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Question 246

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]

Integration Questions

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

Practise Edexcel A Level Maths Integration with exam-style questions for A Level Maths. 437 questions 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, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.

Question bank