| Date | November 2012 | Marks available | 2 | Reference code | 12N.1.sl.TZ0.10 |
| Level | SL only | Paper | 1 | Time zone | TZ0 |
| Command term | Find | Question number | 10 | Adapted from | N/A |
Question
Consider the quadratic function y = f (x) , where f (x) = 5 − x + ax2.
It is given that f (2) = −5 . Find the value of a .
Find the equation of the axis of symmetry of the graph of y = f (x) .
Write down the range of this quadratic function.
Markscheme
−5 = 5 − (2) + a(2)2 (M1)
Note: Award (M1) for correct substitution in equation.
(a =) −2 (A1) (C2)
[2 marks]
\(x = - \frac{1}{4}\) (–0.25) (A1)(A1)(ft) (C2)
Notes: Follow through from their part (a). Award (A1)(A0)(ft) for “ x = constant”. Award (A0)(A1)(ft) for \(y = - \frac{1}{4}\).
[2 marks]
f (x) ≤ 5.125 (A1)(A1)(ft) (C2)
Notes: Award (A1) for f (x) ≤ (accept y). Do not accept strict inequality. Award (A1)(ft) for 5.125 (accept 5.13). Accept other correct notation, for example, (−∞, 5.125]. Follow through from their answer to part (b).
[2 marks]
Examiners report
This question proved to be quite a discriminator with a significant number of candidates achieving, at most, one or two marks in part (a). Part (b) was tested in the May 2012 series of examinations but the same errors were prevalent here as they were then. A number of candidates simply wrote the equation of the axis of symmetry in terms of y rather than x or just wrote down a numerical value rather than an equation. Expressions for the required range in part (c) fared little better with again much confusion between the variables x and y. A strict inequality was required at the turning point and a mark was lost where this was not indicated. Alternative forms for the range such as (–∞, 5.125] were, of course, accepted.
This question proved to be quite a discriminator with a significant number of candidates achieving, at most, one or two marks in part (a). Part (b) was tested in the May 2012 series of examinations but the same errors were prevalent here as they were then. A number of candidates simply wrote the equation of the axis of symmetry in terms of y rather than x or just wrote down a numerical value rather than an equation. Expressions for the required range in part (c) fared little better with again much confusion between the variables x and y. A strict inequality was required at the turning point and a mark was lost where this was not indicated. Alternative forms for the range such as (–∞ , 5.125] were, of course, accepted.
This question proved to be quite a discriminator with a significant number of candidates achieving, at most, one or two marks in part (a). Part (b) was tested in the May 2012 series of examinations but the same errors were prevalent here as they were then. A number of candidates simply wrote the equation of the axis of symmetry in terms of y rather than x or just wrote down a numerical value rather than an equation. Expressions for the required range in part (c) fared little better with again much confusion between the variables x and y. A strict inequality was required at the turning point and a mark was lost where this was not indicated. Alternative forms for the range such as (–∞ , 5.125] were, of course, accepted.
