Mathematics

Test Content

1. Numerical Sets and Algebra

1.1. Numerical sets: natural, integer, rational, real numbers
1.2. Ordering and comparison
1.3. Order of magnitude and scientific notation
1.4. Operations and their properties
1.5. Proportions and percentages
1.6. Powers with integer and rational exponents and their properties
1.7. Radicals and their properties
1.8. Logarithms (base 10 and base e) and their properties
1.9. Elements of combinatorial calculus
1.10. Algebraic expressions and polynomials
1.11. Special products and the n-th power of a binomial
1.12. Factorization of polynomials
1.13. Algebraic fractions
1.14. First- and second-degree algebraic equations and inequalities
1.15. Systems of equations

2. Functions

2.1. Fundamental notions about functions and their graphic representations
2.2. Domain and codomain
2.3. Sign analysis
2.4. Continuity
2.5. Maxima and minima
2.6. Increasing and decreasing behavior
2.7. Elementary functions
2.7.1. Polynomial and rational
2.7.2. Exponential
2.7.3. Logarithmic
2.7.4. Trigonometric
2.8. Composite functions
2.9. Inverse functions
2.10. Trigonometric equations and inequalities

3. Geometry

3.1. Polygons and their properties
3.2. Circumference and circle
3.3. Measurement of lengths, surfaces, and volumes
3.4. Isometries, similarities, and equivalences in the plane
3.5. Geometric loci
3.6. Measurement of angles (degrees and radians)
3.7. Sine, cosine, tangent of an angle and notable values
3.8. Trigonometric formulas
3.9. Triangle solving
3.10. Cartesian coordinate system in the plane
3.11. Distance between two points and midpoint of a segment
3.12. Equation of the line
3.13. Conditions of parallelism and perpendicularity
3.14. Distance from a point to a line
3.15. Equations and representations in the Cartesian plane
3.15.1. Circumference
3.15.2. Parabola
3.15.3. Hyperbola
3.15.4. Ellipse
3.16. Pythagoras’ theorem
3.17. Euclid’s first and second theorems

Test Content

1. Numerical Sets and Algebra

1.1. Numerical sets: natural, integer, rational, real numbers

1.2. Ordering and comparison

1.3. Order of magnitude and scientific notation

1.4. Operations and their properties

1.5. Proportions and percentages

1.6. Powers with integer and rational exponents and their properties

1.7. Radicals and their properties

1.8. Logarithms (base 10 and base e) and their properties

1.9. Elements of combinatorial calculus

1.10. Algebraic expressions and polynomials

1.11. Special products and the n-th power of a binomial

1.12. Factorization of polynomials

1.13. Algebraic fractions

1.14. First- and second-degree algebraic equations and inequalities

1.15. Systems of equations

2. Functions

2.1. Fundamental notions about functions and their graphic representations

2.2. Domain and codomain

2.3. Sign analysis

2.4. Continuity

2.5. Maxima and minima

2.6. Increasing and decreasing behavior

2.7. Elementary functions

2.7.1. Polynomial and rational

2.7.2. Exponential

2.7.3. Logarithmic

2.7.4. Trigonometric

2.8. Composite functions

2.9. Inverse functions

2.10. Trigonometric equations and inequalities

3. Geometry

3.1. Polygons and their properties

3.2. Circumference and circle

3.3. Measurement of lengths, surfaces, and volumes

3.4. Isometries, similarities, and equivalences in the plane

3.5. Geometric loci

3.6. Measurement of angles (degrees and radians)

3.7. Sine, cosine, tangent of an angle and notable values

3.8. Trigonometric formulas

3.9. Triangle solving

3.10. Cartesian coordinate system in the plane

3.11. Distance between two points and midpoint of a segment

3.12. Equation of the line

3.13. Conditions of parallelism and perpendicularity

3.14. Distance from a point to a line

3.15. Equations and representations in the Cartesian plane

3.15.1. Circumference

3.15.2. Parabola

3.15.3. Hyperbola

3.15.4. Ellipse

3.16. Pythagoras’ theorem

3.17. Euclid’s first and second theorems

4. Probability and Statistics

4.1. Frequency distributions by variable type and main graphical representations

4.2. Random experiments and events

4.3. Probability and frequency

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