gaokao 2024 Q10

gaokao · China · beijing 4 marks Areas Between Curves Area Between Curves with Parametric or Implicit Region Definition

If the set $\left\{ y \mid y = x + t \left( x ^ { 2 } - x \right) , 0 \leq t \leq 1, 1 \leq x \leq 2 \right\}$ represents a figure where the maximum distance between two points is $d$ and the area is $S$,
A. $d = 3 , S < 1$
B. $d = 3 , S > 1$
C. $d = \sqrt { 10 } , S < 1$
D. $d = \sqrt { 10 } , S > 1$

If the set $\left\{ y \mid y = x + t \left( x ^ { 2 } - x \right) , 0 \leq t \leq 1, 1 \leq x \leq 2 \right\}$ represents a figure where the maximum distance between two points is $d$ and the area is $S$,\\
A. $d = 3 , S < 1$\\
B. $d = 3 , S > 1$\\
C. $d = \sqrt { 10 } , S < 1$\\
D. $d = \sqrt { 10 } , S > 1$

Paper Questions

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