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1.1 Algebra and functions

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Question 77

Given that

g(x)=4x2−13x+13x−3 g(x) = \frac{4x^2 - 13x + 13}{x - 3} g(x)=x−34x2−13x+13​
a.

Write g(x)g(x)g(x) in the form

Ax+B+Cx−3 Ax + B + \frac{C}{x - 3} Ax+B+x−3C​

where AAA, BBB, and CCC are integers to be found.

[4]
b.

Hence use algebraic integration to show that

∫46g(x) dx=α+βln⁡3 \int_{4}^{6} g(x) \, dx = \alpha + \beta \ln 3 ∫46​g(x)dx=α+βln3

where α\alphaα and β\betaβ are integers to be found.

[4]
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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