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1.5 B: Algebra and functions

1.5 B: Algebra and functions

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Question 204

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

1.5 B: Algebra and functions Questions

  1. A Level
  2. /Maths
  3. /1.5 B: Algebra and functions

532 exam-style questions on AQA A Level Maths 1.5 B: Algebra and functions, covering 1.5.1 Laws of indices, 1.5.2 Surds, 1.5.3 Quadratic functions, 1.5.4 Simultaneous equations, 1.5.5 Linear and quadratic inequalities, 1.5.6 Polynomials and rational expressions, 1.5.7 Graphs of functions and proportion, 1.5.8 Composite and inverse functions (A-level only), 1.5.9 Transformations of graphs, 1.5.10 Partial fractions (A-level only), and 1.5.11 Functions in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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