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A-LevelMathematicsAlgebra9709/21 · Oct/Nov 2019 · Q47 Marks

The polynomial p(x) is defined by p(x) = ax³ + ax² – 15x – 18, where a is a constant. It is given that (x – 2) is a factor of p(x).

  1. (i)Find the value of a.[2]
  2. (ii)Using this value of a, factorise p(x) completely.[3]
  3. (iii)Hence solve the equation p(e^(√y)) = 0, giving the answer correct to 2 significant figures.[2]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.

  1. [M1] Substitute x = 2, equate to zero and attempt solution
  2. [A1] Obtain a = 4
  3. [M1] Divide by x-2 at least as far as the x term By inspection or use of identity
  4. [A1] Obtain 4x² +12x+9
  5. [A1] Conclude (x-2)(2x + 3)² Each factor must be simplified to integer form
  6. [M1] Attempt correct process to solve e^(√y) = k where k > 0 For y = (lnk)²
  7. [A1] Obtain 0.48 and no others AWRT

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About this question

Topic
Algebra, A-Level Mathematics (syllabus 9709). Structured question, 7 marks.
Source
A-Level Mathematics, Oct/Nov 2019 Paper 2 Variant 1, question 4.

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