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1.11 H: Integration

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Question 46

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

1.11 H: Integration Questions

  1. A Level
  2. /Maths
  3. /1.11 H: Integration

480 exam-style questions on AQA A Level Maths 1.11 H: Integration, covering 1.11.1 Fundamental Theorem of Calculus, 1.11.2 Integrating standard functions, 1.11.3 Definite integrals and areas, 1.11.4 Integration as the limit of a sum (A-level only), 1.11.5 Integration by substitution and by parts (A-level only), 1.11.6 Integration using partial fractions (A-level only), 1.11.7 Differential equations with separable variables (A-level only), and 1.11.8 Interpreting solutions of differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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