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1EDEXCEL C4 June 2014 Q1
A curve C has the equation x^3 + 2xy - x - y^3 - 20 = 0. (a) Find dy/dx in terms of x and y. (5) (b) Find an equation of the tangent to C at the point (3, -2), giving your answer in the form ax + by + c = 0, where a, b and c are integers. (2)
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2EDEXCEL C4 June 2013 Q7
Question image is broken on examsolutions.net (dead upload, reported). The video solution below walks through the question.
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3EDEXCEL C4 June 2012 Q5
The curve C has equation 16y^3 + 9x^2y - 54x = 0. (a) Find dy/dx in terms of x and y. (5) (b) Find the coordinates of the points on C where dy/dx = 0. (7)
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4EDEXCEL C4 January 2012 Q1
The curve C has the equation 2x + 3y^2 + 3x^2y = 4x^2. The point P on the curve has coordinates (-1, 1). (a) Find the gradient of the curve at P. (5) (b) Hence find the equation of the normal to C at P, giving your answer in the form ax + by + c = 0, where a, b and c are integers. (3)
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5EDEXCEL C4 June 2010 Q3
A curve C has equation 2^x + y^2 = 2xy. Find the exact value of dy/dx at the point on C with coordinates (3, 2). (7)
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6EDEXCEL C4 January 2010 Q3
The curve C has the equation cos(2x) + cos(3y) = 1, -pi/4 <= x <= pi/4, 0 <= y <= pi/6. (a) Find dy/dx in terms of x and y. (3) The point P lies on C where x = pi/6. (b) Find the value of y at P. (3) (c) Find the equation of the tangent to C at P, giving your answer in the form ax + by + c*pi = 0, where a, b and c are integers. (3)
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7EDEXCEL C4 June 2009 Q4
The curve C has the equation y*e^(-2x) = 2x + y^2. (a) Find dy/dx in terms of x and y. (5) The point P on C has coordinates (0, 1). (b) Find the equation of the normal to C at P, giving your answer in the form ax + by + c = 0, where a, b and c are integers. (4)
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8EDEXCEL C4 January 2009 Q1
A curve C has the equation y^2 - 3y = x^3 + 8. (a) Find dy/dx in terms of x and y. (4) (b) Hence find the gradient of C at the point where y = 3. (3)
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9EDEXCEL C4 June 2008 Q4
A curve has equation 3x^2 - y^2 + xy = 4. The points P and Q lie on the curve. The gradient of the tangent to the curve is 8/3 at P and at Q. (a) Use implicit differentiation to show that y - 2x = 0 at P and at Q. (6) (b) Find the coordinates of P and Q. (3)
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10EDEXCEL C4 January 2008 Q5
A curve is described by the equation x^3 - 4y^2 = 12xy. (a) Find the coordinates of the two points on the curve where x = -8. (3) (b) Find the gradient of the curve at each of these points. (6)
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11Edexcel A Level June 2019 Paper 2 Q11
Figure 8 shows a sketch of the curve C with equation y = x^x, x > 0. (a) Find, by firstly taking logarithms, the x coordinate of the turning point of C. (Solutions based entirely on graphical or numerical methods are not acceptable.) (5) The point P(alpha, 2) lies on C. (b) Show that 1.5 < alpha < 1.6. (2) A possible iteration formula that could be used in an attempt to find alpha is x_(n+1) = 2x_n^(1-x_n). Using this formula with x_1 = 1.5, (c) find x_4 to 3 decimal places, (2) (d) describe the long-term behaviour of x_n. (2)
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12Edexcel A Level June 2023 Paper 2 Q7
In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. A curve has equation x^3 + 2xy + 3y^2 = 47. (a) Find dy/dx in terms of x and y. (4) The point P(-2, 5) lies on the curve. (b) Find the equation of the normal to the curve at P, giving your answer in the form ax + by + c = 0, where a, b and c are integers to be found. (3)
13Edexcel A Level June 2024 Paper 2 Q15
The curve C has equation (x + y)^3 = 3x^2 - 3y - 2. (a) Find an expression for dy/dx in terms of x and y. (5) The point P(1, 0) lies on C. (b) Show that the normal to C at P has equation y = -2x + 2. (2) (c) Prove that the normal to C at P does not meet C again. You should use algebra for your proof and make your reasoning clear. (5)
