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1.2 Algebra and Functions

1.2 Algebra and Functions

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Question 172

The pressure, PPP, in a chemical reactor at time τ\tauτ is modeled by the function

P(τ)=4τ3−10τ2+10τ+λ,τ≥0 P(\tau) = 4\tau^3 - 10\tau^2 + 10\tau + \lambda, \quad \tau \ge 0 P(τ)=4τ3−10τ2+10τ+λ,τ≥0

where λ\lambdaλ is a constant.

It is observed that the pressure reaches a zero-state when τ=0.5\tau = 0.5τ=0.5, suggesting that (2τ−1)(2\tau - 1)(2τ−1) is a factor of P(τ)P(\tau)P(τ).

a.

Use the factor theorem to show that λ=−3\lambda = -3λ=−3.

[3]
b.

Show that P(τ)=0P(\tau) = 0P(τ)=0 has no other real solutions for τ\tauτ.

[4]
Markscheme

1.2 Algebra and Functions Questions

  1. A Level
  2. /Maths
  3. /1.2 Algebra and Functions

302 exam-style questions on WJEC A Level Maths 1.2 Algebra and Functions, covering 1.2.1 Algebra and Functions, 1.2.2 Algebra and Functions, 1.2.3 Algebra and Functions, 1.2.4 Algebra and Functions, 1.2.5 Algebra and Functions, 1.2.6 Algebra and Functions, 1.2.7 Algebra and Functions, 1.2.8 Algebra and Functions, 1.2.9 Algebra and Functions, 1.2.10 Algebra and Functions, 1.2.11 Algebra and Functions, and 1.2.12 Algebra and Functions. Each one has a worked solution and a mark scheme showing where the marks go.

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