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Algebraic Methods

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Question 83

A model for the concentration of a catalyst, CCC, at a distance x x\,x millimetres from the center of a reaction chamber is given by the function

C(x)=(x−4)(3x2+16x+k)+340 C(x) = (x - 4)(3x^2 + 16x + k) + 340 C(x)=(x−4)(3x2+16x+k)+340

where k k\,k is a constant.

a.

State the value of the concentration at x=4x = 4x=4.

[1]
b.

Given that (3x−2)(3x - 2)(3x−2) is a factor of C(x)C(x)C(x),

show that k=90k = 90k=90.

[4]
c.

Hence

(i) fully factorise the expression for C(x)C(x)C(x),

(ii) determine the number of real values of x x\,x for which the concentration is zero, giving a reason for your answer.

[5]

Algebraic Methods Questions

  1. A Level
  2. /Maths
  3. /Algebraic Methods

Practise Edexcel A Level Maths Algebraic Methods with exam-style questions for A Level Maths. 226 questions covering 1.1 Proof by Contradiction, 1.2 Algebraic Fractions, 1.3 Partial Fractions, 1.4 Repeated Factors, and 1.5 Algebraic Division, 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