csat-suneung 2012 Q4

csat-suneung · South-Korea · csat__math-science 3 marks Inequalities Set Operations Using Inequality-Defined Sets

For two sets
$$A = \left\{ x \left\lvert \, \frac { ( x - 2 ) ^ { 2 } } { x - 4 } \leq 0 \right. \right\} , \quad B = \left\{ x \mid x ^ { 2 } - 8 x + a \leq 0 \right\}$$
When $A \cup B = \{ x \mid x \leq 5 \}$, what is the value of the constant $a$? [3 points]
(1) 7
(2) 10
(3) 12
(4) 15
(5) 16

For two sets

$$A = \left\{ x \left\lvert \, \frac { ( x - 2 ) ^ { 2 } } { x - 4 } \leq 0 \right. \right\} , \quad B = \left\{ x \mid x ^ { 2 } - 8 x + a \leq 0 \right\}$$

When $A \cup B = \{ x \mid x \leq 5 \}$, what is the value of the constant $a$? [3 points]\\
(1) 7\\
(2) 10\\
(3) 12\\
(4) 15\\
(5) 16

Paper Questions

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