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Algebraic Methods

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Question 222

The thermal resilience index, RRR, of a specific polymer during a stress test is modeled by the function

R(t)=5t2−202t2+9t+10−22t+5,t∈R, t>1 R(t) = \frac{5t^2 - 20}{2t^2 + 9t + 10} - \frac{2}{2t + 5}, \quad t \in \mathbb{R}, \ t > 1 R(t)=2t2+9t+105t2−20​−2t+52​,t∈R, t>1

where ttt is the duration of the test in hours.

a.

Show that R(t)=5t−122t+5R(t) = \frac{5t - 12}{2t + 5}R(t)=2t+55t−12​.

[4]
b.

Show, using calculus, that RRR is an increasing function for all t>1t > 1t>1. You must make your reasoning clear.

[3]
c.

The monitoring function HHH is defined by

H(t)=8+2ln⁡t,t≥1 H(t) = 8 + 2 \ln t, \quad t \ge 1 H(t)=8+2lnt,t≥1

Find H−1(x)H^{-1}(x)H−1(x).

[3]
d.

Find the exact value of aaa for which HR(a)=9HR(a) = 9HR(a)=9.

[3]
Markscheme

Algebraic Methods Questions

  1. A Level
  2. /Maths
  3. /Algebraic Methods

368 exam-style questions on Edexcel A Level Maths Algebraic Methods, covering 1.1 Proof by Contradiction, 1.2 Algebraic Fractions, 1.3 Partial Fractions, 1.4 Repeated Factors, and 1.5 Algebraic Division. Each one has a worked solution and a mark scheme showing where the marks go.

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