csat-suneung 2015 Q30

csat-suneung · South-Korea · csat__math-A 4 marks Curve Sketching Lattice Points and Counting via Graph Geometry

In the coordinate plane, let $f ( n )$ denote the number of triangles OAB satisfying the following conditions for a natural number $n$. Find the value of $f ( 1 ) + f ( 2 ) + f ( 3 )$. (Here, O is the origin.) [4 points] (가) The coordinates of point A are $\left( - 2,3 ^ { n } \right)$. (나) If the coordinates of point B are $( a , b )$, then $a$ and $b$ are natural numbers and satisfy $b \leq \log _ { 2 } a$. (다) The area of triangle OAB is at most 50.

In the coordinate plane, let $f ( n )$ denote the number of triangles OAB satisfying the following conditions for a natural number $n$. Find the value of $f ( 1 ) + f ( 2 ) + f ( 3 )$. (Here, O is the origin.) [4 points]\\
(가) The coordinates of point A are $\left( - 2,3 ^ { n } \right)$.\\
(나) If the coordinates of point B are $( a , b )$, then $a$ and $b$ are natural numbers and satisfy $b \leq \log _ { 2 } a$.\\
(다) The area of triangle OAB is at most 50.

Paper Questions

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20 Q21 Q22 Q23 Q24 Q25 Q26 Q27 Q28 Q29 Q30