Mathematics for the Academic Studies didactic units

DIDACTIC UNITS

Mathematics 2^nd E.S.O.

Página actualizada por última vez el 3 Marzo, 2024

DIDACTIC UNIT : CONTENTS:

1. Integers, powers and roots Definitions: natural numbers, integers, opposite of an integer, absolute value. Operations with integers: addition, subtraction, multiplication and division. Hierarchy. Powers. Roots. Divisibility. Exercises.

2. Fractions Definitions: irreducible fraction, equivalent fractions, comparison of fractions. Operations with fractions: addition, subtraction, multiplication and division. Power and square root of a fraction. Combined operations. Exercises.

3. Decimals Definitions. Comparison of decimals. Decimal expression of a fraction. Decimals and their corresponding fraction. Operations with decimals: addition, subtraction, multiplication and division. Square root. Approximations. Scientific notation. Exercises.

4. Numerical proportionality and percentages Direct proportionality. Ratios and proportions. Direct rule of three. Inverse proportionality: inverse rule of three. Percentages. Exercises.

5. Polynomials Albebraic language. Monomials: definitions and operations. Numerical value of a polynomial. Operations with polynomials: addition, products, basic quotients. Taking out common factor. Notable products. Exercises.

6. Equations and simultaneous equations 1^st-degree equations. Complete and incomplete 2^nd-degree equations. Simultaneous equations: substitution, equating & elimination method. Exercises.

7. Geometry Geometrical proportionality. Thales' theorem. Similarity. Pythagoras theorem. areas of figures. Surface areas and volumes of solids. Euler's formula. . Exercises.

8.Statistics Definitions: population, sample, census. Types of variables: categorical, quantitative discrete or quantitative continuous. Frequencies and tables. Statistical graphs (histogram, column graph, polygon of frequencies, pie chart...). Central parameters (mean, median and mode) and dispersion parameters (range and mean deviation). 24 solved exercises.

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DIDACTIC UNIT :	CONTENTS:
1. Integers, powers and roots	Definitions: natural numbers, integers, opposite of an integer, absolute value. Operations with integers: addition, subtraction, multiplication and division. Hierarchy. Powers. Roots. Divisibility. Exercises.
2. Fractions	Definitions: irreducible fraction, equivalent fractions, comparison of fractions. Operations with fractions: addition, subtraction, multiplication and division. Power and square root of a fraction. Combined operations. Exercises.
3. Decimals	Definitions. Comparison of decimals. Decimal expression of a fraction. Decimals and their corresponding fraction. Operations with decimals: addition, subtraction, multiplication and division. Square root. Approximations. Scientific notation. Exercises.
4. Numerical proportionality and percentages	Direct proportionality. Ratios and proportions. Direct rule of three. Inverse proportionality: inverse rule of three. Percentages. Exercises.
5. Polynomials	Albebraic language. Monomials: definitions and operations. Numerical value of a polynomial. Operations with polynomials: addition, products, basic quotients. Taking out common factor. Notable products. Exercises.
6. Equations and simultaneous equations	1^st-degree equations. Complete and incomplete 2^nd-degree equations. Simultaneous equations: substitution, equating & elimination method. Exercises.
7. Geometry	Geometrical proportionality. Thales' theorem. Similarity. Pythagoras theorem. areas of figures. Surface areas and volumes of solids. Euler's formula. . Exercises.
8.Statistics	Definitions: population, sample, census. Types of variables: categorical, quantitative discrete or quantitative continuous. Frequencies and tables. Statistical graphs (histogram, column graph, polygon of frequencies, pie chart...). Central parameters (mean, median and mode) and dispersion parameters (range and mean deviation). 24 solved exercises.