MathDB

day 1

Part of 2017 Indonesia Juniors

Problems(1)

Indonesia Juniors 2017 day 1 OSN SMP

Source:

11/7/2021
p1. Find all real numbers xx that satisfy the inequality x2−3x2−1+x2+5x2+3≥x2−5x2−3+x2+3x2+1\frac{x^2-3}{x^2-1}+ \frac{x^2 + 5}{x^2 + 3} \ge \frac{x^2-5}{x^2-3}+\frac{x^2 + 3}{x^2 + 1}
p2. It is known that mm is a four-digit natural number with the same units and thousands digits. If mm is a square of an integer, find all possible numbers mm.
p3. In the following figure, △ABP\vartriangle ABP is an isosceles triangle, with AB=BPAB = BP and point CC on BPBP. Calculate the volume of the object obtained by rotating △ABC \vartriangle ABC around the line APAP https://cdn.artofproblemsolving.com/attachments/c/a/65157e2d49d0d4f0f087f3732c75d96a49036d.png
p4. A class farewell event is attended by 1010 male students and 12 12 female students. Homeroom teacher from the class provides six prizes to randomly selected students. Gifts that provided are one school bag, two novels, and three calculators. If the total students The number of male students who received prizes was equal to the total number of female students who received prizes. How many possible arrangements are there of the student who gets the prize?
p5. It is known that S={1945,1946,1947,...,2016,2017}S =\{1945, 1946, 1947, ..., 2016, 2017\}. If A={a,b,c,d,e}A = \{a, b, c, d, e\} a subset of SS where a+b+c+d+ea + b + c + d + e is divisible by 55, find the number of possible AA's.
algebrageometrycombinatoricsnumber theoryindonesia juniors