Algebra
Expressions with powers, roots and polynomials; equations, inequalities and systems of the first and second degree, including absolute values. Algebra 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 18 lessons, each with the rule that solves it and a diagram.
Powers and exponent rules
Same base: multiply → add exponents, divide → subtract, power of a power → multiply. a⁰ = 1 and a⁻ⁿ = 1/aⁿ. To compare big powers, rewrite them with the same base or the same exponent.
Roots and radicals
A root is a fractional power: the n-th root of a is a^(1/n). Simplify by pulling out perfect squares (√50 = 5√2), add only like roots, and clear a root from a denominator with the conjugate.
Polynomials and identities
Multiply polynomials term by term and collect like terms. The identities (a ± b)², (a + b)(a − b) and (a ± b)³ save the work, and read backwards they factor.
Factoring
Take out the common factor first, then look for an identity, a trinomial x² + bx + c = (x + p)(x + q) with pq = c and p + q = b, or grouping. P(a) = 0 means (x − a) is a factor.
Rational expressions
Factor top and bottom, then cancel common factors, never single terms. Add over a common denominator. The values that make a denominator zero stay excluded after simplifying.
First-degree equations
Undo the operations in reverse order, doing the same to both sides. ax = b has one solution if a ≠ 0, none if a = 0 and b ≠ 0, and every x is a solution if a = b = 0.
Second-degree equations
Solve ax² + bx + c = 0 by factoring, completing the square or the formula. The discriminant Δ = b² − 4ac tells you how many real roots there are before you solve.
Roots and coefficients
For ax² + bx + c = 0 the roots satisfy x₁ + x₂ = −b/a and x₁x₂ = c/a. Use this to build an equation from its roots, to read the signs of the roots and in parameter questions.
Equations that reduce to quadratics
In fractional equations, note where denominators vanish, clear them, then check. Substitute t = x² (or t = |x|, t = 1/x) to turn higher powers into a quadratic. In root equations, square both sides and test every answer.
Rearranging formulas
To make one quantity the subject, undo what surrounds it step by step. If it appears twice, gather its terms on one side and factor it out; only divide by expressions you know are not zero.
Relations between quantities
Chain relations by substitution to write one quantity in terms of another. In y = kxⁿ, multiplying x by c multiplies y by cⁿ: direct proportion has n = 1, inverse proportion n = −1.
First-degree inequalities
Solve like an equation, but flip the sign when you multiply or divide by a negative. The answer is an interval; for a system of inequalities, intersect the intervals.
Second-degree inequalities
Find the roots and picture the parabola. With a > 0 the expression is negative between the roots and positive outside; if Δ < 0 it keeps the sign of a everywhere.
Product and quotient inequalities
Move everything to one side, factor, and mark every zero of the top and bottom on a line. Read the sign of each factor in each interval; the zeros of the bottom are always excluded.
Linear systems
Eliminate one unknown by adding multiples of the equations, or substitute one into the other. Two lines meet once (one solution), never (parallel, no solution) or everywhere (the same line).
Second-degree systems
Solve the linear equation for one unknown and substitute into the other: you get a quadratic whose Δ counts the solutions. Given x + y and xy, the numbers are the roots of t² − (x + y)t + xy = 0.
Absolute value equations
|x − a| is the distance from x to a. |A| = k has two solutions if k > 0, one if k = 0 and none if k < 0. For |A| = B, require B ≥ 0 or split into cases.
Absolute value inequalities
|A| < k means −k < A < k, the points closer than k; |A| > k means A < −k or A > k, the points farther than k. With a variable on the right, split into cases.
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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