6 problemas del concurso Fermat para entrenar. Nivel medio superior

In this video, I present 6 problems from the FERMAT COMPETITION. These problems were proposed in 2004 for the UPPER SECONDARY level of the competition. If you have any questions or suggestions, please write them in the comments section. I hope you enjoy them! Don't forget to leave a comment, a "like," and subscribe to the channel! It would help me a lot to grow my channel. You can access the test directly at this link! https://forms.gle/zW3mwvXhCycBjwip6 0:00 Intro and explanations 1:11 Problem 1 7:09 Problem 2 10:06 Problem 3 13:57 Problem 4 17:01 Problem 5 26:49 Problem 6 29:44 Thank you so much! #fermatcontest #mathematics #profecampi You can also find problems for the Kangaroo Math Test, the Math Olympiad, the history of mathematics, women mathematicians, mathematics in nature, puzzles, and more on this channel. Thank you for watching! If you'd like to support me: https://paypal.me/profecampi?locale.x... SUBSCRIBE!    / @profecampi   FACEBOOK:   / 427823765182467   INSTAGRAM: #PROFE_CAMPI Problem 1 In a unit circle, we have: θ_1=1, θ_2=2, θ_3=3,…, θ_n=n Where θ_i is the angle formed by the x-axis and the segment joining the points (0,0) and (x_i,y_i), then: x_1^2+x_2^2+x_3^2+⋯+x_n^2+y_1^2+y_2^2+y_3^2+⋯+y_n^2 Problem 2 Juan's math grades The scores were 9, x, y, z, and 3. The average of all the scores is 6, and the average of any two of the unknown scores is also 6. What is the product of the unknown scores that Juan obtained? Problem 3 If x = log₂(2) + log₂(4) + log₂(8) + ... How many addends are needed for x = 325? Problem 4 What is the result of the following sum: 1.01 + 2.02 + ... + 99.99? Problem 5 Let f(x) = x² + x⁴ + x² + ... + x³ + x² + 1 Which of the following relationships is true? Problem 6 If the graph of f(x) = ax³ + 2x + b intersects the x-axis at 1, then f(x) is: even? odd? decimal? cannot be determined