TIEC Mathematics: Topics and VPI

The Mathematics section of the Cattolica TIEC accounts for 12 questions out of 48 (25% of the test) and has a dual role: it contributes to the final score and determines the VPI (Verifica della Preparazione Iniziale). The official syllabus includes 14 topics, from algebraic manipulation to the basics of trigonometry, aligned with the final-year high-school programme. VPI thresholds: 7 or more correct out of 12 = VPI passed; 4, 5 or 6 = Math OFA assigned; fewer than 4 = test failed. For many candidates the first target is not the highest possible total, but reaching 7+ correct answers in math to avoid the OFA.

In this guide:

• Why TIEC math counts twice
• The official syllabus: 14 topics
• VPI thresholds and the Math OFA
• Topics by study priority
• Preparation strategy
• Mistakes to avoid
• FAQ

Why TIEC math counts twice

The TIEC Mathematics section has two distinct functions. On one hand it contributes to the total score (12 questions out of 48); on the other it determines the VPI and the possible assignment of the Math OFA. A low math score not only reduces your chances of a strong position in the ranking, but may also mean a mandatory remedial course for the whole first year — or, below a certain threshold, complete ineligibility.

Every TIEC section carries the same nominal weight: 12 questions, +1.05 per correct answer. But the Mathematics section stands out for two systemic features worth knowing before planning your preparation.

First: the minimum threshold is section-specific. To be eligible for the TIEC you need at least 25 total points, 6 correct answers in Logic, Reading Comprehension and English, and at least 4 correct answers in Mathematics. The other three sections have higher absolute minimum thresholds, but those are independent of each other. The Mathematics section is the only one that, below its floor, automatically makes you ineligible.

Second: the VPI is integrated in the test. Unlike other universities (and notably Bocconi, where initial-competence checks are separate from the selection test), at Cattolica the Verifica della Preparazione Iniziale for Mathematics is part of the TIEC itself. The number of correct answers in the math area automatically determines whether the VPI is passed, whether an OFA is assigned, or whether you are not eligible.

For an overall view of the TIEC structure see Cattolica TIEC: complete guide; here we focus on the math detail.

The official syllabus: 14 topics

The TIEC math programme is published on the admission pages of all seven Economics bachelor programmes at Cattolica Milan. It covers 14 topics ranging from set theory and algebraic manipulation to basic trigonometry, including first and second-degree equations and inequalities, analytic geometry, and exponentials and logarithms.

The Mathematics syllabus for the TIEC is published on the admission page for Economia e gestione aziendale di Milano (and is identical on the pages of the other six bachelor programmes). The 14 official topics are:

1. Elementary notions of set theory. Union, intersection, difference, complement, subsets, empty set, power set.
2. Numerical sets and their representation. Natural, integer, rational, real numbers. Number line representation, intervals, absolute value.
3. Inequalities and percentages. Manipulating inequalities, percentage problems, percentage variations.
4. Powers and their properties. Integer, rational and negative exponents. Operational properties.
5. Exponentials and logarithms and their properties. Definitions, logarithm properties, change of base.
6. Ordering of real numbers. Number comparison, approximate values, scientific notation.
7. Algebraic manipulation. Monomials and polynomials, operations, notable products, prime factorization, GCD and LCM.
8. Algebraic fractions. Simplification, operations, existence conditions.
9. First and second-degree equations, whole and fractional. Solving methods, discriminant analysis.
10. First and second-degree inequalities, whole and fractional. Sign study, number line representation.
11. Systems of first and second-degree equations and inequalities. Substitution method, comparison, reduction, graphical solutions.
12. Basic exponential and logarithmic equations and inequalities. Solving via properties and variable substitution.
13. Analytic geometry. Cartesian coordinates, distance between two points, midpoint of a segment, equations of line, circle and parabola, parallel and perpendicular lines, point-on-curve membership.
14. Basics of trigonometry. Definitions of trigonometric functions, notable values, basic formulas, elementary applications.

Important note. Some prep manuals and online materials omit point 14 (Basics of trigonometry), because trigonometry questions have historically been rare on the TIEC. The official admission pages explicitly list it as part of the syllabus: it is worth preparing on this topic as well, even at the basic level the bando indicates ("cenni"). On this point and the others the official TIEC bando page is the only source to follow.

Overall level

The required level is that of the final year of an Italian scientific high school or a strong classical high school. There are no university-level topics: no derivatives, no integrals, no calculus. The TIEC assesses mastery of the prerequisites for an economics-area university path, not advanced knowledge.

Candidates from a scientific high school with passing grades generally already have all the prerequisites. Those coming from a linguistic high school, a technical institute not specialised in math, or any programme with systemic gaps in algebra and analytic geometry should budget more preparation time, potentially with the support of targeted math tutoring.

VPI thresholds and the Math OFA

The TIEC Mathematics section has three operational thresholds. With 7 or more correct answers out of 12 the VPI is passed and no additional obligation applies. With 4, 5 or 6 correct answers a Math OFA is assigned: a mandatory remedial course with at least 70% attendance and a final test to be passed by the end of the first year. With fewer than 4 correct answers the test fails overall: you are not eligible, regardless of your total.

What the Math OFA means in practice

The OFA (Obbligo Formativo Aggiuntivo) for Mathematics is a specific remedial course for students who enter with a math preparation judged insufficient but above the minimum floor. The university organises these classes during the first year. To complete the OFA you need:

• At least 70% attendance at the remedial course.
• Passing the final OFA test.

The OFA must be cleared by the end of the first academic year. Those who miss attendance or fail the final test face concrete consequences: in the worst case, they may be required to repeat the first year. For a student planning a smooth academic path, the cost of an OFA is not only time (extra classes during the year) but also risk.

The strategic implication: for many candidates the "first target" of the TIEC is not so much the total score as reaching 7+ correct answers in Mathematics, avoiding the OFA.

What failing below threshold means

Below 4 correct answers in Mathematics, the TIEC is not passed. Even if the other totals are perfect, even if you have certification bonuses that push you past 30, eligibility requires meeting all three constraints simultaneously: total score >= 25, minimum floors in the other three sections, and at least 4 correct answers in Mathematics. Missing one of the three conditions means not eligible.

Topics by study priority

All 14 syllabus topics can be examined, but some groups recur in past sessions and have a more favourable prep-to-score ratio: algebra and equations (high priority), inequalities and systems (high priority), analytic geometry (medium priority), exponentials and logarithms (medium priority), basics of trigonometry (low priority but not to be ignored). The probability of seeing questions on each group varies year to year: the only reliable rule is that the entire syllabus is potentially in scope.

The syllabus is not prioritised in the bando: all 14 points are "in test." Analysis of the official preparation materials and of the practice sessions published by the university for the math simulations suggests a frequency distribution. This is a qualitative estimate, not a guarantee.

High priority: the algebra block

Algebraic manipulation, first and second-degree equations and inequalities (whole and fractional), systems of equations. This block is the "core" of TIEC math preparation. Solid mastery of this block alone covers most of the points realistically available to a student with standard preparation.

Investment: the block covers about 40% of the syllabus by extent and typically the majority of the questions. It is worth devoting the first phase of preparation (2-3 weeks) to consolidating these topics.

High priority: inequalities and systems

Closely linked to the algebra block but with their own question types. Fractional inequalities and mixed systems (equation + inequality) are often "discriminator" questions: candidates who know the theory but haven't practised enough tend to make method errors (for example, forgetting to study the sign of factors, getting the domain wrong).

Investment: 1 week of intensive practice on inequalities and systems after consolidating the algebra block.

Medium priority: analytic geometry

Line, parabola, circle, distances, midpoint, parallelism and perpendicularity. TIEC analytic-geometry questions tend to be standard: distance between two points, equation of the line through two points, intersection between a line and a parabola, tangency condition for the circle. Preparation requires automating the formulas and being able to set up problems in coordinates.

Investment: 1 week, focused on problem-setup exercises.

Medium priority: exponentials and logarithms

Operational properties, basic equations and inequalities. Typical TIEC questions ask to apply logarithm properties to solve equations via variable substitution (for example by setting log x = y), or to compare numbers written in different forms. No analysis of complex exponential or logarithmic functions is required: this is basic-level material.

Investment: 4-5 days of targeted practice.

Low priority but not zero: basics of trigonometry

Definitions of trigonometric functions, notable values (e.g., sin 30 deg, cos 60 deg, tan 45 deg), basic formulas, elementary applications to right triangles. The level is low (the bando says "cenni") but the programme lists it explicitly: occasional trigonometry questions are possible, and skipping the topic entirely is an unnecessary risk.

Investment: 2-3 days of review. There's no need to study deep trigonometry — just be solid on notable values and fundamental relations.

Support topics: set theory, powers, ordering

These are often "embedded" in questions on other areas (for example, a fractional inequality requires working with existence sets; a proportion requires applying power properties). They don't need long dedicated study, but they should be solid before tackling the rest of the syllabus.

Investment: quick review at the start of the path (1-2 days).

Preparation strategy

A preparation focused on the TIEC Mathematics section requires 5-8 weeks at 6-8 hours per week for candidates with a solid scientific high school base, and 8-12 weeks at 8-10 hours per week for those starting from weaker foundations. The sequential plan is: weeks 1-2 algebra, week 3 inequalities and systems, week 4 analytic geometry, week 5 exponentials and logarithms, week 6 trigonometry + review, weeks 7-8 timed simulations.

Weeks 1-2: the algebra block

Start with algebraic manipulation, notable products, factorizations. Then move to first and second-degree equations, fractional equations, algebraic fractions. Target: mastery of 90% of pure-algebra questions.

Materials: exercises from the official Cattolica preparation book for the math area (included in the university-provided resources), a standard final-year high-school math textbook, the math simulations available on the official platform.

Week 3: inequalities and systems

First and second-degree inequalities, fractional inequalities, mixed systems. Pay particular attention to sign study and solution representation on the number line. Timed exercises: after 5-6 days of theory-practice, try to solve 8-10 inequalities in 15-20 minutes to simulate the test pace.

Week 4: analytic geometry

Coordinates, distances, midpoint, line. Then circle, parabola. Exercises on intersections between curves and on tangency conditions. Target: be able to set up a standard analytic-geometry problem in 2-3 minutes.

Week 5: exponentials and logarithms

Logarithm properties, basic exponential and logarithmic equations, change of base. Exercises comparing numbers in different forms (logarithmic, exponential, decimal). Question type to automate: given a logarithmic expression, simplify and compute its value.

Week 6: trigonometry and review

Notable values of trigonometric functions, fundamental relations, applications to right triangles. Short but systematic study. In the second half of the week, transversal review: revisit topics from previous weeks where you struggled.

Weeks 7-8: timed simulations

Simulate the TIEC Mathematics section under real conditions: 12 questions in 15 minutes (proportional to the 60 total minutes for 48 questions, given that many candidates spend slightly more time on math). Alternate math-only simulations with full TIEC simulations.

After every simulation: detailed error analysis by category (concept error vs. calculation error vs. method error vs. distraction). Individual tutor sessions should focus on recurring errors.

On the Up to Ten simulation platform we track time per question and error type, allowing work with a Cattolica tutor on the areas where improvement is fastest. The TIEC preparation path integrates timed simulations, error analysis and targeted review.

Mistakes to avoid

The four most common mistakes in TIEC math preparation: ignoring trigonometry because "it never shows up anyway," focusing only on theory without timed practice, mishandling doubtful questions (the expected-value rule: answer if you can eliminate at least one option), underestimating the OFA risk by aiming only at the total.

Ignoring trigonometry. The bando explicitly lists "basics of trigonometry" among the programme topics. Even if trigonometry questions are historically rare, completely skipping the topic is an unnecessary risk: 2-3 days of study cover the programme at the required level.

Focusing only on theory. The TIEC averages 60 seconds per question across all areas, and the math section is dense with calculations. Knowing how to solve a problem isn't enough: you need to solve it quickly. The last 2-3 weeks of preparation should be primarily timed practice, not theoretical study.

Mishandling doubtful questions. The -0.21 penalty is calibrated to discourage completely random guesses but make answering worthwhile when you can eliminate at least one option. When facing a doubtful question, apply the rule: if you can rule out at least one option with reasonable confidence, answer; otherwise skip. There's no shame in skipping — there is shame in being wrong because you rushed.

Aiming only at the total. A candidate scoring 30 points overall but only 5 correct answers in Mathematics is eligible, but with an OFA to clear during the first year. A candidate scoring 28 points total with 7 correct answers in Mathematics is eligible without OFA. For students who already have a heavy academic plan, avoiding the OFA can be worth more than a slightly higher total.

FAQ

How many math questions are there in the TIEC? 12 questions out of 48, i.e. 25% of the total test.

Is trigonometry part of the programme? Yes. The bando explicitly lists "basics of trigonometry" among the 14 syllabus topics. The required level is basic (notable values, fundamental relations, applications to right triangles), but the topic should not be ignored.

How many correct math answers do I need to avoid the OFA? At least 7 out of 12. With 4, 5 or 6 correct answers the Math OFA is assigned; with fewer than 4 the test fails overall.

Can I be eligible for the TIEC without passing the VPI? Yes. With 4, 5 or 6 correct math answers (and meeting all other eligibility conditions) you are admitted, but with a Math OFA — a mandatory remedial course during the first year.

How long does preparation for the Math section alone take? For candidates with a solid scientific high school base: 5-8 weeks at 6-8 hours per week. For those starting from weaker foundations: 8-12 weeks at 8-10 hours per week. A complete TIEC preparation integrates the math area with the other three sections.

Does the TIEC include calculus (derivatives, integrals)? No. The syllabus stops at the final year of high school: no derivatives, no integrals, no calculus. Questions cover algebra, analytic geometry, equations and inequalities, logarithms/exponentials and basics of trigonometry.

Can I use a calculator? No. The TIEC does not allow calculators. Math questions are designed to be solvable by hand — they require quick calculations and mastery of algebraic properties.

Should I guess on doubtful questions? Statistically, guessing on a 4-option question has a slightly positive expected value (+0.105 points). But the expected value rises to +0.21 if you can eliminate just one option. Practical rule: answer if you're sure or if you can rule out at least one option; skip if you're completely in the dark.

Want to prepare for TIEC math with timed simulations and a Cattolica tutor? The Up to Ten TIEC path integrates an initial diagnostic, focus on weak areas, and full simulations on our simulation platform. Discover the TIEC path.