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Exam Review

Key Facts: TOLC-I Exam

50 questions

Core exam questions across 4 sections

CISIA TOLC-I Structure

110 minutes

Core exam duration (plus 15 min for English)

CISIA Regolamento TOLC

€35

Standard CISIA registration fee per attempt

CISIA Fee Regulations

+1 / -0.25

Scoring: +1 correct, -0.25 wrong, 0 blank

CISIA Scoring Rules

20 questions

Mathematics section questions (50 minutes)

CISIA TOLC-I Syllabus

Monthly

Allowed retake frequency (once per calendar month)

CISIA Regolamento TOLC

The TOLC-I is the official standardized computer-based entrance exam required by Italian universities for Engineering and technical-scientific degree programs. It features 50 core questions in 110 minutes spanning mathematics, logic, physical sciences, and verbal comprehension, scored at +1 for correct answers and -0.25 for incorrect answers.

Sample TOLC-I Practice Questions

Try these sample questions to review concepts for the TOLC-I exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 98+ question experience with AI tutoring.

1Simplify the radical expression: \frac{\sqrt{32} - \sqrt{8}}{\sqrt{2}}.
A.1
B.2
C.\sqrt{2}
D.4
Explanation: Simplify each radical: \sqrt{32} = \sqrt{16 \times 2} = 4\sqrt{2}, and \sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2}. Subtracting them yields 4\sqrt{2} - 2\sqrt{2} = 2\sqrt{2}. Dividing by \sqrt{2} gives \frac{2\sqrt{2}}{\sqrt{2}} = 2.
2Evaluate the arithmetic expression involving logarithms: \log_2(64) + \log_3(1/27) - \ln(e^2).
A.0
B.1
C.2
D.3
Explanation: Compute each logarithm individually using base definitions: \log_2(64) = 6 because 2^6 = 64; \log_3(1/27) = -3 because 3^{-3} = 1/27; \ln(e^2) = 2. Adding and subtracting gives 6 + (-3) - 2 = 1.
3What is the least common multiple (LCM) of the three integers 24, 36, and 40?
A.180
B.240
C.360
D.720
Explanation: Determine the prime factorisations: 24 = 2^3 \times 3, 36 = 2^2 \times 3^2, and 40 = 2^3 \times 5. The LCM takes the highest power of each prime appearing in the factorisations: 2^3 \times 3^2 \times 5 = 8 \times 9 \times 5 = 360.
4A production line output increases by 20% in the first quarter and then decreases by 25% in the second quarter. What is the net overall percentage change relative to the initial production?
A.5% decrease
B.10% decrease
C.15% decrease
D.No change (0%)
Explanation: Let the original production be P. An increase of 20% multiplies P by 1.20, giving 1.20P. A subsequent decrease of 25% multiplies that value by (1 - 0.25) = 0.75. The final output is 1.20 \times 0.75 \times P = 0.90P, which represents a net decrease of 10%.
5Solve the linear equation for x: \frac{2x - 3}{4} - \frac{x - 1}{3} = \frac{5}{12}.
A.x = 3
B.x = 4
C.x = 5
D.x = 6
Explanation: Clear the denominators by multiplying both sides by the least common multiple, 12: 3(2x - 3) - 4(x - 1) = 5. Expanding gives 6x - 9 - 4x + 4 = 5. Combining like terms yields 2x - 5 = 5, which leads to 2x = 10, hence x = 5.
6Find the sum of the solutions of the quadratic equation 3x^2 - 12x + 7 = 0 without solving for the roots directly.
A.-4
B.7/3
C.4
D.12
Explanation: By Vieta's formulas for any quadratic equation ax^2 + bx + c = 0, the sum of the roots x_1 + x_2 equals -b/a. Here, a = 3 and b = -12, so the sum is -(-12)/3 = 12/3 = 4.
7If the polynomial P(x) = x^3 - 4x^2 + kx - 6 is exactly divisible by (x - 2), what is the value of the constant k?
A.5
B.7
C.9
D.-7
Explanation: By the Polynomial Remainder Theorem, P(x) is divisible by (x - 2) if and only if P(2) = 0. Substituting x = 2 into P(x): 2^3 - 4(2^2) + k(2) - 6 = 8 - 16 + 2k - 6 = 2k - 14 = 0. Solving gives 2k = 14, so k = 7.
8What is the solution set of the rational inequality \frac{x - 3}{x + 2} \le 0?
A.(-2, 3]
B.[-2, 3]
C.(-\infty, -2) \cup [3, +\infty)
D.(-2, 3)
Explanation: The critical points occur where the numerator is zero (x = 3) and where the denominator is zero (x = -2). Testing intervals shows the fraction is negative between -2 and 3. Because the inequality is non-strict (\le 0), the numerator zero x = 3 is included, but x = -2 must be excluded because division by zero is undefined. Thus, the solution set is (-2, 3].
9Consider the linear system: \begin{cases} 2x + 3y = 13 \\ 5x - 2y = 4 \end{cases}. If (x, y) is the unique solution to this system, what is the value of x^2 + y^2?
A.10
B.13
C.17
D.25
Explanation: Multiply the first equation by 2 and the second by 3: 4x + 6y = 26 and 15x - 6y = 12. Adding them eliminates y: 19x = 38, so x = 2. Substitute x = 2 into 2(2) + 3y = 13: 4 + 3y = 13 \implies 3y = 9 \implies y = 3. Therefore, x^2 + y^2 = 2^2 + 3^2 = 4 + 9 = 13.
10Simplify the algebraic fraction \frac{x^2 - 9}{x^2 - 5x + 6} for all real values of x where it is defined.
A.\frac{x + 3}{x - 2}
B.\frac{x - 3}{x - 2}
C.\frac{x + 3}{x + 2}
D.\frac{x - 3}{x + 2}
Explanation: Factor the numerator as a difference of two squares: x^2 - 9 = (x - 3)(x + 3). Factor the denominator quadratic: x^2 - 5x + 6 = (x - 3)(x - 2). Canceling the common factor (x - 3) yields \frac{x + 3}{x - 2}.

About the TOLC-I Exam

The TOLC-I (Test OnLine CISIA Ingegneria) is the standardized university entrance and orientation examination administered by CISIA for admission into undergraduate degree programs (Laurea Triennale) in Engineering, Computer Science, and technical-scientific fields across Italian universities. The official examination comprises 50 multiple-choice questions delivered in 110 minutes across four dedicated sections: Mathematics (20 questions, 50 min), Logic (10 questions, 20 min), Science (10 questions covering Physics and Chemistry, 20 min), and Verbal Comprehension (10 questions, 20 min), followed by a 30-question English language placement section (15 min). This practice question bank is an independent educational resource created by OpenExamPrep to assist candidates in preparing for the examination syllabus. It is not endorsed, sponsored, or affiliated with CISIA.

Exam sponsor: CISIA — Consorzio Interuniversitario Sistemi Integrati per l'Accesso. The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

50 multiple-choice core questions in 110 minutes: 20 mathematics (50 min), 10 logic (20 min), 10 science (20 min), 10 verbal comprehension (20 min), followed by an English section (30 questions, 15 min). Core scoring: +1 correct, -0.25 wrong, 0 blank.

Time Limit

110 minutes (+ 15 minutes for English section)

Passing Score

Scored +1 for correct, -0.25 for wrong, 0 for blank. Ranking cutoffs and OFA remedial thresholds determined by individual engineering faculties.

Exam / Certification Fees

€35

Exam sponsor website

Fees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.

Our practice resources: topics covered

We aim to reflect publicly available exam outlines and topic information in our study resources. Coverage, format, and difficulty may differ from the actual exam, and we cannot guarantee that every detail is accurate or current. Confirm exam requirements, fees, and policies with the official exam sponsor.

40%

Mathematics

Numbers and operations, algebra, polynomial division and roots, linear and quadratic equations/inequalities, systems of equations, analytic geometry of lines and conics, functions and graphing, trigonometry, and probability/statistics (20 questions, 50 minutes)

20%

Logic

Propositional logic, truth tables, negations and implications, conditionality (necessary and sufficient conditions), deductive reasoning, categorical syllogisms, and spatial-analytical reasoning (10 questions, 20 minutes)

20%

Science

Classical mechanics (kinematics, dynamics, energy, momentum), thermodynamics, electromagnetism (electrostatics, DC circuits, magnetic fields), atomic structure, chemical bonding, stoichiometry, and solutions/acids-bases (10 questions, 20 minutes)

20%

Verbal Comprehension

Technical and scientific expository reading passages evaluating thesis identification, textual deduction, implicit meaning, and technical vocabulary analysis (10 questions, 20 minutes)

Preparing for the TOLC-I Exam

What You Need to Know

  • Passing score: Scored +1 for correct, -0.25 for wrong, 0 for blank. Ranking cutoffs and OFA remedial thresholds determined by individual engineering faculties.
  • Assessment: 50 multiple-choice core questions in 110 minutes: 20 mathematics (50 min), 10 logic (20 min), 10 science (20 min), 10 verbal comprehension (20 min), followed by an English section (30 questions, 15 min). Core scoring: +1 correct, -0.25 wrong, 0 blank.
  • Time limit: 110 minutes (+ 15 minutes for English section)
  • Exam / certification fees: €35 Official sources

Using Our Practice Resources

  • Work through all 98 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
  • Use our AI tutor for tough concepts

TOLC-I: Suggested Study Strategy

1Mathematics carries 40% of the core score (20 out of 50 questions) and is the primary section used to determine OFA remedial obligations; prioritize mastering polynomial algebra, conic sections, and trigonometric identities.
2Calculators are strictly forbidden during both TOLC@UNI and TOLC@CASA; practice doing mental math, fraction simplification, and scientific notation calculations by hand.
3Manage the strict sectional timing: you cannot bank time from one section to spend on another. In Mathematics you have 2.5 minutes per question, whereas in Logic and Science you have 2 minutes per question.
4Understand the negative marking penalty (-0.25 points per wrong answer): eliminate answers you know are wrong before choosing, and leave questions blank if you are completely guessing without eliminating any options.
5For verbal comprehension, read the passage questions first to identify key terms and thesis markers before reading the text thoroughly.

Frequently Asked Questions

What is the TOLC-I and who needs to take it?

The TOLC-I is CISIA's standardized admissions and placement examination for undergraduate engineering degrees (e.g., Mechanical, Civil, Aerospace, Chemical, Electrical, Computer Engineering) and select technical-scientific programs across Italian universities, including Politecnico di Milano, Politecnico di Torino, Sapienza, and dozens of other state and private universities.

How is the core TOLC-I structured and timed?

The core TOLC-I consists of 50 multiple-choice questions divided into four distinct timed sections: Mathematics (20 questions in 50 minutes), Logic (10 questions in 20 minutes), Science (10 questions in 20 minutes), and Verbal Comprehension (10 questions in 20 minutes), totaling 110 minutes. Once a section's time expires or the candidate moves forward, returning to previous sections is not permitted. An additional 30-question English section (15 minutes) is administered at the end.

How does scoring work on the TOLC-I?

In the core sections, each correct response earns +1 point, an unanswered question receives 0 points, and an incorrect response incurs a penalty of -0.25 points, with a maximum possible core score of 50 points. The English section is scored separately (+1 for correct, 0 for blank or wrong) and does not penalize incorrect responses.

What is an OFA (Obbligo Formativo Aggiuntivo)?

An OFA is an Additional Educational Obligation assigned to admitted students who achieve below a specific threshold (commonly in the Mathematics section, often set between 8/20 and 12/20 depending on the university). Students with an OFA must pass remedial tests or specific introductory courses during their first year.

Is the TOLC-I available in English?

Yes. CISIA administers both the Italian TOLC-I and the English TOLC-I, which share the exact same section distribution, syllabus, timing, and scoring system, designed for English-taught engineering programs.

Are these practice questions official CISIA materials?

No. This question bank is an independent prep resource developed by OpenExamPrep. It is not affiliated with, licensed by, or endorsed by CISIA. All questions are original practice items created to reflect the official syllabus topics.