| Date | November 2009 | Marks available | 5 | Reference code | 09N.1.hl.TZ0.1 |
| Level | HL only | Paper | 1 | Time zone | TZ0 |
| Command term | Find | Question number | 1 | Adapted from | N/A |
Question
When \(3{x^5} - ax + b\) is divided by x −1 and x +1 the remainders are equal. Given that a , \(b \in \mathbb{R}\) , find
(a) the value of a ;
(b) the set of values of b .
Markscheme
(a) \(f(1) = 3 - a + b\) (A1)
\(f( - 1) = - 3 + a + b\) (A1)
\(3 - a + b = - 3 + a + b\) M1
\(2a = 6\)
\(a = 3\) A1 N4
(b) b is any real number A1
[5 marks]
Examiners report
Many candidates answered part (a) successfully. For part (b), some candidates did not consider that the entire set of real numbers was asked for.
