Free ebook for exam mathematics review, covering algebra, geometry, trigonometry, probability, statistics, and calculus.
Free ebook + audiobook content
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Natural numbers and basic operations
+ Exercise: Which of the following statements is true about the natural numbers and basic operations, according to the text? 3 minutes
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Rational and irrational numbers
+ Exercise: Which of the following statements is true about rational and irrational numbers? 3 minutes
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Complex numbers
+ Exercise: Which of the following statements about complex numbers is true? 3 minutes
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Set Theory
+ Exercise: Which of the following statements about set theory is correct? 4 minutes
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Prime numbers and the fundamental theorem of arithmetic
+ Exercise: Which of the following statements is true about prime numbers and the Fundamental Theorem of Arithmetic? 3 minutes
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Operations with radicals
+ Exercise: What are the basic operations that can be performed with radicals and what are the conditions for carrying them out? 3 minutes
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Functions of the first and second degrees
+ Exercise: Which of the following statements is true about first and second degree functions in mathematics? 3 minutes
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Exponential and logarithmic functions
+ Exercise: Which of the following statements is true about exponential and logarithmic functions? 3 minutes
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Polynomials
+ Exercise: What is a polynomial and how is it represented? 4 minutes
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Logarithms
+ Exercise: Which of the following statements about logarithms is true? 3 minutes
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Solving equations and inequalities
+ Exercise: What is the main difference between solving equations and inequalities as mentioned in the text? 3 minutes
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Inverse functions
+ Exercise: What is an inverse function in mathematics? 3 minutes
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Remainder and factor theorem
+ Exercise: Which of the following statements correctly describes the Remainder Theorem and the Factor Theorem? 3 minutes
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Composite functions
+ Exercise: What are composite functions in mathematics? 3 minutes
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Injective, surjective and bijective functions
+ Exercise: Which of the following statements correctly describes a bijective function? 3 minutes
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Study of the signs of a function
+ Exercise: Which of the following statements correctly describes studying the signs of a function? 3 minutes
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Study of the variation of a function
+ Exercise: What is a function in mathematics and how can we study its variation? 2 minutes
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Trigonometry
+ Exercise: What does the word 'trigonometry' mean and what are the six main trigonometric functions you need to know for the ENEM test? 2 minutes
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Flat geometry
+ Exercise: Which of the following is a correct description of a polygon from the text? 4 minutes
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Spatial geometry
+ Exercise: Which of the following statements about spatial geometry is true? 3 minutes
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Pythagorean Theorem
+ Exercise: What does the Pythagorean Theorem state about the right triangle? 3 minutes
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Circles and their properties
+ Exercise: Which of the following statements about the properties of circles is correct? 2 minutes
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Areas and volumes of geometric figures
+ Exercise: Which of the following statements is correct about the area and volume of geometric figures? 3 minutes
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Trigonometric functions
+ Exercise: What are the six basic trigonometric functions and what do they represent? 3 minutes
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Trigonometric identities
+ Exercise: Which of the following statements correctly describes one of the trigonometric identities mentioned in the text? 3 minutes
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Solving triangles
+ Exercise: Which of the following statements correctly describes the Law of Cosines in solving triangles? 3 minutes
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Trigonometric equations
+ Exercise: What are the six basic trigonometric functions mentioned in the text? 3 minutes
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Metric relations in the right triangle
+ Exercise: Which of the following statements about metric relationships in right triangles is true? 3 minutes
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Metric ratios on the circumference
+ Exercise: Which of the following statements is true about metric ratios on the circumference? 3 minutes
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Thales Theorem
+ Exercise: What is the correct statement about Thales' Theorem? 3 minutes
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Euclid's Theorem
+ Exercise: What is Euclid's Theorem and how is it used? 2 minutes
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Stevin's theorem
+ Exercise: What is the main contribution of Stevin's Theorem to physics, and how can it be expressed mathematically? 2 minutes
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Analytical geometry
+ Exercise: What is the general equation of the line in Analytical Geometry? 3 minutes
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Matrices and determinants
+ Exercise: Which of the following statements is true about matrices and determinants? 3 minutes
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Linear systems
+ Exercise: Which of the following methods is used to solve linear systems and involves the use of determinants of matrices? 3 minutes
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Vectors
+ Exercise: Which of the following statements is true about vectors? 3 minutes
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Geometry of position
+ Exercise: Which of the following concepts is correct about Position Geometry? 3 minutes
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Conics
+ Exercise: Which of the following statements about conics is correct? 3 minutes
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Geometric transformations
+ Exercise: Which of the following statements best describes the geometric transformation known as rotation? 3 minutes
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Combinatorial analysis
+ Exercise: Which of the following concepts is correctly defined in Combinatorics? 3 minutes
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Probability
+ Exercise: According to the text, which of the following statements is true about probability in the context of the ENEM? 3 minutes
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Statistics
+ Exercise: Which of the following statements about statistics is true, according to the text? 3 minutes
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Measures of central tendency
+ Exercise: What are the three measures of central tendency mentioned in the text and how are they calculated? 3 minutes
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Dispersion measures
+ Exercise: Which of the following statements about dispersion measures is correct? 3 minutes
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Conditional probability
+ Exercise: What is conditional probability and how is it calculated in mathematics? 3 minutes
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Bayes theorem
3 minutes
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Graphs and tables
+ Exercise: What is the importance of graphs and tables for the ENEM math test? 3 minutes
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Numerical sequences and series
+ Exercise: Which of the following statements is true about numerical sequences and series? 3 minutes
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Arithmetic and geometric progressions
+ Exercise: Which of the following statements is true about Arithmetic Progressions (AP) and Geometric Progressions (PG)? 3 minutes
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Newton's binomial
+ Exercise: What is the expansion of the binomial (a+b)^3 using Newton's Binomial? 3 minutes
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Ratios and proportions
+ Exercise: What is the correct definition of ratio and proportion in mathematics, and how are they used? 3 minutes
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Rule of three simple and compound
+ Exercise: What is the difference between the simple rule of three and the rule of compound three? 3 minutes
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Percentage
+ Exercise: Which of the following statements about percentage is correct? 3 minutes
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Simple and compound interest
+ Exercise: What's the main difference between simple and compound interest, and how might that affect the total amount you earn over time? 3 minutes
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Sequences and geometric series
+ Exercise: What happens to the sum of the terms of a geometric series when the ratio r is greater than 1 or less than -1? 3 minutes
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Financial Mathematics
+ Exercise: What is the main objective of Financial Mathematics, one of the disciplines that make up the syllabus of Mathematics for the Enem test? 3 minutes
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Limits and derivatives
+ Exercise: Which of the following concepts is a measure of the rate at which the function is changing at a given point? 3 minutes
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Definite and indefinite integral
+ Exercise: What is the difference between indefinite integral and definite integral? 3 minutes
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Intermediate Value Theorem
+ Exercise: What does the Intermediate Value Theorem (TVI) say about a continuous function? 3 minutes
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Extreme Value Theorem
+ Exercise: What does the Extreme Value Theorem say about a continuous function on a closed interval? 3 minutes
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Confrontation theorem
+ Exercise: What does the Matchup Theorem say about two sequences or series of numbers? 3 minutes
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Rolle's Theorem
+ Exercise: What is the correct statement about Rolle's Theorem as described in the text? 2 minutes
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Lagrange's theorem
+ Exercise: What does Lagrange's Theorem say about groups and subgroups in mathematics? 3 minutes
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Cauchy's theorem
+ Exercise: What is the main claim of Cauchy's Theorem in Complex Analysis? 3 minutes
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L'Hopital's Theorem
+ Exercise: Which of the following statements about L'Hopital's Theorem is true? 4 minutes
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Bolzano's theorem
+ Exercise: What does Bolzano's Theorem, also known as the Intermediate Value Theorem, state? 3 minutes
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Weierstrass theorem
+ Exercise: What is the main statement of Weierstrass' Theorem? 3 minutes
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Heine's Theorem
+ Exercise: What does Heine's Theorem state in simple terms in mathematics? 3 minutes
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D'Alembert's theorem
+ Exercise: What is the main application of D'Alembert's Theorem, also known as D'Alembert's rule? 3 minutes
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Gauss's theorem
+ Exercise: What does Gauss's theorem say about electric flux and total charge? 3 minutes
About the free ebook with audio
Comprehensive Mathematics Course for Exams
Build a solid foundation for mathematics exams with this free online ebook covering essential algebra, geometry, trigonometry, probability, statistics, and introductory calculus.
Strengthen your exam-solving skills
Work through core number systems, equations, inequalities, functions, logarithms, matrices, polynomials, and sequences. The material also supports problem solving with ratios, percentages, financial mathematics, and data interpretation.
Connect concepts across mathematics
Develop confidence in coordinate geometry, vectors, conics, plane and spatial geometry, trigonometric relationships, counting methods, and probability. Advanced sections introduce limits, derivatives, integrals, and key theorems used in mathematical analysis.
A practical study resource
Use this ebook to review formulas, understand relationships between topics, and prepare methodically for school and entrance examinations. Its broad coverage helps learners revisit individual subjects or reinforce a complete mathematics revision plan.
Does this mathematics ebook cover derivatives and integrals?
Yes. It includes limits, derivatives, definite integrals, indefinite integrals, and related analysis theorems.
Which probability topics are included in the ebook?
It covers combinatorial analysis, probability, conditional probability, Bayes' theorem, and statistics.
Does the ebook include financial mathematics formulas?
Yes. It addresses percentages, ratios, simple and compound interest, and financial mathematics.
This ebook/audiobook includes:
4 hours and 2 minutes of audio content
Digital certificate of course completion (Free)
Exercises to train your knowledge
100% free, from content to certificate
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