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IMAT Mathematics Course Book: Visual Guide

Build the IMAT maths you need: ratios and unit conversion, logarithms, conditional probability and screening, and correlation versus causation.

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About this book

This visual course book covers IMAT mathematics for students preparing for the medical entrance exam in Italy. It focuses on the maths that appears in the test and explains each idea with clear visuals rather than long derivations.

The chapters run from arithmetic, ratios, percentages and units through algebra, linear equations and graphs, quadratics and graph interpretation, and functions, exponentials and logarithms. Geometry and trigonometry cover angles, circles, area, volume and right-triangle trigonometry. The probability chapter includes counting principles and conditional probability with screening examples, and the statistics chapter deals with spread, distributions, and correlation versus causation.

The final chapter brings sequences, an intuitive approach to rates of change and maxima, and multi-step word problems together, so you can practise combining topics the way IMAT questions often do.

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Browse the full contents and read the opening topic.

Sample · 00-Introduction

0.1 How to Use This Book

How to Use This Mathematics Book

This book is designed for students preparing for IMAT who need mathematics to be visual, structured and connected to real problems.

English onlyOriginal visualsMedicine/Dentistry links8 VerityPrep MCQs per topicHTML only

Contents

Chapter 01 — Arithmetic, Ratios, Percentages and Units Chapter 02 — Algebra, Linear Equations and Graphs Chapter 03 — Quadratics and Graph Interpretation Chapter 04 — Functions, Exponentials and Logarithms Chapter 05 — Geometry and Trigonometry Chapter 06 — Probability and Risk Chapter 07 — Statistics and Data Interpretation Chapter 08 — Sequences, Calculus Intuition and Mixed Strategy

1.0 Chapter Overview

Chapter 01 — Arithmetic, Ratios, Percentages and Units

Big idea: This chapter builds quantitative tools for IMAT problem solving and future medical or dental study.
Quantitative foundationsNumbers used in IMAT and medicine1Fractions, decimals and percentages2Ratios and rates3Unit conversion4Estimation and reasonablenessVerityPrep visual rule: identify the structure, choose the method, then calculate carefully.Original schematic visual — Quantitative foundations
Percentage formula mapFormula map and method choicepercent = part/whole × 100percentagenew = old × multipliergrowth/decaychange/original × 100percentage changeFormula visual — Percentage formula map

1.1 Fractions, decimals and percentages

Fractions, decimals and percentages

Deeper explanation

Students must move fluently between fractions, decimals and percentages. Percent means per hundred, so 18% = 0.18 = 18/100. In medicine, percentages can describe risk, concentration, prevalence or change.

VerityPrep approach: identify the mathematical structure, draw a small diagram or table, choose the method, calculate, and check whether the answer is reasonable.

Where is this used in real life?

Percentages are used in discounts, exam scores, concentration labels, population data and risk communication.

Where is this used in Medicine / Dentistry?

Doctors and dentists use percentages to interpret risk reduction, prevalence, sensitivity, success rates and concentration changes.

How to read this visually: mark known values, label the unknown, write the relationship, estimate before calculating.

8 VerityPrep Standard MCQs — Fractions, decimals and percentages

Standard: A–E options, one correct answer, plausible distractors, direct topic link, and short teaching explanation.
Percentage change
1. A dose increases from 80 mg to 100 mg. Percentage increase?
  1. 25%
  2. 20%
  3. 80%
  4. 100%
  5. 125%
Reverse percent
2. A value after 20% discount is 48. Original value?
  1. 57.6
  2. 60
  3. 40
  4. 68
  5. 50
Percent of amount
3. 30% of 40 students is:
  1. 10
  2. 14
  3. 12
  4. 30
  5. 70
Relative change
4. A concentration rises from 5 to 8 g/L. Percentage increase?
  1. 37.5%
  2. 3%
  3. 160%
  4. 60%
  5. 40%
Algebra
5. 18% of x is:
  1. 18x
  2. x/18
  3. 1.8x
  4. 0.018x
  5. 0.18x
Risk
6. Risk decreases from 12% to 9%. Relative decrease?
  1. 25%
  2. 3%
  3. 33.3%
  4. 75%
  5. 21%
Medical link
7. Why are percentages important in medicine?
  1. They replace units.
  2. They compare relative dose, risk, prevalence and change.
  3. They are only geometry.
  4. They always mean mg.
  5. They cannot describe change.
Trap
8. Common percentage trap:
  1. Dividing by 100.
  2. Finding the difference.
  3. Using the final value as base instead of the initial value.
  4. Writing percent sign.
  5. Checking the base.

Continue reading — 9 chapters, worked examples and practice.

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Built for IMAT preparation

Topics follow the IMAT syllabus with visual explanations and worked solutions close to the lesson content.

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