p1. Is there any natural number n such that n2+5n+1 is divisible by 49 ? Explain.
p2. It is known that the parabola y=ax2+bx+c passes through the points (−3,4) and (3,16), and does not
cut the x-axis. Find all possible abscissa values for the vertex point of the parabola.
p3. It is known that T.ABC is a regular triangular pyramid with side lengths of 2 cm. The points P,Q,R, and S are the centroids of triangles ABC, TAB, TBC and TCA, respectively . Determine the volume of the triangular pyramid P.QRS .
p4. At an event invited 13 special guests consisting of 8 people men and 5 women. Especially for all those special guests provided 13 seats in a special row. If it is not expected two women sitting next to each other, determine the number of sitting positions possible for all those special guests.
p5. A table of size n rows and n columns will be filled with numbers 1 or −1 so that the product of all the numbers in each row and the product of all the numbers in each column is −1. How many different ways to fill the table? geometryalgebracombinatoricsnumber theoryindonesia juniors