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1.5 B: Algebra and functions

1.5 B: Algebra and functions

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Question 242

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

1.5 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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