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1.2 Algebra and Functions

1.2 Algebra and Functions

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Question 174

The internal stress in a structural component is modeled by the cubic polynomial S(x)=3x3+Ax2+Bx−10S(x) = 3x^3 + Ax^2 + Bx - 10S(x)=3x3+Ax2+Bx−10, where AAA and BBB are integer constants and xxx represents the position along the component.

It is known that:

  • when S(x)S(x)S(x) is divided by (x−2)(x - 2)(x−2), the remainder is RRR
  • when S(x)S(x)S(x) is divided by (x+1)(x + 1)(x+1), the remainder is −2R-2R−2R
  • RRR is a real constant
a.

Show that 3A+B=−53A + B = -53A+B=−5.

[4]
b.

Given that the stress is zero at position x=23x = \frac{2}{3}x=32​, such that (3x−2)(3x - 2)(3x−2) is a factor of S(x)S(x)S(x), find the value of AAA and the value of BBB.

[3]
c.

Hence determine the quadratic expression Q(x)Q(x)Q(x) such that S(x)=(3x−2)Q(x)S(x) = (3x - 2)Q(x)S(x)=(3x−2)Q(x).

[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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