TOLC-I · section 1

TOLC-I Mathematics section: topics, timing and mistakes

It is the longest section of the TOLC-I: 20 questions in 50 minutes, twice the questions and more than twice the time of any other scored section. Much of the ranking is decided here.

At a glance

Questions: 20
Minutes: 50
Average time per question: about 2.5 minutes
Scoring: +1 correct, 0 blank, −0.25 wrong

Where this section sits in the TOLC-I
Section	Questions	Minutes
Mathematics	20	50
Logic	10	20
Sciences	10	20
Reading comprehension	10	20
English	30	15

Each section has its own time limit: finishing early does not give minutes to the others, and you cannot go back to a closed section. Universities use the score with their own thresholds, so read the call of the degree you are applying to.

Structure and scoring from the official CISIA page: TOLC-I structure and syllabus (cisiaonline.it). Compared with the official page on 19 October 2026.

What this section measures

Mathematics measures how well you master school algebra, geometry and functions, with short questions and no long calculations. Calculus is not needed: derivatives and integrals do not appear in the CISIA list.

The topic changes on every question, so the difficulty is not one concept but the speed of switching from a fractional equation to a solid-geometry problem, at two and a half minutes each on average.

Topics in the official syllabus

Arithmetic and algebra: number systems, powers and roots, logarithms, polynomials, first- and second-degree equations and inequalities, systems, radical and fractional equations.
Geometry: segments, angles, lines and planes, plane figures (perimeters and areas), solid figures (surface areas and volumes).
Analytic geometry and functions: Cartesian coordinates, functions, equations of conics, elementary functions and graphs, logarithmic and exponential equations and inequalities.
Trigonometry: graphs and properties of sine, cosine and tangent, main identities, trigonometric equations and inequalities, relations in triangles.
Statistics: permutations, combinations, mean, variance, frequency, reading histograms.

Summarised from the CISIA page above; the 2026 syllabus PDF has the exact wording.

Where points are lost

Forgetting the existence conditions

In a fractional equation the algebraic result can be a value that zeroes a denominator. Writing the existence conditions first costs ten seconds and saves the question; it is exactly the step the solved question below puts first.
Stopping halfway

The wrong options are built on intermediate steps: the value of an expression before the last operation, the sign flipped in an inequality. Reread the question before marking: does it ask for the value of x, the number of solutions or the solution set?

How to prepare

Start from the CISIA syllabus and mark the topics where you slip: in our bank the exercises are split by topic, so you can train one weak point at a time.
Practise against the clock: the target is one question every two and a half minutes, leaving time to review doubts. A question that stalls you for more than a minute and a half is marked and revisited at the end.
With −0.25 for a wrong answer, answer only when you can rule out at least two options; otherwise leave it blank.
Repeat the full simulation days apart: questions are drawn from the bank, and the trend over time tells you whether you are really improving.

Our bank holds 310 questions for this section.

A solved question from our bank

A fractional equation of medium difficulty: watch the order of the steps, because it is the one you will use in the exam room.

Topic: Algebra: equazioni e disequazioni · difficulty 2/3

Qual è la soluzione dell'equazione $\frac{2}{x - 1} = \frac{3}{x + 2} ?$

A $x = 7$ correct
B $x = - 7$
C $x = 1$
D $x = - \frac{1}{5}$
E Nessuna soluzione (l'equazione è impossibile)

Guided solution

Passo 1 — Condizioni di esistenza. I denominatori non possono annullarsi: $x \neq = 1$ e $x \neq = - 2$ .

Passo 2 — Elimino i denominatori con il prodotto in croce e risolvo.

$\frac{2}{x - 1} = \frac{3}{x + 2} ⟹ 2 (x + 2) = 3 (x - 1) ⟹ 2 x + 4 = 3 x - 3 ⟹ x = 7$

Passo 3 — Controllo le C.E. $x = 7$ è diverso sia da $1$ che da $- 2$ : è accettabile.

La soluzione è $x = 7$ . Chi sceglie un valore diverso ha probabilmente sbagliato un segno spostando i termini durante il prodotto in croce, ad esempio scrivendo $2 x + 4 = 3 x + 3$ invece di $2 x + 4 = 3 x - 3$ .

The question comes from our own TOLC-I practice bank, written on the CISIA syllabus: it is not a real exam question. The questions in our bank are in Italian, also on this English page.

The other TOLC-I sections

Five pages, one per section: each section has its own tactics.

FAQ

Questions about this section

How much time do I have per Mathematics question?

On average two and a half minutes: 50 minutes for 20 questions. Some questions close in half a minute and free time for the long ones.

Are there derivatives and integrals in TOLC-I Mathematics?

They are not in the topic list published by CISIA: the syllabus covers algebra, geometry, elementary functions, trigonometry and basic statistics.

Should I guess?

Each wrong answer costs 0.25 points and a blank is worth 0. With five options a purely random answer has an expected value of zero: answer once you have ruled out a couple of options.

Keep reading

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TOLC-I Mathematics section: topics, timing and mistakes

Topics in the official syllabus

Forgetting the existence conditions

Stopping halfway

Want to see where you lose points?