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1.2.11 Simplifying rational expressions

1.2.11 Simplifying rational expressions

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Question 6

The curve CCC has equation

y=2x3+18x+5,x>0 y = 2x^3 + \frac{18}{x} + 5, \quad x > 0 y=2x3+x18​+5,x>0
a.

Find dydx\frac{\mathrm{d}y}{\mathrm{d}x}dxdy​, giving your answer in simplest form.

[2]
b.

Given that

  • the point PPP lies on CCC
  • the line with equation y=k−24xy = k - 24xy=k−24x, where kkk is a constant, is the tangent to CCC at PPP

Show that the xxx-coordinate of PPP satisfies the equation

x4+4x2−3=0 x^4 + 4x^2 - 3 = 0 x4+4x2−3=0
[3]
c.

Hence find the exact value of kkk.

[4]
Markscheme

1.2.11 Simplifying rational expressions Questions

  1. A Level
  2. /Maths
  3. /1.2.11 Simplifying rational expressions

16 exam-style questions on OCR A Level Maths 1.2.11 Simplifying rational expressions. Each one has a worked solution and a mark scheme showing where the marks go.

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