| Date | November 2010 | Marks available | 2 | Reference code | 10N.1.sl.TZ0.10 |
| Level | SL only | Paper | 1 | Time zone | TZ0 |
| Command term | Write down | Question number | 10 | Adapted from | N/A |
Question
The following is the graph of the quadratic function y = f (x).
Write down the solutions to the equation f (x) = 0.
Write down the equation of the axis of symmetry of the graph of f (x).
The equation f (x) = 12 has two solutions. One of these solutions is x = 6. Use the symmetry of the graph to find the other solution.
The minimum value for y is – 4. Write down the range of f (x).
Markscheme
x = 0, x = 4 (A1)(A1) (C2)
Notes: Accept 0 and 4.
[2 marks]
x = 2 (A1)(A1) (C2)
Note: Award (A1) for x = constant, (A1) for 2. [2 marks]
x = –2 (A1) (C1)
Note: Accept –2.
[1 mark]
\(y \geqslant -4{\text{ }}(f(x) \geqslant -4)\) (A1) (C1)
Notes: Accept alternative notations.
Award (A0) for use of strict inequality.
[1 mark]
Examiners report
A number of candidates left out this question which indicated that this topic was either entirely unfamiliar, that this topic of the syllabus had perhaps not been taught, or was barely familiar. A few candidates wrote down coordinate pairs when asked for a solution to the equation. A number of candidates wrote down the formula for the equation of the axis of symmetry without being able to substitute values for a and b. When given the minimum value of the graph a small number of candidates could identify the range of the function correctly. Overall this question proved to be difficult with its demands for reading and interpreting the graph, and dealing with additional information about the quadratic function given in the different parts.
A number of candidates left out this question which indicated that this topic was either entirely unfamiliar, that this topic of the syllabus had perhaps not been taught, or was barely familiar. A few candidates wrote down coordinate pairs when asked for a solution to the equation. A number of candidates wrote down the formula for the equation of the axis of symmetry without being able to substitute values for a and b. When given the minimum value of the graph a small number of candidates could identify the range of the function correctly. Overall this question proved to be difficult with its demands for reading and interpreting the graph, and dealing with additional information about the quadratic function given in the different parts.
A number of candidates left out this question which indicated that this topic was either entirely unfamiliar, that this topic of the syllabus had perhaps not been taught, or was barely familiar. A few candidates wrote down coordinate pairs when asked for a solution to the equation. A number of candidates wrote down the formula for the equation of the axis of symmetry without being able to substitute values for a and b. When given the minimum value of the graph a small number of candidates could identify the range of the function correctly. Overall this question proved to be difficult with its demands for reading and interpreting the graph, and dealing with additional information about the quadratic function given in the different parts.
A number of candidates left out this question which indicated that this topic was either entirely unfamiliar, that this topic of the syllabus had perhaps not been taught, or was barely familiar. A few candidates wrote down coordinate pairs when asked for a solution to the equation. A number of candidates wrote down the formula for the equation of the axis of symmetry without being able to substitute values for a and b. When given the minimum value of the graph a small number of candidates could identify the range of the function correctly. Overall this question proved to be difficult with its demands for reading and interpreting the graph, and dealing with additional information about the quadratic function given in the different parts.
