Maths in the Bocconi test: topics and exercises

Today, 29 September 2026, the Early (Anticipata) session of the Bocconi test closes. If you are in Year 5 and let it pass — or you tried and want a better score — the road remains open with the Winter session: applications run from 25 November 2026 to 26 January 2027, that is about eight weeks from now, and the last date on which you can sit the test is 21 January 2027 (booking at least 48 hours ahead, limited places). They are two different dates — “last day for the test” and “last day for the application” — and it is worth keeping them apart from now on, because it is a mistake I often see made by people who organise their preparation at the last minute.

Eight weeks is a realistic time to fine-tune precisely the section where I see the most marks lost by those coming from a non-science high school (classical, languages, human sciences): maths. Not because logic is missing — that is usually there — but because the automatic reflexes are missing on topics that a science-oriented student reviews for years and that a classical or languages student saw only once, perhaps in Year 3. This post concentrates only on that section: for the general structure of the test (the four sections, the scoring, the weight of the school record) I have already written a complete guide in How to prepare for the Bocconi test, which is worth reading before this one if you do not yet know the test.

What the maths section covers

The 24 maths questions (out of 50 in all) cover algebra, functions (powers, exponentials, logarithms), plane and analytic geometry, trigonometry, sets, probability, descriptive statistics and combinatorics — the syllabus of a well-run science-oriented high school up to the end of Year 4, with no derivatives or integrals. Those from other courses have often seen all this, but spread differently over time or with fewer weekly hours devoted to it: the problem is not “I don’t know it”, it is “I don’t remember it quickly enough”.

And speed is precisely the point: 75 minutes in total with no clock dedicated to the single section, shared with reading comprehension, numerical reasoning and critical thinking. On 24 maths questions, a realistic pace is under two minutes per question — which is not enough to redo a calculation from scratch if the first attempt goes wrong.

How to reason about a timed question

Three techniques that I use with the people I prepare, in order of how much time they save:

1. Estimate before calculating. Many multiple-choice questions have options spaced far enough apart that you can rule out half the answers just by looking at the order of magnitude, even before setting up the equation. If the result must be a number between 0 and 1 (a probability, a percentage) and two options out of four are greater than 1, they are already out.
2. Substitution instead of solving. On equations, systems and inequalities with the options already written, it is often worth trying to substitute the proposed values into the original equation rather than solving it from scratch: it is faster when the equation is complicated and the options are simple numbers.
3. Systematic elimination. If you do not reach the exact answer in good time, eliminate the clearly wrong options (inverted sign, wrong order of magnitude, violation of a domain) before deciding whether to answer or leave it blank.

The penalty does not change from topic to topic

What I already explained in the general guide holds: correct answer +1, omitted 0, wrong −0.2 (the exception at −0.33 concerns only critical thinking, which has three options instead of four or five). In maths guess only if you have ruled out at least two options out of four with certainty: below that threshold the expected value of a random attempt is too close to zero to be worth the risk, especially on a question that perhaps hides a sign error that is easy to spot calmly but that, at random, is worth a coin toss.

Eight worked questions

I wrote these eight questions in the style of the test: the same multiple-choice wording, the same range of topics as the real section. Try them against the clock — under two minutes each — before reading the solution.

1. Percentages and compound changes. A price rises by 20% and then falls by 20%. Compared with the initial price, the final price is:

A) equal to the initial price · B) up 4% · C) down 4% · D) down 20%

Solution: percentage changes multiply, they do not add. Starting from a price $P$: after the rise it is $1.20P$; after the 20% fall on that new value it is $1.20P\times 0.80=0.96P$. The final price is 96% of the initial one, that is down 4%. Answer C. The typical mistake is to think that $+20\%$ and $-20\%$ cancel out: it happens only if the two percentages are applied to the same starting value, not in sequence.

2. Quadratic inequalities. Solve: $x^2-5x+6<0$.

A) $x<2$ or $x>3$ · B) $2<x<3$ · C) $x<-2$ or $x>-3$ · D) no solution

Solution: the trinomial factorises as $(x-2)(x-3)$, with roots $x=2$ and $x=3$. The parabola $y=x^2-5x+6$ opens upwards, so it is negative between the roots. Answer B, $2<x<3$. Quick check: for $x=2.5$, $(2.5{)}^2-5(2.5)+6=6.25-12.5+6=-0.25<0$, consistent.

3. Linear systems. What is the solution of the system $\{\begin{array}{l}2x+y=7\\ x-y=2\end{array}$?

A) $(3,1)$ · B) $(1,3)$ · C) $(2,3)$ · D) $(4,-1)$

Solution: adding the two equations side by side, the $y$ term cancels: $2x+y+x-y=7+2\Rightarrow 3x=9\Rightarrow x=3$. Substituting into the second equation: $3-y=2\Rightarrow y=1$. Answer A, $(3,1)$. Check in both: $2(3)+1=7$ ✓, $3-1=2$ ✓.

4. Functions and domain. What is the domain of $f(x)=\frac{\sqrt{x-3}}{x-5}$?

A) $x\ge 3$ · B) $x\ge 3$ and $x\ne 5$ · C) $x>3$ · D) $x\ne 5$

Solution: two independent conditions to put into a system. The root requires $x-3\ge 0$, so $x\ge 3$. The denominator cannot vanish: $x\ne 5$. The two conditions together give $x\ge 3$ and $x\ne 5$. Answer B. The typical mistake is to stop at the first condition and forget the denominator, or vice versa.

5. Exponentials. Solve the equation $2^{x+1}=32$.

A) $3$ · B) $4$ · C) $5$ · D) $16$

Solution: I write $32$ as a power of 2: $32=2^5$. The equation becomes $2^{x+1}=2^5$, and with equal bases the exponents must coincide: $x+1=5\Rightarrow x=4$. Answer B. Check: $2^{4+1}=2^5=32$ ✓.

6. Probability. A card is drawn at random from a 40-card Italian (Neapolitan) deck. What is the probability that it is a card of the coins suit (denari) or an ace?

A) $\frac{14}{40}$ · B) $\frac{13}{40}$ · C) $\frac{11}{40}$ · D) $\frac{10}{40}$

Solution: I use the union formula, $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. The cards of the coins suit are 10 out of 40, the aces are 4 out of 40 (one per suit), and the ace of coins is counted in both groups, so it must be subtracted once: $\frac{10}{40}+\frac{4}{40}-\frac{1}{40}=\frac{13}{40}$. Answer B. The typical mistake is to add $10+4=14$ without removing the doubly counted case.

7. Combinatorics. In a group of 6 students you have to choose a representative and a deputy (distinct roles, nobody can hold both). In how many ways can it be done?

A) $15$ · B) $30$ · C) $36$ · D) $720$

Solution: the roles are distinct, so order matters — it is an arrangement, not a combination. For the representative there are 6 possible choices; for the deputy, once the first is chosen, 5 choices remain: $6\times 5=30$. Answer B. If the two roles were identical (two equal representatives) the answer would be $\left(\genfrac{}{}{0ex}{}{6}{2}\right)=15$, option A: it is the trap designed for those who do not distinguish arrangements from combinations.

8. Analytic geometry. What is the equation of the line through the points $A(1,2)$ and $B(3,8)$?

A) $y=3x-1$ · B) $y=2x+1$ · C) $y=3x+2$ · D) $y=x+3$

Solution: the slope is $m=\frac{8-2}{3-1}=\frac{6}{2}=3$. I use the point $A(1,2)$ in the form $y-y_0=m(x-x_0)$: $y-2=3(x-1)\Rightarrow y=3x-1$. Answer A. Check with $B$: $3(3)-1=8$ ✓.

Typical mistakes I see (besides those in the individual exercises)

• Stopping at the first domain constraint (root or denominator) and forgetting the second, as in question 4.
• Confusing arrangements and combinations: if order or role matters, you multiply; if not, you divide by the ways of reordering — it is the difference between question 7 and its variant with identical roles.
• Adding percentages instead of multiplying the factors in compound changes (question 1): $+20\%$ then $-20\%$ do not cancel.
• Applying the properties of logarithms wrongly, in particular $\log (a+b)\ne \log a+\log b$ — it does not appear in these eight questions but it is the most frequent mistake I see on exponentials and logarithms together.
• Not checking the result in the starting equation when time allows: the final substitution (as in questions 3, 5 and 8) costs a few seconds and catches most calculation errors.

An eight-week plan up to the application

From now to 25 November, when the window for the Winter session opens, you have about eight weeks. A realistic plan for maths alone, to be run alongside the rest (reading comprehension, numerical reasoning, critical thinking):

• Weeks 1-2: diagnosis with the free Bocconi test practice paper and mapping of weak topics. Targeted review of basic algebra — equations, inequalities, systems — because everything else rests on these reflexes.
• Weeks 3-4: functions, exponentials and logarithms, analytic geometry. These are the topics where those from a non-science high school have seen fewer hours of practice.
• Weeks 5-6: probability and combinatorics, basic trigonometry, descriptive statistics. Batteries of timed questions, not just theory. For multi-step probability, the interactive probability tree shows where you multiply and where you add.
• Weeks 7-8: complete timed practice papers of all four sections together (not just maths in isolation), with analysis of the mistakes — understanding why you went wrong, not just how many mistakes.

If you are also considering the TOLC-E (the Italian economics admission test) as an alternative or parallel route, I have written a comparison in Bocconi test or TOLC-E: which to prepare; if instead the TOLC-E is already your main route, the specific preparation is in How to prepare for the TOLC-E.

How we work on this section

For the review of maths in general, including what is needed for the other admission tests, I work on the same principles as in this post: reflexes before theory, a final check of the result, time management per section. I always start from a diagnostic practice paper — the same Bocconi test practice paper linked above — to build a plan on the topics that are really weak, not on those that seem logical to review.

If you want to work out where to start with a view to the Winter session, the half-hour free introductory call is the quickest way to do it: we look together at where you are losing marks.