11. Let $f(x)$ be a real cubic polynomial with leading coefficient 1. Given that $f(1) = 1, f(2) = 2, f(5) = 5$, in which of the following intervals must $f(x) = 0$ have a real root? (1) $(-\infty, 0)$ (2) $(0, 1)$ (3) $(1, 2)$ (4) $(2, 5)$ (5) $(5, \infty)$
Part Two: Fill-in Questions (45 points)
Instructions: 1. For questions A through I, mark your answers on the "Answer Sheet" at the row numbers indicated (12–41). 2. Each completely correct answer receives 5 points. Wrong answers do not result in deduction. Incomplete answers receive no points. A. Let real number $x$ satisfy $0 < x < 1$ and $\log_x 4 - \log_2 x = 1$. Then $x = $ (12). (Express as a fraction in lowest terms) B. In $\triangle ABC$ on the coordinate plane, $P$ is the midpoint of side $\overline{BC}$, and $Q$ is on side $\overline{AC}$ such that $\overline{AQ} = 2\overline{QC}$. Given that $\overrightarrow{PA} = (4, 3)$ and $\overrightarrow{PQ} = (1, 5)$, then $\overrightarrow{BC} = ($ (14) (15), (16) (17) $)$. C. In a certain talent competition, to avoid excessive subjective influence from individual judges on contestants' scores, the
& 2，4 & & 22 & 0 & \multirow{10}{*}{} & &
11. Let $f(x)$ be a real cubic polynomial with leading coefficient 1. Given that $f(1) = 1, f(2) = 2, f(5) = 5$, in which of the following intervals must $f(x) = 0$ have a real root?\\
(1) $(-\infty, 0)$\\
(2) $(0, 1)$\\
(3) $(1, 2)$\\
(4) $(2, 5)$\\
(5) $(5, \infty)$
\section*{Part Two: Fill-in Questions (45 points)}
Instructions: 1. For questions A through I, mark your answers on the "Answer Sheet" at the row numbers indicated (12–41).\\
2. Each completely correct answer receives 5 points. Wrong answers do not result in deduction. Incomplete answers receive no points.\\
A. Let real number $x$ satisfy $0 < x < 1$ and $\log_x 4 - \log_2 x = 1$. Then $x = $ (12). (Express as a fraction in lowest terms)
B. In $\triangle ABC$ on the coordinate plane, $P$ is the midpoint of side $\overline{BC}$, and $Q$ is on side $\overline{AC}$ such that $\overline{AQ} = 2\overline{QC}$. Given that $\overrightarrow{PA} = (4, 3)$ and $\overrightarrow{PQ} = (1, 5)$, then $\overrightarrow{BC} = ($ (14) (15), (16) (17) $)$.
C. In a certain talent competition, to avoid excessive subjective influence from individual judges on contestants' scores, the