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A-LevelMathematicsAlgebra9709/22 · Feb/Mar 2024 · Q37 Marks

The polynomial p(x) is defined by p(x) = 6x³ + ax²+3x-10, where a is a constant. It is given that (2x – 1) is a factor of p(x).

  1. (a)Find the value of a and hence factorise p(x) completely.[5]
  2. (b)Solve the equation p(cosec θ) = 0 for -90° < θ < 90°.[2]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2024). The mark or mark type is shown in brackets.

  1. [M1] (a) Substitute x=1/2, equate to zero and attempt solution
  2. [A1] (a) Obtain a=31
  3. [M1] (a) Divide by 2x-1 at least as far as 3x² + mx [Or equivalent (for example by inspection, ...).]
  4. [A1] (a) Obtain 3x² +17x+10
  5. [A1] (a) Obtain (2x-1)(3x+2)(x+5)
  6. [M1] (b) Attempt solution of sinθ=k where k is valid constant from answer to part (a)
  7. [A1] (b) Obtain -11.5 [Or greater accuracy.]

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About this question

Topic
Algebra, A-Level Mathematics (syllabus 9709). Structured question, 7 marks.
Source
A-Level Mathematics, Feb/Mar 2024 Paper 2 Variant 2, question 3.

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