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1.1 Algebra and functions

1.1 Algebra and functions

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Question 105

A data engineer models the throughput T(x)T(x)T(x) of a high-frequency trading link, measured in terabits per millisecond, as a function of the signal frequency xxx in gigahertz:

T(x)=2x4−13x3+29x2−39x+41(x−3)2,x∈R,  x>3 T(x) = \frac{2x^4 - 13x^3 + 29x^2 - 39x + 41}{(x-3)^2}, \quad x \in \mathbb{R}, \; x > 3 T(x)=(x−3)22x4−13x3+29x2−39x+41​,x∈R,x>3
a.

Determine the values of the constants AAA, BBB, CCC and DDD such that

T(x)=Ax2+Bx+C+D(x−3)2 T(x) = Ax^2 + Bx + C + \frac{D}{(x-3)^2} T(x)=Ax2+Bx+C+(x−3)2D​
[4]
b.

Hence find

∫T(x) dx \int T(x) \, dx ∫T(x)dx
[3]
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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