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1.2 Algebra

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Question 16

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 Algebra Questions

  1. A Level
  2. /Maths
  3. /1.2 Algebra

303 exam-style questions on OCR (MEI) A Level Maths 1.2 Algebra, covering 1.2.1 Algebraic vocabulary and notation, 1.2.2 Solve linear equations, 1.2.3 Change the subject of a formula, 1.2.4 Solve quadratic equations, 1.2.5 Discriminant of a quadratic, 1.2.6 Linear simultaneous equations, 1.2.7 One linear one quadratic simultaneous equations, 1.2.8 Points of intersection and solutions, 1.2.9 Linear inequalities, 1.2.10 Quadratic inequalities, 1.2.11 Expressing solutions of inequalities, 1.2.12 Use and manipulate surds, 1.2.13 Rationalise the denominator, 1.2.14 Laws of indices, 1.2.15 Negative, fractional and zero indices, 1.2.16 Proportional relationships, 1.2.17 Partial fractions (A-level only), and 1.2.18 Simplify rational expressions (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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