Mathematics · 24 questions in the exam

Functions

Mathematical notation, domain and range, composition and inverse functions, and the graphs of the elementary functions. Functions 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 7 lessons, each with the rule that solves it and a diagram.

Mathematical notation

Read the symbols precisely: ∈ “belongs to”, ⊂ “is a subset of”, ∀ “for every”, ∃ “there exists”, ⇒ “implies”, ⇔ “if and only if”. Σ adds a pattern and n! multiplies 1 to n.

RuleΣ k² for k = 1…4 is 1 + 4 + 9 + 16 = 30; 5! = 120

What a function is

A function gives every input exactly one output. f(x + 1) means writing x + 1 wherever x was. A graph is a function if no vertical line meets it twice.

Rulef(x) = x² − 3x ⇒ f(x + 1) = x² − x − 2

Domain

The domain is every x where the formula makes sense: denominators ≠ 0, even roots of numbers ≥ 0, logarithms of numbers > 0. Write each condition, then intersect them.

Rule√(x − 1)/(x − 3): x ≥ 1 and x ≠ 3

Composition of functions

(f ∘ g)(x) = f(g(x)): apply g first, then f. The order matters, and x must be in the domain of g with g(x) in the domain of f.

Rulef(x) = x + 3, g(x) = 2x: f(g(x)) = 2x + 3, g(f(x)) = 2x + 6

Inverse functions

Only a one-to-one function has an inverse. Swap x and y, then solve for y. The graph of f⁻¹ is the mirror image of f in the line y = x, and domain and range swap.

Rulef(x) = 2x − 1 ⇒ f⁻¹(x) = (x + 1)/2

Graphs of the elementary functions

Know the shapes of x, x², x³, √x, 1/x and |x| by heart: where each is defined, where it rises or falls, its symmetry and the points (0, 0) and (1, 1).

RuleEven: f(−x) = f(x) (x², |x|); odd: f(−x) = −f(x) (x, x³, 1/x)

Transforming graphs

f(x) + k moves the graph up by k; f(x − h) moves it right by h; −f(x) reflects it in the x-axis and f(−x) in the y-axis; |f(x)| folds the part below the axis upwards.

Ruley = (x − 2)² + 1 has its vertex at (2, 1)

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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