Source: ITA – 2nd phase Mathematics exam. Files on the ITA past exams page. The 2nd phase Mathematics exam of ITA 2024 has 10 written questions. ITA does not publish official solutions for the 2nd phase; the solutions below are ours, and each answer was checked by a second route (substitution, another formula or a computer check). Answers Question Topic Answer 1 Arithmetic and geometric progressions $n = 4$ 2 Paths over the bridges (Euler path) 32 (16 in each direction) 3 Inequality with absolute values of logarithms $-4 < x < -\frac14$ or $\frac14 < x < 4$ 4 Positive definite matrix $-1 < b < 1$ 5 Polynomial symmetric about $x = 1$ $1 \pm \sqrt{3}$ and $1 \pm i\sqrt{6}$ 6 Longest segment inside a solid $\frac{4\sqrt{161}}{5}$ 7 Circle tangent to the $y$-axis $(x - 4 - \sqrt{6})^2 + (y - 3 + \sqrt{6})^2 = (4 + \sqrt{6})^2$ 8 Trapezoid with vertices on the parabola $\frac{483}{64}$ 9 Complex roots and area $4\sqrt{5}$ 10 Tangent of the half angle $\frac{1 + \sqrt{5}}{2}$, $\frac{\sqrt{5}}{5}$ and $\frac{5 - \sqrt{5}}{10}$ Question 1: How many terms of the geometric progression add up to −80? Statement Let $(a_n)$ be an arithmetic progression and $(b_n)$ a geometric progression. If the common difference of $(a_n)$ is $r$, $r \ne 0$, the ratio of $(b_n)$ is $q = 1/r$, $a_1 = b_1 = 4$ and
Source: FUVEST – 2nd phase test, 2nd day (questions M01 to M06), available in the FUVEST collection 2025. The 2nd phase of FUVEST 2025 had, on the 2nd day, specific discursive questions for career; The Mathematics test has six questions, M01 to M06. Each candidate solved only the subjects of your career (the six questions, or just the four or first three). The 2nd phase does not have a multiple choice answer sheet: FUVEST published a Answer Guide with the answers expected by the panel. The resolutions below are ours, and each The result was checked with this guide and through a second path.
Source: FUVEST – General Knowledge test, version V1 and official answer key from the 1st phase (17/11/2024), available in the FUVEST collection 2025. The 1st phase of FUVEST 2025 was a General Knowledge test with 90 questions from all disciplines. This post only covers mathematics questions. The numbering used here is that of Proof V1; in versions V2, V3 and V4 the same issues appear with other numbers. Template Question Subject Template 16 Percentage: slope of ramps C 17 Distance between points on the plane C 45 Arithmetic mean E 48 Graph reading and percentage D 52 Cosine function: graph transformation D 69 Modular function and parabolas B 70 Arithmetic progression A 75 Cone Trunk Volume A 76 Volume and lateral area of cylinders D 77 Relative position of circles E Question 16: Slope of an accessible ramp (percentage) Statement The construction of a ramp that is accessible to wheelchair users must follow the ABNT NBR 9050 standard. This document regulates the inclination that the ramp must depend on the maximum difference in level of each ramp segment, according to the following table: