| Date | May 2012 | Marks available | 3 | Reference code | 12M.1.sl.TZ1.4 |
| Level | SL only | Paper | 1 | Time zone | TZ1 |
| Command term | Sketch | Question number | 4 | Adapted from | N/A |
Question
y = f (x) is a quadratic function. The graph of f (x) intersects the y-axis at the point A(0, 6) and the x-axis at the point B(1, 0). The vertex of the graph is at the point C(2, –2).
Write down the equation of the axis of symmetry.
Sketch the graph of y = f (x) on the axes below for 0 ≤ x ≤ 4 . Mark clearly on the sketch the points A , B , and C.
The graph of y = f (x) intersects the x-axis for a second time at point D.
Write down the x-coordinate of point D.
Markscheme
x = 2 (A1)(A1) (C2)
Notes: Award (A1)(A0) for “ x = constant” (other than 2). Award (A0)(A1) for y = 2. Award (A0)(A0) for only seeing 2. Award (A0)(A0) for 2 = –b / 2a.
[2 marks]
(A1) for correctly plotting and labelling A, B and C
(A1) for a smooth curve passing through the three given points
(A1) for completing the symmetry of the curve over the domain given. (A3) (C3)
Notes: For A marks to be awarded for the curve, each segment must be a reasonable attempt at a continuous curve. If straight line segments are used, penalise once only in the last two marks.
[3 marks]
3 (A1)(ft) (C1)
Notes: (A0) for coordinates. Accept x = 3 or D = 3 .
[1 mark]
Examiners report
(a) Identifying '2' and leaving this as the answer was not sufficient for any marks in this part of the question as was simply leaving the equation \(2 + \frac{{ - b}}{{2a}}\).
In part (b) whilst much good work was seen by some candidates in sketching the correct curve, others failed to recognise the symmetry, joined the given points with straight lines or simply drew curved segments which were far from smooth.
Part (c) required, for one mark, the writing down of the x-coordinate of the point D. A significant number of candidates, including very able candidates, lost this mark by writing down (3,0).
