Mathematics for the Academic Studies didactic units

DIDACTIC UNITS

Mathematics 3^rd E.S.O.

Página actualizada por última vez el 8 Agosto, 2024

DIDACTIC UNIT : CONTENTS:

Integers Definitions: absolut value, multiples and divisors, prime and composite numbers, LCM & GCF, etc. Operations with integers: addition, subtraction, multiplication and division. Hierarchy. Exercises.

Fractions Definitions: irreducible fraction, equivalent fractions, etc. Operations with fractions: addition, multiplication and division. Combined operations and hierarchy. Types of decimals, and their corresponding fraction. Directly proportional distribution problems. Compound rule of 3. Exercises.

Powers Positive-exponent powers. Laws of indexes. Negative-exponent powers. Scientific notation: operations and use of the calculator. Compound interest. Exercises.

Radicals Definition of n-th root. Equivalent roots & simplification of roots. Operations with roots. Like radicals. Classification of real numbers. Intervals. Approximations & errors. Exercises.

Sequences & progressions General term of a sequence. Arithmetic and geometric progressions. Sequences defined by a recurrence relation. The Fibonacci sequence. Exercises.

Polynomials Monomials: definitions and operations. Numerical value of a polynomial. Operations with polynomials: addition, products, quotients. Ruffini's rule. Taking out common factor. Notable products. Factoring polynomials using Ruffini's method. Exercises.

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

Functions Concept of function. Definitions. Graph of a f(x). Properties of a function: Domain and range, increasing intervals, maxima and minima, symmetry, continuity, intersection points with axes, tendency & asymptotes. Straight lines. Slope. Forms of expressing lines: general form, gradient-intercept form & point-slope form. Parabolas. Hyperbolas. Exercises.

Geometry Pythagoras theorem. Areas of shapes: triangles and quadrilaterals, polygons, circular figures. Surface areas & volumes: polyhedra, prisms, pyramids, cylinders, cones & sphere. Euler's formula. Exercises.

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.

Statistics Definitions. Frequencies and tables. Statistical graphs: column graphs, histograms, polygons, pie chart, etc. Measures of central tendency: mean, median, mode. Measures of spread: range, variance, standard deviation. Exercises.

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DIDACTIC UNIT :	CONTENTS:
Integers	Definitions: absolut value, multiples and divisors, prime and composite numbers, LCM & GCF, etc. Operations with integers: addition, subtraction, multiplication and division. Hierarchy. Exercises.
Fractions	Definitions: irreducible fraction, equivalent fractions, etc. Operations with fractions: addition, multiplication and division. Combined operations and hierarchy. Types of decimals, and their corresponding fraction. Directly proportional distribution problems. Compound rule of 3. Exercises.
Powers	Positive-exponent powers. Laws of indexes. Negative-exponent powers. Scientific notation: operations and use of the calculator. Compound interest. Exercises.
Radicals	Definition of n-th root. Equivalent roots & simplification of roots. Operations with roots. Like radicals. Classification of real numbers. Intervals. Approximations & errors. Exercises.
Sequences & progressions	General term of a sequence. Arithmetic and geometric progressions. Sequences defined by a recurrence relation. The Fibonacci sequence. Exercises.
Polynomials	Monomials: definitions and operations. Numerical value of a polynomial. Operations with polynomials: addition, products, quotients. Ruffini's rule. Taking out common factor. Notable products. Factoring polynomials using Ruffini's method. Exercises.
Equations and systems	1^st-degree equations. Complete and incomplete 2^nd-degree equations. Simultaneous equations: substitution, equating & elimination method. Exercises.
Functions	Concept of function. Definitions. Graph of a f(x). Properties of a function: Domain and range, increasing intervals, maxima and minima, symmetry, continuity, intersection points with axes, tendency & asymptotes. Straight lines. Slope. Forms of expressing lines: general form, gradient-intercept form & point-slope form. Parabolas. Hyperbolas. Exercises.
Geometry	Pythagoras theorem. Areas of shapes: triangles and quadrilaterals, polygons, circular figures. Surface areas & volumes: polyhedra, prisms, pyramids, cylinders, cones & sphere. Euler's formula. Exercises.
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.
Statistics	Definitions. Frequencies and tables. Statistical graphs: column graphs, histograms, polygons, pie chart, etc. Measures of central tendency: mean, median, mode. Measures of spread: range, variance, standard deviation. Exercises.