of f (1). Solution We are required to find f(1) but we are not given f(x) but f ′(x). f ′(x) = 3×2 − 3x + 5 Therefore, we need to […]

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

Question Given that , , find, in their simplest form, a.   b.   . Solution a.   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  is: Rule for differentiation is of  is: […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2011 | June | Q#6

Question Given that  can be written in the form , a.   Write down the value of p and the value of q. Given that  , and that y=90 when x=4; b.   find  in terms of x, simplifying the coefficient of each term. Solution a.   We are given; b.   We are required to find y […]