Plane geometry
Triangles, circles and quadrilaterals: angles, lengths and areas, and how to combine them in shaded figures. Plane geometry is tested in the Mathematics section of the Bocconi Test, which has 24 of the 50 questions (75 minutes in total, 2027/28 format). This guide covers it in 6 lessons, each with the rule that solves it and a diagram.
Triangles: angles, sides, area
The angles add up to 180°, and an exterior angle equals the two interior angles not next to it. Equal sides face equal angles. A third side lies strictly between the difference and the sum of the other two. The area is half the base times the perpendicular height.
Right triangles and Pythagoras
a² + b² = c², with c the hypotenuse. Learn the triples 3-4-5, 5-12-13 and 8-15-17 and the two special triangles: 45°-45°-90° has sides s, s, s√2 and 30°-60°-90° has sides x, x√3, 2x.
Similar triangles and Thales
Two equal angles make two triangles similar. Corresponding sides are in a fixed ratio k; perimeters scale by k and areas by k². A line parallel to a side cuts off a similar triangle, and parallel lines cut transversals into proportional pieces.
Circle and disc
C = 2πr and A = πr²; arcs and sectors are the fraction θ/360° of them. An inscribed angle is half the central angle on the same arc, so an angle in a semicircle is 90°. A tangent is perpendicular to the radius.
Square, rhombus, trapezoid
Parallelogram: base × height. Rhombus: half the product of its perpendicular diagonals. Trapezoid: average of the bases × height. The angles of a polygon with n sides add up to (n − 2) · 180°.
Shaded areas
Write the shaded region with standard shapes: outer minus inner, or a sum of pieces. A circle in a square has r = s/2; a square in a circle has its diagonal equal to the diameter. Overlap = sum of the areas − union.
What is the Bocconi Test format?
Online Bocconi Test for admission in academic year 2027/28, as published by Università Bocconi.
- Questions / time
- 50 / 75 minutes
- Distribution
- 24 mathematics · 11 reading · 6 numerical reasoning · 9 critical thinking
- Scoring
- +1 correct · 0 blank · −0.2 wrong
- Question languages
- English · Italian
- Three-option questions
- Some critical thinking questions have three options; a wrong answer there costs −0.33
- Minimum score
- Below 17 points the test is not considered for selection
- AI degree
- Mathematical and Computing Sciences for Artificial Intelligence also needs at least 11 of 24 points in mathematics
- Law test
- A separate test, 50 questions / 75 minutes: 5 mathematics · 11 reading · 6 numerical reasoning · 18 logic and critical thinking · 10 verbal reasoning; same scoring
Source: Università Bocconi, Online Bocconi Test page (checked October 7, 2026)
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