| Date | May 2010 | Marks available | 1 | Reference code | 10M.1.sl.TZ1.14 |
| Level | SL only | Paper | 1 | Time zone | TZ1 |
| Command term | Find | Question number | 14 | Adapted from | N/A |
Question
A quadratic function, \(f(x) = a{x^2} + bx\), is represented by the mapping diagram below.
Use the mapping diagram to write down two equations in terms of a and b.
Find the value of a.
Find the value of b.
Calculate the x-coordinate of the vertex of the graph of f (x).
Markscheme
4a + 2b = 20
a + b = 8 (A1)
a – b = –4 (A1) (C2)
Note: Award (A1)(A1) for any two of the given or equivalent equations.
[2 marks]
a = 2 (A1)(ft)
[1 mark]
b = 6 (A1)(ft) (C2)
Note: Follow through from their (a).
[1 mark]
\(x = - \frac{6}{{2(2)}}\) (M1)
Note: Award (M1) for correct substitution in correct formula.
\( = -1.5\) (A1)(ft) (C2)
[2 marks]
Examiners report
Most candidates attempted this question but very few of them completed it entirely. A number of students wrote incorrect equations in part (a), which shows that the mapping diagram was poorly understood and read. Part (c) proved to be difficult for many who didn’t know how to find the x-coordinate of the vertex of the graph of the function. Some students gave the two coordinates instead of the x-coordinate only.
Most candidates attempted this question but very few of them completed it entirely. A number of students wrote incorrect equations in part (a), which shows that the mapping diagram was poorly understood and read. Part (c) proved to be difficult for many who didn’t know how to find the x-coordinate of the vertex of the graph of the function. Some students gave the two coordinates instead of the x-coordinate only.
Most candidates attempted this question but very few of them completed it entirely. A numberof students wrote incorrect equations in part (a), which shows that the mapping diagram was poorly understood and read. Part (c) proved to be difficult for many who didn’t know how to find the x-coordinate of the vertex of the graph of the function. Some students gave the two coordinates instead of the x-coordinate only.
Most candidates attempted this question but very few of them completed it entirely. A number of students wrote incorrect equations in part (a), which shows that the mapping diagram was poorly understood and read. Part (c) proved to be difficult for many who didn’t know how to find the x-coordinate of the vertex of the graph of the function. Some students gave the two coordinates instead of the x-coordinate only.
