A bag contains 12 balls that are indistinguishable by touch, 5 of which are red. Two balls are drawn without replacement. What is the probability that no red ball is drawn?
Pick an answer to see the explanation
Mathematics shares a 13-question block with Physics. In the official papers it took 7 questions in 2024 and 2025 and 6 in 2026 — about 9–10 of the 90 points. A few quantitative items also appear in the Logical Reasoning block.
The level is upper-secondary school with no calculus: algebra, functions, geometry and basic probability. Questions are short but often combine two ideas — an inequality and its domain, a circle equation and a point.
Question distribution analysis
IMAT Mathematics Topics: Frequency
Which topics demand your deepest attention? Below is the topic breakdown from our IMAT question data:
| Topic | Total | |
|---|---|---|
| Algebra: Equations & Inequalities | 6 | |
| Geometry | 4 | |
| Exponentials & Logarithms | 3 | |
| Probability & Statistics | 2 | |
| Trigonometry | 2 | |
| Sets | 1 | |
| Numbers, Powers & Radicals | 1 | |
| Functions & Graphs | 1 |
*Question counts per topic in the official IMAT 2024, 2025 and 2026 papers (MUR), mathematics questions of the 13-question Physics & Mathematics block, tagged by the PrepTest question bank. Topics are grouped by PrepTest; the topic mix changes from year to year, so treat the table as a guide to priorities, not a prediction.
Key Takeaways
- Algebra leads over three years (6 questions): equations with parameters, quadratic and linear inequalities, factorisation.
- Geometry appears every year (4): rectangles and circles, cylinder volume, inscribed angles, the equation of a circle.
- Exponentials & logarithms (3) and probability (2) alternate between years — one-step equations and drawing balls from a bag.
- Trigonometry appeared in 2024 and 2025 only; sets and number manipulation take at most one question.
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
Probability & Statistics 1 weekHard
Functions, Exponentials & Logarithms 1–1.5 weeksMedium
Trigonometry 4–5 daysMedium
Algebra: Equations & Inequalities 1–1.5 weeksMedium
Geometry 1 weekEasy
Numbers, Powers & Sets 3–4 daysNot Sure Where to Begin Your Preparation?
Take the free IMAT diagnostic test: see your baseline in every section and get a personalised AI study plan.
Take Diagnostic TestOfficial syllabus breakdown
IMAT Mathematics Topics: How Each Is Tested
A topic-by-topic look at the Mathematics section of the official MUR IMAT syllabus (DM 1005/2026, Allegato A):
01
Number Sets & Algebra Medium
- Natural, integer, rational and real numbers; order of magnitude and scientific notation.
- Powers, radicals, logarithms; proportions and percentages.
- Polynomials and factorisation; 1st and 2nd degree equations, inequalities and systems.
How it appears on IMAT: Recognising perfect squares, equations with a parameter (‘for which a is it impossible?’) and quadratic inequalities.
02
Functions Hard
- Domain, sign, monotonicity, maxima and minima of a function and its graph.
- Polynomial, rational, exponential, logarithmic and trigonometric functions.
- Composite and inverse functions; trigonometric equations and inequalities.
How it appears on IMAT: Parabolas through a given point, exponential and logarithmic equations (log₁₀x = 6), and the solution set of .
03
Geometry & Trigonometry Medium
- Polygons, circles; lengths, areas and volumes; similarity.
- Cartesian plane: lines, circles, parabolas.
- Sine, cosine and tangent; solving triangles.
How it appears on IMAT: Short computations (cylinder volume, rectangle from its perimeter), circle equations and right-triangle relations such as .
04
Probability & Statistics Hard
- Random experiments, events and probability.
- Draws with and without replacement.
- Frequency distributions and their graphs.
How it appears on IMAT: Drawing balls from a bag, with or without replacement. The two cases are deliberately contrasted in the options.
Official MUR Syllabus
The official IMAT programme is Allegato A of the Ministry of University and Research decree for the 2026/27 admission test:
MUR — DM n. 1005 of 06-08-2026Solved exam problems
IMAT Mathematics Sample Questions & Elimination Tactics
See how IMAT mathematics questions are built and how disciplined elimination avoids the −0.4 penalty:
A circle has the equation . Which of the following statements is true?
Pick an answer to see the explanation
Which is the solution to the inequality ?
Pick an answer to see the explanation
Candidate trap analysis
5 Most Common Mistakes in IMAT Mathematics
Recurring conceptual and tactical errors that cost students crucial points:
01
With vs without replacement
Without replacement the second denominator drops by one. Read the drawing rule before multiplying.
02
Inside vs outside the roots
For an upward parabola, ‘≤ 0’ is between the roots and ‘≥ 0’ is outside. Sketch the parabola.
03
Domain of logs and roots
The argument of a logarithm must be positive; options outside the domain are planted on purpose.
04
Parameters that make an equation impossible
In the value removes entirely. Check when the coefficient of the unknown vanishes.
05
Guessing blindly
A wrong answer costs −0.4, more than a quarter of a correct one, so a blind guess loses points on average. Rule out at least one option before guessing.
Study roadmap
10-Week Strategic Study Roadmap
Weeks 1–2
Diagnostic & Foundations
Take a timed diagnostic; rebuild the topics marked ‘Easy’ and note every error type: concept, reading or calculation.
Weeks 3–5
Biology & Chemistry First
38 of the 60 questions are Biology and Chemistry. Work through their ‘Medium’ and ‘Hard’ topics in the order of the frequency tables.
Weeks 6–7
Physics, Maths & Logic
Cover the 13-question Physics & Mathematics block and the 5 logic questions with short mixed sets; aim for about 90 seconds per question.
Weeks 8–9
Full Mocks
One full 60-question, 100-minute IMAT mock per week; review every wrong and every guessed answer.
Week 10
Final Polish
Re-do your error log, revise the traps, and practise the skip-or-answer rule: a wrong answer costs −0.4, a blank costs nothing.