| Date | November 2013 | Marks available | 3 | Reference code | 13N.2.sl.TZ0.2 |
| Level | SL only | Paper | 2 | Time zone | TZ0 |
| Command term | Find | Question number | 2 | Adapted from | N/A |
Question
Let \(f(x) = (x - 1)(x - 4)\).
Find the \(x\)-intercepts of the graph of \(f\).
[3]
a.
The region enclosed by the graph of \(f\) and the \(x\)-axis is rotated \(360^\circ\) about the \(x\)-axis.
Find the volume of the solid formed.
[3]
b.
Markscheme
valid approach (M1)
eg \(f(x) = 0\), sketch of parabola showing two \(x\)-intercepts
\(x = 1,{\text{ }}x = 4{\text{ }}\left( {{\text{accept (1, 0), (4, 0)}}} \right)\) A1A1 N3
[3 marks]
a.
attempt to substitute either limits or the function into formula involving \({f^2}\) (M1)
eg \(\int_1^4 {{{\left( {f(x)} \right)}^2}{\text{d}}x,{\text{ }}\pi \int {{{\left( {(x - 1)(x - 4)} \right)}^2}} } \)
\({\text{volume}} = 8.1\pi {\text{ (exact), 25.4}}\) A2 N3
[3 marks]
b.
Examiners report
[N/A]
a.
[N/A]
b.
Syllabus sections
Topic 2 - Functions and equations » 2.4 » The quadratic function \(x \mapsto a{x^2} + bx + c\) : its graph, \(y\)-intercept \((0, c)\). Axis of symmetry.
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