p1. Known points A(−1.2), B(0,2), C(3,0), and D(3,−1) as seen in the following picture.
Determine the measure of the angle AOD .
https://cdn.artofproblemsolving.com/attachments/f/2/ca857aaf54c803db34d8d52505ef9a80e7130f.png
p2. Determine all prime numbers p>2 until p divides 712−372−51.
p3. A ball if dropped perpendicular to the ground from a height then it will bounce back perpendicular along the high third again, down back upright and bouncing back a third of its height, and next. If the distance traveled by the ball when it touches the ground the fourth time is equal to 106 meters. From what height is the ball was dropped?
p4. The beam ABCD.EFGH is obtained by pasting two unit cubes ABCD.PQRS and PQRS.EFGH. The point K is the midpoint of the edge AB, while the point L is the midpoint of the edge SH. What is the length of the line segment KL?
p5. How many integer numbers are no greater than 2004, with remainder 1 when divided by 2, with remainder 2 when divided by 3, with remainder 3 when divided by 4, and with remainder 4 when divided by 5? algebrageometrycombinatoricsnumber theoryindonesia juniors