Source: ITA – 1st phase exam and official answer key. Files on the ITA past exams page. The 1st phase of ITA 2026 had 48 multiple-choice questions: 12 in Mathematics, 12 in Physics, 12 in Chemistry and 12 in English. This post covers the mathematics questions, numbered 1 to 12 as in the exam. Exam conventions. $i^2 = -1$; $\bar{z}$ is the conjugate of $z$; $]a, b[$ is the open interval $a < x < b$.
Source: ITA – 2nd phase Mathematics exam. Files on the ITA past exams page. The 2nd phase Mathematics exam of ITA 2023 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 Homogeneous linear system $b = 2a$; $\{(-15t, -16t, 17t) : t \in \mathbb{R}\}$ 2 Matrices: when $M$ is invertible $\alpha \notin \{0, 2, 3 - \sqrt{15}, 3 + \sqrt{15}\}$ 3 Logarithmic inequality with a variable base $]-2, 0[$ 4 Polynomial division and roots $q = x^6 + x^5 - x - 1$, $r = 0$; roots $\operatorname{cis}\frac{\pi}{5}, \operatorname{cis}\frac{3\pi}{5}, \operatorname{cis}\frac{7\pi}{5}, \operatorname{cis}\frac{9\pi}{5}$ 5 Trigonometry: sum to product $\sin(\alpha - \beta) = \frac{2AB}{A^2 + B^2}$ 6 Radius of the incircle $\frac{6\sqrt{7} - 3\sqrt{3}}{10}$ 7 Ellipse: a 60° angle between the focal radii $\left(\pm\frac{4\sqrt{2}}{3}, \pm\frac{1}{3}\right)$ 8 Equilateral cylinder with a sphere $400\pi$ cm² and $\frac{4000\pi}{3}$ cm³ 9 Law of sines: sides of the triangle $6 + \sqrt{11}$ and $6 - \sqrt{11}$ 10 Counting: pairs of diagonals of a decagon 175 Question 1: When the homogeneous system has a non-trivial solution Statement Let $a$ and $b$ be positive real numbers. Consider the linear system in the unknowns $x$, $y$ and $z$:
Source: ITA – 2nd phase Mathematics exam. Files on the ITA past exams page. The 2nd phase Mathematics exam of ITA 2022 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 numerical check). The notation conventions are the same as in the 1st phase: $i^2 = -1$, $m(\overline{AB})$ is the length of segment $\overline{AB}$ and $A\hat{O}B$ is the angle with vertex $O$.