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1.5 B: Algebra and functions

1.5 B: Algebra and functions

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Question 306

The rate at which a specific toxin accumulates in a filtration system, R(t)R(t)R(t) in mg per hour, is modeled for t≥0t \ge 0t≥0 by the function:

R(t)=2t4+11t3+16t2+15t+46(t+3)2 R(t) = \frac{2t^4 + 11t^3 + 16t^2 + 15t + 46}{(t+3)^2} R(t)=(t+3)22t4+11t3+16t2+15t+46​
a.

Determine the values of the constants A,B,C,A, B, C,A,B,C, and DDD such that

R(t)=At2+Bt+C+D(t+3)2 R(t) = At^2 + Bt + C + \frac{D}{(t+3)^2} R(t)=At2+Bt+C+(t+3)2D​
[4]
b.

Hence find

∫R(t) dt \int R(t) \, dt ∫R(t)dt
[3]
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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