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1.7 Integration

1.7 Integration

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Question 55

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

1.7 Integration Questions

  1. A Level
  2. /Maths
  3. /1.7 Integration

133 exam-style questions on CCEA A Level Maths 1.7 Integration, covering 1.7.1 Integration, 1.7.2 Integration, and 1.7.3 Integration. Each one has a worked solution and a mark scheme showing where the marks go.

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