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1.2 Algebra and Functions

1.2 Algebra and Functions

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Question 119

The pressure P P\,P in a specialized hydraulic chamber is modeled by the cubic function

P(x)=kx3−11x2−26x+24 P(x) = kx^3 - 11x^2 - 26x + 24 P(x)=kx3−11x2−26x+24

where x x\,x represents the displacement of a control valve in millimetres and k k\,k is a design constant.

a.

Given that (x+2)(x + 2)(x+2) is a factor of P(x)P(x)P(x), show that k=4k = 4k=4.

[2]
b.

Using algebra and showing each step of your working, fully factorise P(x)P(x)P(x).

[3]
c.

Solve, for 0∘≤θ<360∘0^\circ \le \theta < 360^\circ0∘≤θ<360∘, the equation

4cos⁡3θ−11cos⁡2θ−26cos⁡θ+24=0 4\cos^3 \theta - 11\cos^2 \theta - 26\cos \theta + 24 = 0 4cos3θ−11cos2θ−26cosθ+24=0

giving your answers to one decimal place.

[3]
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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