Mathematics for the Academic Studies didactic units

DIDACTIC UNITS

Mathematics 2^nd E.S.O.

Página actualizada por última vez el 2 Agosto, 2024

DIDACTIC UNIT : CONTENTS:

1. Operations with integers Definitions: natural numbers, integers, opposite of an integer, absolute value. Operations with integers: addition, subtraction, multiplication and division. Hierarchy. Exercises.

2. Powers and roots Properties of powers. Operations with powers. Definition of nth root. Properties of roots. Operations with roots. Exercises.

3. Divisibility Divisibility criteria. Multiples and divisors. Prime and composite numbers. GCF and LCM. Exercises.

4. 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.

5. 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.

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

7. 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.

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

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

10. Probability Definitions: sample space, types of events, etc. Operations with events: union and intersection. Laws of the operations among events. Laplace's rule. Laws of probability. Compound events. Tree diagrams. Exercises.

11. 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.

12. Functions Concept of function. Definitions. Graph of a f(x). Increasing intervals, maxima and minima. Straight lines. Slope. Parabolas. Hyperbolas. Exercises.

I will greatly appreciate your detected errata submitted here to

I welcome your feedback: alfonsogonzalopez@yahoo.es

Powered by:

Hosted by:

El contenido de esta página requiere una versión más reciente de Adobe Flash Player.

DIDACTIC UNIT :	CONTENTS:
1. Operations with integers	Definitions: natural numbers, integers, opposite of an integer, absolute value. Operations with integers: addition, subtraction, multiplication and division. Hierarchy. Exercises.
2. Powers and roots	Properties of powers. Operations with powers. Definition of nth root. Properties of roots. Operations with roots. Exercises.
3. Divisibility	Divisibility criteria. Multiples and divisors. Prime and composite numbers. GCF and LCM. Exercises.
4. 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.
5. 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.
6. Numerical proportionality and percentages	Direct proportionality. Ratios and proportions. Direct rule of three. Inverse proportionality: inverse rule of three. Percentages. Exercises.
7. 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.
8. Equations and simultaneous equations	1^st-degree equations. Complete and incomplete 2^nd-degree equations. Simultaneous equations: substitution, equating & elimination method. Exercises.
9. Geometry	Geometrical proportionality. Thales' theorem. Similarity. Pythagoras theorem. areas of figures. Surface areas and volumes of solids. Euler's formula. . Exercises.
10. Probability	Definitions: sample space, types of events, etc. Operations with events: union and intersection. Laws of the operations among events. Laplace's rule. Laws of probability. Compound events. Tree diagrams. Exercises.
11. 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.
12. Functions	Concept of function. Definitions. Graph of a f(x). Increasing intervals, maxima and minima. Straight lines. Slope. Parabolas. Hyperbolas. Exercises.