CEnT-S MATHEMATICS TOPICS · EXAM BLUEPRINT

What to Focus & How to Prepare?

Complete syllabus breakdown, question-bank frequency analysis, difficulty rankings, solved sample problems and a 10-week study plan. Master the 15 mathematics questions in 30 minutes.

15 Mathematics Questions (15 Pts)30 Minutes Section TimerTopic Difficulty Rankings10-Week Study Schedule
Take Free Diagnostic TestView all CEnT-S topics
15 MCQsMathematics Questions
7 Core TopicsIn the CISIA Syllabus
2 minAverage Time per Question
−0.25Penalty per Wrong Answer

The Mathematics section is the first and largest block of CEnT-S: 15 questions in 30 minutes — exactly 2 minutes per question. It is benchmarked against Italian upper-secondary (liceo) mathematics: algebra, function graphs, geometry and basic probability.

Together with Reasoning on Texts and Data, Mathematics delivers 30 of the 65 questions (46% of the score). Every point here is worth the same as a point in Physics — but there are three times as many of them.

Question distribution analysis

CEnT-S Mathematics Topics: Frequency

Which topics demand your deepest attention? Below is the topic breakdown from our CEnT-S question data:

TopicExam 1Exam 2Exam 3Total
Algebra & Equations52310
Probability, Combinatorics & Statistics4228
Functions & Graphs1337
Geometry & Coordinates1337
Numbers & Arithmetic2125
Sets & Logic1214
Exponentials & Logarithms1214

*Question counts per topic in 3 CEnT-S past exams from our question bank; each exam has the full 15 Mathematics questions. Exams are numbered, not dated. These figures are derived from the past-exam question samples that have reached us; the samples may be incomplete or contain errors, and the topic mix can change from one exam session to the next. Treat them as a guide to priorities, not a prediction of your exam.

Key Takeaways

  • Algebra leads the past exams (10 of 45 questions) — equivalent forms, factorisation and 2nd-degree inequalities.
  • Probability & counting is second (8 of 45), mostly real-life counting.
  • Functions & graphs follow closely (7 of 45): composition, domain and graph transformations.
  • Exponentials & logarithms appear in every exam (1–2 questions): one-step equations and inequalities.
  • Trigonometry is practically absent — do not over-invest in it.
Difficulty analysis

Topic Difficulty & Recommended Study Allocation

Not all topics require the same time investment. Some need extensive problem-solving practice, others rely on precise conceptual recall:

Hard
Combinatorics & Probability 2 weeks
Hard
Functions & Graphs 1.5–2 weeks
Medium
Algebra 1.5–2 weeks
Medium
Exponentials & Logarithms 1 week
Medium
Geometry & Coordinates 1 week
Easy
Basic Statistics 3–4 days
Easy
Numbers 3–4 days

Not Sure Where to Begin Your Preparation?

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Official syllabus breakdown

CEnT-S Mathematics Topics: How Each Is Tested

A topic-by-topic look at the Mathematics section of the official CISIA CEnT-S syllabus:

01

Numbers Easy

  • Operations and ordering of integers, rationals and reals.
  • Division with remainder, factorisation, divisors and multiples (GCD/LCM).
  • Powers, roots, percentages and evaluation of numerical expressions.

How it appears on CEnT-S: Fast mental arithmetic. Expect order-of-magnitude comparisons, percentage changes and ‘which number is largest’ items without a calculator.

02

Algebra Medium

  • Literal expressions, identities, equalities and inequalities.
  • Polynomial factorisation and roots; 1st and 2nd degree equations and inequalities.
  • Linear systems of equations.

How it appears on CEnT-S: Very often asks ‘which equality is NOT equivalent’. Traps: dividing by a variable that may be zero, and flipping the inequality sign.

03

Geometry Medium

  • Plane and solid figures: perimeters, areas, volumes.
  • Similarity and proportions between figures.
  • Cartesian plane: distance, midpoint, equation of a line and of a circle.

How it appears on CEnT-S: Short coordinate-geometry questions and scaling: if lengths double, areas ×4 and volumes ×8.

04

Functions Hard

  • Concept of function, composition and invertibility.
  • Graph transformations: shifts, reflections, stretches.
  • Elementary functions: power, polynomial, 1/(ax+b), absolute value.

How it appears on CEnT-S: Graph-matching questions and compositions f(f(x)). Domain restrictions are the favourite distractor source.

05

Exponentials & Logarithms Medium

  • Definitions and algebraic properties of powers and logarithms.
  • Elementary exponential and logarithmic equations.
  • Elementary exponential and logarithmic inequalities.

How it appears on CEnT-S: Clean one-step equations. Remember the argument of a log must be positive and that a base < 1 reverses inequalities.

06

Combinatorics & Probability Hard

  • Counting finite sets; dispositions, permutations, combinations.
  • Probability of an event; union and intersection of events.
  • Complementary events and independent events.

How it appears on CEnT-S: Real-life counting (outfits, codes, menus). Most errors come from double counting or forgetting the ‘none’ case.

07

Basic Statistics Easy

  • Data representation: tables, histograms, pie charts.
  • Absolute and relative frequency.
  • Mean, median and mode.

How it appears on CEnT-S: Reading a chart and computing a mean or median; weighted averages are a common twist.

Official CISIA Syllabus

The full, official CEnT-S syllabus and test structure are published by CISIA:

cisiaonline.it — CEnT-S structure and syllabus
Solved exam problems

CEnT-S Mathematics Sample Questions & Elimination Tactics

See how CEnT-S mathematics questions are built and how disciplined elimination avoids the −0.25 penalty:

01Algebra & Equivalent FormsQuestion 1
Let xx and yy be real numbers, x≠0x \neq 0, and yx=y2−2y\dfrac{y}{x} = y^2 - 2y. All the following equalities are true except one. Which one?
Pick an answer to see the explanation
02CombinatoricsQuestion 2
A T-shirt is available in 6 colours. It may have no print, one of 3 phrases, one of 4 pictures, or both one phrase and one picture. How many different T-shirts are possible?
Pick an answer to see the explanation
03Algebra · Quick InsightQuestion 3
Consider xy=zxy = z and x2−2xy+y2=0x^2 - 2xy + y^2 = 0. If (x,−1,y)(x, -1, y) is a solution, what is x−yx - y?
Pick an answer to see the explanation
Candidate trap analysis

5 Most Common Mistakes in CEnT-S Mathematics

Recurring conceptual and tactical errors that cost students crucial points:

01

Dividing by a variable

Cancelling xx or yy without checking it can be zero loses solutions — and CISIA builds the wrong option from exactly that.

02

Inequality sign flips

Multiplying by a negative number, or using a logarithm/exponential with base < 1, reverses the inequality.

03

Double counting

In combinatorics, decide first whether order matters and whether cases overlap; add disjoint cases, multiply independent choices.

04

Forgetting the domain

Square roots, logarithms and fractions restrict the domain; options outside it are planted on purpose.

05

Guessing blindly

Each wrong answer costs 0.25. Eliminate two options before guessing — then the expected value is positive.

Study roadmap

10-Week Strategic Study Roadmap

Weeks 1–2

Diagnostic & Foundations

Take a timed diagnostic; rebuild the Foundation topics marked ‘Easy’ and note every error type.

Weeks 3–5

Core Topics

Work through the ‘Medium’ and ‘Hard’ topics in the order of the frequency table; 20–30 targeted questions per topic.

Weeks 6–7

Mixed Practice

Mixed sets under section timing (2 min/question). Keep an error log: concept, reading or calculation.

Weeks 8–9

Full Mocks

One full 65-question CEnT-S mock per week with real section timers; review every wrong and every guessed answer.

Week 10

Final Polish

Re-do your error log, revise traps, and practise the skip-or-guess rule for the −0.25 penalty.

Other CEnT-S Section Guides