| Date | May 2009 | Marks available | 5 | Reference code | 09M.1.hl.TZ2.1 |
| Level | HL only | Paper | 1 | Time zone | TZ2 |
| Command term | Find | Question number | 1 | Adapted from | N/A |
Question
When the function \(q(x) = {x^3} + k{x^2} - 7x + 3\) is divided by (x + 1) the remainder is seven times the remainder that is found when the function is divided by (x + 2) .
Find the value of k .
Markscheme
\(q( - 1) = k + 9\) M1A1
\(q( - 2) = 4k + 9\) A1
\(k + 9 = 7(4k + 9)\) M1
\(k = - 2\) A1
Notes: The first M1 is for one substitution and the consequent equations.
Accept expressions for \(q( - 1)\) and \(q( - 2)\) that are not simplified.
[5 marks]
Examiners report
Most candidates were able to access this question although the number who used either synthetic division or long division was surprising as this often lead to difficulty and errors. The most common error was in applying the factor of 7 to the wrong side of the equation. It was also disappointing the number of students who made simple algebraic errors late in the question.
