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1.5 B: Algebra and functions

1.5 B: Algebra and functions

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Question 166

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

1.5 B: Algebra and functions Questions

  1. A Level
  2. /Maths
  3. /1.5 B: Algebra and functions

532 exam-style questions on AQA A Level Maths 1.5 B: Algebra and functions, covering 1.5.1 Laws of indices, 1.5.2 Surds, 1.5.3 Quadratic functions, 1.5.4 Simultaneous equations, 1.5.5 Linear and quadratic inequalities, 1.5.6 Polynomials and rational expressions, 1.5.7 Graphs of functions and proportion, 1.5.8 Composite and inverse functions (A-level only), 1.5.9 Transformations of graphs, 1.5.10 Partial fractions (A-level only), and 1.5.11 Functions in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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