taiwan-gsat 2024 Q4

taiwan-gsat · Other · gsat__math-b 5 marks Completing the square and sketching Optimization on a constrained domain via completing the square

Given a vector $\vec { v } = ( - 2,3 )$ and two points $A$ and $B$ on the coordinate plane, where the $x$-coordinate and $y$-coordinate of point $A$, and the $x$-coordinate and $y$-coordinate of point $B$ all lie in the interval $[ 0,1 ]$, what is the maximum value of $| \vec { v } + \overrightarrow { A B } |$?
(1) $\sqrt { 13 }$
(2) $\sqrt { 17 }$
(3) $3 \sqrt { 2 }$
(4) 5
(5) $\sqrt { 2 } + \sqrt { 13 }$

Given a vector $\vec { v } = ( - 2,3 )$ and two points $A$ and $B$ on the coordinate plane, where the $x$-coordinate and $y$-coordinate of point $A$, and the $x$-coordinate and $y$-coordinate of point $B$ all lie in the interval $[ 0,1 ]$, what is the maximum value of $| \vec { v } + \overrightarrow { A B } |$?\\
(1) $\sqrt { 13 }$\\
(2) $\sqrt { 17 }$\\
(3) $3 \sqrt { 2 }$\\
(4) 5\\
(5) $\sqrt { 2 } + \sqrt { 13 }$

Paper Questions

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20