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Question 604

The curve C has equation y=f(x),x>0y = \mathrm{f}(x), x > 0y=f(x),x>0. Given that:

  • the point P(9,−2)P(9, -2)P(9,−2) lies on CCC
  • f′(x)=3x2+ax+b2x\mathrm{f}'(x) = \dfrac{3x^2 + ax + b}{2\sqrt{x}}f′(x)=2x​3x2+ax+b​, where aaa and bbb are constants
  • the gradient of the tangent to CCC at PPP is 353535
a.

Show that 9a+b=−339a + b = -339a+b=−33.

[2]
b.

Given also that a−b=13a - b = 13a−b=13

Find, in simplest form, f(x)\mathrm{f}(x)f(x).

[6]
c.

Curve CCC is transformed to the curve with equation y=f(x+4)y = \mathrm{f}(x + 4)y=f(x+4). Given that point PPP is transformed to the point QQQ,

State the coordinates of QQQ.

[2]
Markscheme

Integration Questions

  1. A Level
  2. /Maths
  3. /Integration

864 exam-style questions on Edexcel A Level Maths Integration, covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations. Each one has a worked solution and a mark scheme showing where the marks go.

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