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1.1 Algebra and functions

1.1 Algebra and functions

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Question 100

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]
Markscheme

1.1 Algebra and functions Questions

  1. A Level
  2. /Maths
  3. /1.1 Algebra and functions

306 exam-style questions on CCEA A Level Maths 1.1 Algebra and functions, covering 1.1.1 Algebra and functions, 1.1.2 Algebra and functions, 1.1.3 Algebra and functions, 1.1.4 Algebra and functions, 1.1.5 Algebra and functions, 1.1.6 Algebra and functions, 1.1.7 Algebra and functions, 1.1.8 Algebra and functions, 1.1.9 Algebra and functions, 1.1.10 Algebra and functions, 1.1.11 Algebra and functions, 1.1.12 Algebra and functions, 1.1.13 Algebra and functions, and 1.1.14 Algebra and functions. Each one has a worked solution and a mark scheme showing where the marks go.

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