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?
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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.
Análisis de la distribución de preguntas
Temas de Mathematics de IMAT: frecuencia
¿Qué temas requieren más atención? Este es el desglose por temas a partir de nuestros datos de preguntas de IMAT:
| Tema | 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.
Ideas clave
- 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.
Análisis de dificultad
Dificultad de los temas y reparto de estudio recomendado
No todos los temas exigen el mismo tiempo. Algunos requieren mucha práctica resolviendo problemas; otros dependen de recordar con precisión conceptos concretos:
Difícil
Probability & Statistics 1 weekDifícil
Functions, Exponentials & Logarithms 1–1.5 weeksMedio
Trigonometry 4–5 daysMedio
Algebra: Equations & Inequalities 1–1.5 weeksMedio
Geometry 1 weekFácil
Numbers, Powers & Sets 3–4 days¿No sabes por dónde empezar tu preparación?
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Temas de Mathematics de IMAT: cómo se evalúa cada uno
Un repaso tema por tema de la sección de Mathematics del official MUR IMAT syllabus (DM 1005/2026, Allegato A):
01
Number Sets & Algebra Medio
- 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.
Cómo aparece en IMAT: Recognising perfect squares, equations with a parameter (‘for which a is it impossible?’) and quadratic inequalities.
02
Functions Difícil
- 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.
Cómo aparece en IMAT: Parabolas through a given point, exponential and logarithmic equations (log₁₀x = 6), and the solution set of .
03
Geometry & Trigonometry Medio
- Polygons, circles; lengths, areas and volumes; similarity.
- Cartesian plane: lines, circles, parabolas.
- Sine, cosine and tangent; solving triangles.
Cómo aparece en IMAT: Short computations (cylinder volume, rectangle from its perimeter), circle equations and right-triangle relations such as .
04
Probability & Statistics Difícil
- Random experiments, events and probability.
- Draws with and without replacement.
- Frequency distributions and their graphs.
Cómo aparece en 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 06-08-2026Problemas de examen resueltos
Preguntas de ejemplo de Mathematics de IMAT y tácticas de eliminación
Descubre cómo se construyen las preguntas de mathematics de IMAT y cómo una eliminación disciplinada evita la penalización de −0.4:
A circle has the equation . Which of the following statements is true?
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Which is the solution to the inequality ?
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Análisis de trampas del examen
Los 5 errores más comunes en Mathematics de IMAT
Errores conceptuales y tácticos recurrentes que les cuestan puntos decisivos a los estudiantes:
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.
Hoja de ruta de estudio
Hoja de ruta estratégica de estudio de 10 semanas
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.