| Date | May 2012 | Marks available | 4 | Reference code | 12M.1.hl.TZ1.2 |
| Level | HL only | Paper | 1 | Time zone | TZ1 |
| Command term | Hence and State | Question number | 2 | Adapted from | N/A |
Question
The graphs of \(y = \left| {x + 1} \right|\) and \(y = \left| {x - 3} \right|\) are shown below.
Let f (x) = \(\left| {\,x + 1\,} \right| - \left| {\,x - 3\,} \right|\).
Draw the graph of y = f (x) on the blank grid below.
Hence state the value of
(i) \(f'( - 3)\);
(ii) \(f'(2.7)\);
(iii) \(\int_{ - 3}^{ - 2} {f(x)dx} \).
Markscheme
M1A1A1A1
Note: Award M1 for any of the three sections completely correct, A1 for each correct segment of the graph.
[4 marks]
(i) 0 A1
(ii) 2 A1
(iii) finding area of rectangle (M1)
\( - 4\) A1
Note: Award M1A0 for the answer 4.
[4 marks]
Examiners report
Most candidates were able to produce a good graph, and many were able to interpret that to get correct answers to part (b). The most common error was to give 4 as the answer to (b) (iii). Some candidates did not recognise that the “hence” in the question meant that they had to use their graph to obtain their answers to part (b).
Most candidates were able to produce a good graph, and many were able to interpret that to get correct answers to part (b). The most common error was to give 4 as the answer to (b) (iii). Some candidates did not recognise that the “hence” in the question meant that they had to use their graph to obtain their answers to part (b).
