Analytic geometry
Points, lines, circles and parabolas described by equations: distances, slopes, intersections and tangents. Analytic 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.
Points, distance and midpoint
The distance between two points is Pythagoras on the differences of the coordinates; the midpoint averages the coordinates. From the midpoint and one end, the other end is B = 2M − A.
Slope and equation of a line
The slope is the change in y over the change in x. A line is y = mx + q, where q is the point on the y-axis, or ax + by + c = 0 with slope −a/b. Through a given point: y − y₀ = m(x − x₀).
Parallel and perpendicular lines
Parallel lines have equal slopes; perpendicular lines have slopes whose product is −1. The intersection of two lines solves their system. The distance from a point to ax + by + c = 0 is |ax₀ + by₀ + c| / √(a² + b²).
The equation of a circle
(x − h)² + (y − k)² = r². From x² + y² + ax + by + c = 0 the centre is (−a/2, −b/2) and r² = a²/4 + b²/4 − c, which must be positive. Put a point into the equation to see whether it lies inside, on or outside.
The parabola
y = ax² + bx + c has its vertex at x = −b/(2a) and is symmetric about that vertical line. It opens upwards if a > 0 and downwards if a < 0, and crosses the y-axis at c. The vertex form y = a(x − h)² + k shows the vertex (h, k) directly.
A line and a circle or parabola
Compare the distance d from the centre with the radius: d < r secant, d = r tangent, d > r external. For any curve, substitute the line: the sign of Δ gives two, one or no common points, and Δ = 0 is the tangency condition.
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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