Paris University of Pavia | Ari's Past Student (2020)

7th of April, 2023The International Medical Admissions Test (IMAT) is a crucial exam for students seeking to enter medical schools in Italy in English. The test evaluates applicants’ knowledge and skills in various subjects, including a minor yet significant mathematics section. Although the math portion might not be as extensive as other sections in the IMAT, it is essential for medical students to have a strong foundation in mathematics. Mastering the fundamentals of math can help develop problem-solving, critical thinking, and analytical skills, which are vital in the medical field and also “leak” to other parts of the IMAT exam, such as the logic section, and the physics section.

The IMAT syllabus encompasses the complete high school standard mathematics curriculum. However, it is crucial to keep in mind that, in practice, due to the limited time of 45-60 seconds per question during the exam, the mathematics problems tend to be relatively straightforward and quick to tackle. **These questions typically focus on fundamental mathematical topics, including probability, geometry, Algebra I, and elementary linear functions.**

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As mentioned, mathematics serves as a cornerstone for several other subjects covered in the IMAT exam, such as physics, chemistry, and biology. Excelling in mathematics can enhance your understanding and performance in these other areas. Therefore, it is crucial to allocate sufficient time and effort to master the math topics most likely to appear on the IMAT.

## Overview of IMAT Math Topics

This comprehensive guide will provide an in-depth exploration of the mathematics topics covered on the IMAT exam. It will also offer valuable tips and strategies for mastering these topics and achieving high scores. By understanding the key concepts, practicing effective study habits, and implementing the recommended techniques, you will be well-equipped to tackle the IMAT mathematics section with confidence.

We will break down the syllabus into small parts and suggest you some awesome resources for each that you should utilize when studying mathematics for the IMAT exam!

## Essential IMAT Mathematics Topics

A solid understanding of the essential IMAT mathematics topics is crucial for achieving a high score on the exam. In this section, we will delve into each topic and provide you with an overview, key concepts, and tips to strengthen your knowledge and skills. By mastering these topics, you will not only enhance your mathematical abilities but also improve your understanding of related subjects in the IMAT, such as physics and problem solving.

Mathematics Topics | Keywords |
---|---|

Algebra and numerical sets | natural numbers, integers, rational numbers, real numbers, scientific notation, proportions, percentages, powers, roots, logarithms, combinatorics, polynomial expressions, equations, inequalities, systems |

Functions | graphical representations, domain, codomain, continuity, algebraic functions, exponential functions, logarithmic functions, trigonometric functions, composite functions, inverse functions, trigonometric equations, inequalities |

Geometry | polygons, circle, measurements, isometries, similarities, equivalences, geometric loci, angles, sine, cosine, tangent, trigonometric formulas, Cartesian reference system, distance, midpoint, straight line equation, parallel lines, perpendicular lines, point to a line, equation of circle, parabola, hyperbola, ellipse, Pythagoras’ theorem, Euclid’s theorems |

Probability and statistics | frequency distributions, random experiments, events, probability, frequency |

### Algebra and Numerical Sets

#### Natural numbers, integers, rational and real numbers

The foundation of mathematics lies in understanding the different types of numbers, such as natural numbers, integers, rational, and real numbers. Natural numbers include positive whole numbers, while integers encompass both positive and negative whole numbers, as well as zero. Rational numbers are those that can be expressed as a fraction, and real numbers include both rational and irrational numbers (such as the square root of 2 or pi).

Familiarize yourself with the properties and operations of each number type to enhance your problem-solving abilities and recognize patterns within mathematical expressions, this section is usually quite basic on the IMAT, and basic Algebra is indeed needed to all of the section of the exam that are math-oriented such as physics and problem solving.

**Here is a fantastic playlist covering algebra in detail**

#### Sorting and comparison: scales and scientific notation

Sorting and comparing numbers are essential skills for tackling various math problems. Be comfortable with comparing values using scales (for example, the order of magnitude) and scientific notation, which expresses large or small numbers as a product of a number between 1 and 10 and a power of 10. It will also help you in other subject such as Chemistry, where you need to know how to calculate the pH using the logarithmic scale!

#### Operations and their properties

Understanding the properties of basic arithmetic operations (addition, subtraction, multiplication, and division) is crucial for solving algebraic problems, a tip, start by practicing the very basics of mathematic rules!

#### Proportions and percentages

Proportions and percentages are common in various mathematical problems, including those related to real-life situations. Master the techniques to solve problems involving ratios, proportions, and percentages. Learn how to solve and calculate proportions and percentages fast, it will help you on the IMAT exam!

#### Powers with integer and rational exponents, and their properties

Powers and exponents are crucial concepts in algebra. Be comfortable working with integer and rational exponents, and understand the properties of powers, such as the product of powers, quotient of powers, and power of a power rules.

Memorize the basic exponent rules and practice simplifying expressions involving exponents to improve your speed and accuracy. This topic and many others are mentioned in the playlist I’ve linked above.

#### Roots and their properties

Roots, such as square roots and cube roots, are essential in algebra and other mathematical topics. Understand the properties of roots and be able to simplify expressions involving them.

Tip: Learn how to convert between rational exponents and roots, and practice simplifying expressions with roots to enhance your problem-solving abilities.

#### Logarithms (base 10 and base e) and their properties

Logarithms are used to solve exponential equations and are essential for understanding various mathematical topics. Be familiar with logarithms in base 10 and base e (natural logarithms), and understand their properties, such as the product, quotient, and power rules.

#### Elements of combinatorics

Combinatorics deals with counting and arranging objects in various ways, such as permutations and combinations. Understand the fundamental principles of combinatorics and apply them to solve problems related to arrangements, selections, and counting.

Tip: Master the formulas for permutations and combinations, and practice solving problems involving different combinatorial situations.

#### Algebraic and polynomial expressions

Algebraic and polynomial expressions are vital components of algebra. Familiarize yourself with the structure and terminology of polynomial expressions, such as terms, coefficients, and degrees. Understand how to add, subtract, multiply, and divide polynomials and how to manipulate expressions to simplify or solve problems.

#### Major products and nth binomial expansions, factorization of polynomials

Mastering major product formulas, **such as the difference of squares and the sum and difference of cubes,** is essential for simplifying and factoring polynomial expressions. Also, understand the binomial theorem and be able to expand expressions using the nth binomial expansion. It will also help you with spatial recognition which appears many time on both the math and the problem solving sections of the exam.

#### Algebraic fractions

Algebraic fractions involve expressions with variables in the numerator and/or denominator. Learn how to add, subtract, multiply, and divide algebraic fractions and simplify expressions involving them.

#### Algebraic equations and inequalities of the first and second order

Algebraic equations and inequalities are fundamental components of algebra, and understanding how to solve them is crucial. Be proficient in solving first and second-order linear equations and inequalities, as well as quadratic equations.

Tip: **Familiarize yourself with various methods for solving equations and inequalities**, such as factoring, completing the square, and using the quadratic formula, and practice applying these methods to different problems.

#### Systems of equations

Systems of equations involve multiple equations with common variables. Learn how to solve systems of linear equations using techniques such as substitution, elimination, and matrix methods. Understand the different types of solutions a system can have: unique, infinite or no solutions.

### Functions

#### Basic concepts of functions and their graphical representations

Functions are a crucial concept in mathematics, with applications across various fields. Understand the basic terminology of functions, such as domain, codomain, sign, continuity, maxima, and minima, increasing and decreasing, and be able to interpret their graphical representations.

Tip: **Familiarize yourself with the features of different types of functions**, and practice sketching and analyzing graphs to gain a deeper understanding of function behavior.

#### Elementary functions: whole and fractional algebraic functions

Elementary functions are the building blocks for more advanced mathematical concepts. Be comfortable working with whole and fractional algebraic functions and understand their properties, behavior, and graphical representations.

#### Exponential, logarithmic, and trigonometric functions

Exponential, logarithmic, and trigonometric functions are essential for various mathematical and real-world applications. Master these functions, their properties, and their graphical representations. Understand how to manipulate and solve problems involving these functions.

#### Composite and inverse functions

Composite and inverse functions are important concepts in the study of functions. Understand how to form composite functions and find the inverse of a function, if it exists. Be able to recognize and analyze the graphical representations of composite and inverse functions.

#### Trigonometric equations and inequalities

Trigonometric equations and inequalities involve solving problems using trigonometric functions, such as sine, cosine, and tangent. Be adept at solving trigonometric equations and inequalities using techniques like factoring, trigonometric identities, and substitution. Understand how to analyze the solutions and interpret their real-world applications.

In case you are looking for a good starting book to study from that is also suitable for the IMAT, you should consider using the

”Core 1 & Core 2 Edexcel AS Mathematics, Keith Pledger et al. Published by Heinemann”

### Geometry

#### Polygons and their properties

Polygons are essential in geometry and have various applications. Understand the properties and characteristics of different types of polygons, such as triangles, quadrilaterals, and other multi-sided shapes. Be familiar with angle properties, side relationships, and other geometric features.

Tip: **Practice solving problems involving polygons and their properties to build a strong foundation in geometry** and enhance your problem-solving abilities.

## Circle and circumference

Circles are fundamental shapes in geometry, with numerous real-world applications. **Understand the properties of circles, such as circumference, diameter, radius, arcs, and sectors. **Learn how to solve problems involving these properties and apply them in various contexts.

#### Measurements of lengths, surfaces, and volumes

Being able to measure lengths, surfaces, and volumes is essential for tackling geometry problems and real-world applications. Understand the units of measurement and formulas for calculating lengths, areas, and volumes of various geometric shapes.

Tip: **Memorize the formulas for calculating the measurements of different shapes** and practice applying them to solve problems in different contexts.

#### Isometries, similarities, and equivalences in the plane

Isometries, similarities, and equivalences are essential concepts in geometry that involve transformations and relationships between geometric shapes. Understand the properties of isometries (such as translations, rotations, and reflections), similarities (proportional shapes), and equivalences (shapes with the same area), and learn how to apply these concepts to solve problems.

#### Geometric loci

Geometric loci involve the study of sets of points that satisfy specific conditions or constraints. Be familiar with common types of loci, such as points equidistant from two points or a line, and understand how to determine loci for various geometric problems.

#### Measurement of angles in degrees and radians

Angles are fundamental components of geometry and are measured in degrees and radians. Understand the conversion between degrees and radians and be comfortable working with angles in both units.

#### Sine, cosine, tangent of an angle and their significant values

Trigonometry is an essential part of geometry and involves the study of angles and their relationships with the sides of triangles. Be proficient in calculating the sine, cosine, and tangent of an angle and be familiar with their significant values, such as for 30, 45, and 60 degrees or pi/6, pi/4, and pi/3 radians.

Tip: **Memorize the significant values of sine, cosine, and tangent. **

#### Trigonometric formulas

Trigonometric formulas, such as the Pythagorean identity, sum and difference of angles, double-angle, and half-angle formulas, are essential for solving various geometry and trigonometry problems. Understand these formulas and be able to apply them effectively to solve problems.

#### Solving triangles

Solving triangles is a crucial skill in geometry, which involves finding the lengths of sides and measures of angles in a triangle. Be familiar with different methods for solving triangles, such as the Pythagorean theorem, trigonometric ratios, and the sine and cosine rules.

#### Cartesian reference system in a plane

The Cartesian reference system is a coordinate system used to locate points in a plane using ordered pairs of numbers. Understand the concepts of x and y-axes, quadrants, and coordinates, and be able to plot points and interpret their positions in the coordinate plane.

#### Distance between two points and the midpoint of a segment

Learn how to calculate the distance between two points in a Cartesian plane using the distance formula and how to find the midpoint of a segment using the midpoint formula. These skills are essential for solving various geometry problems involving points, lines, and shapes in a coordinate plane.

#### Straight line equation

Understand the different forms of the straight-line equation, such as slope-intercept, point-slope, and standard form, and be able to determine the equation of a line given specific information, such as points or slope. Also, be proficient in graphing lines and interpreting their properties, such as slope and intercepts.

#### Conditions for parallel and perpendicular lines

Recognize the conditions for parallel and perpendicular lines in a Cartesian plane, which involve the slopes of the lines. Be able to determine whether lines are parallel or perpendicular based on their equations and use this knowledge to solve various geometry problems.

#### Distance of a point to a line

Learn how to calculate the distance of a point to a line using the distance formula and apply this skill to solve geometry problems involving points, lines, and shapes in a coordinate plane.

#### Equation of the circle, the parabola, the hyperbola, the ellipse, and their representation in the Cartesian plane

Understand the standard equations of conic sections, such as circles, parabolas, hyperbolas, and ellipses, and be able to graph and interpret their properties in a Cartesian plane. Be proficient in determining the equations of these shapes given specific information and using this knowledge to solve various geometry problems.

#### Pythagoras’ theorem

Pythagoras’ theorem is a fundamental principle in geometry that relates the lengths of the sides of a right-angled triangle. Understand the theorem and be able to apply it to solve problems involving right-angled triangles and other geometric shapes.

#### Euclid’s first and second theorems

Euclid’s first and second theorems are fundamental principles in geometry that involve the properties of circles and lines. Understand the statements and implications of these theorems and be able to apply them to solve various geometry problems.

### Probability and Statistics

#### Frequency distributions and their graphical representations

Frequency distributions are used to organize and summarize data. Understand the concepts of frequency, relative frequency, and cumulative frequency, and be able to create and interpret frequency distributions, such as histograms and frequency polygons.

#### Concept of random experiments and events

Random experiments are situations in which the outcome is uncertain, and events are specific outcomes or combinations of outcomes. Understand the concepts of random experiments, sample spaces, and events, and **be able to analyze and solve problems involving probability and randomness.**

#### Probability and frequency

Probability is a measure of the likelihood of an event occurring and is closely related to frequency. Understand the concepts of probability and frequency, and be able to calculate probabilities for various events and situations using techniques such as **counting, relative frequency, and probability rules.**

## Strategies and Tips for Mastering IMAT Math Topics

### Focus on Key Topics and Create a Study Schedule

Prioritize your study time by focusing on the most critical math topics and creating a study schedule. Allocate specific time slots for each topic and review sessions to reinforce your understanding.

### Practice with IMAT-style Questions and Understand the Concepts

Familiarize yourself with the types of questions on the IMAT by practicing with sample questions and past exam papers. Ensure you have a deep understanding of the concepts underlying the formulas and techniques.

### Break Down Complex Problems and Utilize Online Resources

Tackle complex problems by breaking them down into smaller parts. Utilize online resources, such as video tutorials and interactive exercises, to strengthen your knowledge and problem-solving skills.

### Collaborate with Others and Seek Help

Join study groups to gain new insights and stay motivated. If you’re struggling with a particular topic, seek help from teachers, tutors, or platforms like Entermedschool. They offer amazing options, from a free IMAT course to the 50+ club for students aiming to gain a competitive edge.

### Review Regularly and Stay Positive

Regularly review the math topics you’ve studied to reinforce your understanding. Maintain a positive attitude and believe in your ability to master the IMAT math topics with dedication, practice, and the right strategies.

## Conclusion

In conclusion, the mathematics section, though not the most critical part of the IMAT exam, plays a significant role in boosting your overall score. By taking the time to study this section, you increase your chances of achieving a higher score and securing admission to your dream university. Focusing on the key topics, practicing with IMAT-style questions, and implementing the strategies and tips outlined in this article will enable you to tackle the math section effectively and with confidence.

It is essential to remember that investing time in understanding the relevant material and seeking additional help when needed can have a considerable impact on your overall performance. Platforms like Entermedschool are dedicated to providing valuable resources and support to help you excel in the IMAT exam. Their free IMAT course and the 50+ club for students looking to gain a competitive advantage offer expert guidance and tutoring to enhance your mathematical skills and overall exam preparedness further.

Additionally, staying positive and maintaining a growth mindset throughout your preparation journey is crucial to your success. Embrace challenges, learn from your mistakes, and continuously strive to improve your understanding of the various math topics covered in the IMAT exam. Surround yourself with like-minded individuals who share the same goal, as they can provide motivation, support, and encouragement during your study sessions.

**In summary, while the mathematics section may not be the primary focus of the IMAT exam, it is an area where you can gain extra points that could make a significant difference in the final outcome.** By dedicating yourself to mastering the relevant material, seeking expert help when necessary, and utilizing the resources available on platforms like **Entermedschool**, you can ensure that you are well-prepared to excel in the mathematics section and ultimately achieve your academic goals. Best of luck on your journey to success!