◈ Oracle PrepSign Up Free
A-LevelMathematicsAlgebra9709/21 · Oct/Nov 2024 · Q48 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. (a)Find the value of a.[2]
  2. (b)Hence factorise p(x) completely.[3]
  3. (c)Solve the equation p(cosec²θ) = 0 for -90° < θ < 90°.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2024). 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 k₁x² + k₂x
  4. [A1] Obtain 4x² - 12x + 9
  5. [A1] Obtain (x + 2)(2x - 3)² or equivalent with integer coefficients only
  6. [M1] Equate sin²θ to appropriate value from factorised form and attempt solution
  7. [A1] Obtain 54.7
  8. [A1] Obtain -54.7

Write your answer and get it marked

On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.

Sign up free →

About this question

Topic
Algebra, A-Level Mathematics (syllabus 9709). Structured question, 8 marks.
Source
A-Level Mathematics, Oct/Nov 2024 Paper 2 Variant 1, question 4.

Questions and mark schemes are from past examination papers and remain the copyright of the exam board. How Oracle Prep builds its content

Related Mathematics questions

AlgebraFeb/Mar 20236m

In the expansion of (x/a + a/x²)⁷ , it is given that (the coefficient of x⁴) / (the coefficient of x) = 3. Find the p…

AlgebraFeb/Mar 20238m

The polynomial p(x) is defined by p(x) = ax³ – ax² + ax + b, where a and b are constants. It is given that (x + 2) is…

AlgebraFeb/Mar 20235m

The polynomial 2x⁴ + ax³ + bx − 1, where a and b are constants, is denoted by p(x). When p(x) is divided by x² – x + …

Probability and statisticsFeb/Mar 20179m

Pack A consists of ten cards numbered 0, 0, 1, 1, 1, 1, 1, 3, 3, 3. Pack B consists of six cards numbered 0, 0, 2, 2,…

Probability and statisticsFeb/Mar 201713m

The lengths, in centimetres, of middle fingers of women in Raneland have a normal distribution with mean u and standa…

DifferentiationFeb/Mar 20184m

A curve has equation y = 4x sin ½ x. Find the equation of the tangent to the curve at the point for which x = π.

← Browse all past-paper questions

© 2026 Oracle Prep