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1.5 B: Algebra and functions

1.5 B: Algebra and functions

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Question 331

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

1.5 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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