Mathematics for Academic Studies 4º ESO

Book overview

Credits

1. Real numbers
Real numbers. Properties of powers

Interactive revision activities on the properties of powers. {j}
Real numbers. Radicals

5 exercises to reinforce knowledge of radicals. {j}
Real numbers. Rationalisation of denominators

Exercises to practice the rationalisation of fractions. {j}
Juega con los números I

Problema para pensar, aprender y reflexionar acerca de las técnicas básicas de resolución de ejercicios matemáticos con números sencillos.{j}
Juega con los números II

Problema para pensar, aprender y reflexionar acerca de las técnicas básicas de resolución de ejercicios matemáticos con números sencillos.{j}
Juega con los números III

Problema para pensar, aprender y reflexionar acerca de las técnicas básicas de resolución de ejercicios matemáticos con números sencillos.{j}
Juega con los números IV

Problema para pensar, aprender y reflexionar acerca de las técnicas básicas de resolución de ejercicios matemáticos con números sencillos.{j}
Juega con los números V

Problema para pensar, aprender y reflexionar acerca de las técnicas básicas de resolución de ejercicios matemáticos con números sencillos.{j}

2. Polynomials and algebraic factions
Polynomials and algebraic fractions

Interactive activities to practice operation of addition, subtraction and polynomial products. {j}
Polynomials and algebraic fractions. The application of Ruffini's rule

Interactive activities to practice division using Ruffini's rule. {j}
Polynomials and algebraic fractions. Notable identities

Interactive activities to reinforce operations with notable identities. {j}
Polynomials and algebraic fractions. Calculation of the GCD and LCM

Interactive activities to practice the greatest common divisor and the least common multiple of two polynomials. {j}
Echa cuentas I

Problema para pensar, aprender y reflexionar acerca de las técnicas básicas de resolución de ejercicios matemáticos.{j}
Echa cuentas II

Problema para pensar, aprender y reflexionar acerca de las técnicas básicas de resolución de ejercicios matemáticos.{j}

3. Equations, inequations and systems
Equations, inequations and systems. Solving first-degree equations

Interactive activities to reinforce solving first degree equations. {j}
Equations, inequations and systems.

An animation and interactive activity to understand how to obtain a second degree equation. {j}
Equations, inequations and systems. Solving equations and problems

Interactive activities and problems to reinforce concepts related to second degree equations. {j}
Equations, inequations and systems. Solving biquadratic equations.

Interactive activities to reinforce solving biquadratic equations. {j}
Equations, inequations and systems. Equations with x in the denominator.

Interactive activities to reinforce solving equations in which there is an unknown in the denominator. {j}
Equations, inequations and systems. Solving equations with radicals.

Interactive activities to reinforce solving equations with radicals. {j}
Equations, inequations and systems. Solvable equations by factorization.

Interactive activities to practice solving equations using factoring. {j}
Equations, inequations and systems. Problem solving with equations

Interactive problems in which a solution must be found by implicitly placing the equations in the statement and, subsequently, solving them. {j}
Echa cuentas I

Problema de introducción al temario para pensar, aprender y reflexionar.{j}
Echa cuentas II

Problema de introducción al temario para pensar, aprender y reflexionar.{j}
Echa cuentas III

Problema de introducción al temario para pensar, aprender y reflexionar.{j}
Echa cuentas IV

Problema de introducción al temario para pensar, aprender y reflexionar.{j}

4. Functions. Characteristics
Functions. Expand: The domain of definition of a function

Activities to introduce the concept of the domain of a function. {j}
Functions. Reinforcement: Domain of definition of a function

Activities to expand on and reinforce the concept of the domain of a function. {j}
Functions. Interpreting graphs

Activity to reinforce the interpretation of graphs. {j}
Mira bien las figuras I

Problema para aprender, reflexionar y desarrollar la capacidad visual crítica de figuras con contenido matemático.{j}
Mira bien las figuras II

Problema para aprender, reflexionar y desarrollar la capacidad visual crítica de figuras con contenido matemático.{j}

5. Basic functions
Basic Functions. The point-slope equation of a line

Activities to review the point-slope equation of a straight line. {j}
Basic Functions. Extend: translation of a parabola

Reinforcement activities to practice the translation of parabolas. {j}
Basic functions. Expand: translation of a hyperbola

Reinforcement activities to practice the translations of hyperbolas. {j}
Echa cuentas I

Problema para pensar, aprender y reflexionar los métodos básicos de resolución de problemas matemáticos sin emplear conocimientos de la unidad.{j}
Echa cuentas II

Problema para pensar, aprender y reflexionar los métodos básicos de resolución de problemas matemáticos sin emplear conocimientos de la unidad.{j}
Echa cuentas III

Problema para pensar, aprender y reflexionar los métodos básicos de resolución de problemas matemáticos sin emplear conocimientos de la unidad.{j}

6. Similarity. Applications
Similarity. Application. Reinforce: similarity of triangles

Activities to practice the similarity of triangles. {j}
Similarity. Application. Problem solving

Extension activities for solving problems related to areas and volumes by applying similarity. {j}
Similarity. Calculation of lengths, areas and volumes of similar figures

nteractive problems to practice the concept of similarity (Lengths, areas and volumes of similar figures). {j}
Similarity. Application. Leg and altitude Theorems

Interactive problems to practice Cathetus (leg) and altitude theorems. Applications of the similarity of triangles. {j}
Mira bien las figuras I

Problema para pensar, aprender, reflexionar y desarrollar la capacidad visual crítica aplicada a figuras de contenido matemático.{j}
Mira bien las figuras II

Problema para pensar, aprender, reflexionar y desarrollar la capacidad visual crítica aplicada a figuras de contenido matemático.{j}
Mira bien las figuras III

Problema para pensar, aprender, reflexionar y desarrollar la capacidad visual crítica aplicada a figuras de contenido matemático.{j}

7. Trigonometry
Trigonometry. Using a calculator

Interactive activities to practice using a calculator in trigonometry problems. {j}
Trigonometry. Solving right-angled triangles

Activities and interactive problems to solve right-angled triangles using trigonometric ratios. {j}
Trigonometry. Trigonometric ratios of any angles

Interactive activities to calculate any angle and to reinforce calculating trigonometric ratios using the goniometric circumference. {j}
Mira bien las figuras I

Problema para pensar, aprender, reflexionar y desarrollar la capacidad visual crítica aplicada a figuras con contenido matemático.{j}
Mira bien las figuras II

Problema para pensar, aprender, reflexionar y desarrollar la capacidad visual crítica aplicada a figuras con contenido matemático.{j}
Resolución de triángulos rectángulos

Hoja de cálculo para la resolución de triángulos rectángulos.{j}

Analytic geometry
Geometry. Reinforce: Equations of straight lines

Practice and reinforcement of straight line equations parallel to the coordinate axes, intersection points, parallelism... {j}
Geometry. Mid-point of a segment

Activity to calculate the midpoint of a segment. {j}
Geometry. Aligned points

Activity to understand the concept of aligned points. {j}
Geometry. Distance between two points

Reinforcement and practice of the distance between two points. {j}
Geometry. Straight lines, parallelism and perpendicularity

The reinforcement of parallelism and perpendicularity between straight lines. {j}
Mira bien las figuras I

Problema para pensar, aprender, reflexionar y desarrollar la capacidad visual crítica aplicada a figuras con contenido matemático.{j}
Mira bien las figuras II

Problema para pensar, aprender, reflexionar y desarrollar la capacidad visual crítica aplicada a figuras con contenido matemático.{j}
Mira bien las figuras III

Problema para pensar, aprender, reflexionar y desarrollar la capacidad visual crítica aplicada a figuras con contenido matemático.{j}
Mira bien las figuras IV

Problema para pensar, aprender, reflexionar y desarrollar la capacidad visual crítica aplicada a figuras con contenido matemático.{j}
Mira bien las figuras V

Problema para pensar, aprender, reflexionar y desarrollar la capacidad visual crítica aplicada a figuras con contenido matemático.{j}

9. Statistics
Statistics. Reinforcement: calculation of the x, σ and C.V.

{j}
Statistics. Reinforcement: Calculating measures of position.

Exercise to reinforce the calculation of measures of location. {j}
Statistics. The elaboration of tables of frequency

Interactive activities to reinforce the elaboration of frequency tables with isolated and grouped data {j}
Statistics. Confidence level - amplitude of confidence interval

Interactive Activities for linking the size of the sample, the confidence level and the size of the confidence interval. {j}
Haz un esquema I

Problema en los que se deben aplicar esquemas o diagramas para su resolución.{j}
Haz un esquema II

Problema en los que se deben aplicar esquemas o diagramas para su resolución.{j}
Tablas de frecuencias, gráficos y cálculo de parámetros estadísticos.

Hojas de cálculo para hallar la media, la varianza, la desviación típica y el coeficiente de variación de una muestra dada de valores discretos y agrupados en intervalos.{j}
Cálculo de medidas de posición introduciendo valores

Hojas de cálculo para hallar medidas de posición.{j}
Cálculo de medidas de posición introduciendo valores y frecuencias

Hoja de cálculo para hallar medidas de posición.{j}
Estimación de la media

Ejercicio en el que se debe estimar la media a partir de valores elegidos de una muestra.{j}

10. Two-dimensional distributions
Two-dimensional distributions. Correlation

Activity to understand and learn how to apply the concept of correlation. {j}
Two-dimensional distributions. Interpretation, point cloud

Activity to understand the concept of correlation and learn how to interpret a scatter diagram or point cloud. {j}
Two-dimensional distributions. Correlation value

Exercise to practice and understand the value of the correlation. {j}
Two-dimensional distributions. The regression line for making estimates

Extension (II): calculating the regression line. {j}
Lógica I

Problema de lógica para pensar y reflexionar usando las capacidades matemáticas elementales antes de enfrentarse a una unidad.{j}
Lógica II

Problema de lógica para pensar y reflexionar usando las capacidades matemáticas elementales antes de enfrentarse a una unidad.{j}

11. Combinatorics
Combinatorics. Product-based strategies

Activity for practicing and reinforcing diverse strategies to solve mathematical problems without using knowledge from this unit. {j}
Combinatorics. When order does not influence

Activity in which the concepts of variations, combinations and permutations are reinforced. {j}
Combinatorics. Expand: factorial and combinatorial numbers

Activity to delve into factorials and combinatorial numbers. {j}
Combina, prueba, tantea... I

Actividad con la que practicar y reforzar diversas estrategias para resolver problemas matemáticos sin emplear conocimientos de la unidad.{j}
Combina, prueba, tantea... II

Actividad con la que practicar y reforzar diversas estrategias para resolver problemas matemáticos sin emplear conocimientos de la unidad.{j}
Combina, prueba, tantea... III

Actividad con la que practicar y reforzar diversas estrategias para resolver problemas matemáticos sin emplear conocimientos de la unidad.{j}
Combina, prueba, tantea... IV

Actividad con la que practicar y reforzar diversas estrategias para resolver problemas matemáticos sin emplear conocimientos de la unidad.{j}

12. Calculating probability
Statistics. Calculation of simple probabilities

Interactive activities to reinforce the calculation of probabilities using Laplace's law. {j}
Statistics. Distinction between dependent and independent experiences

Interactive activities to reinforce the distinction between dependent and independent experiences. {j}
Probability. Reinforce: relationships between an event and its opposite

Activities to reinforce the relationship between an event and its opposite. {j}
Probability. Review: random experiment, sample space and event

Introductory exercises: sample space, random events. {j}
Probability. Reinforce: Calculating probabilities with independent experiences.

Activities to reinforce the calculation of probabilities with independent experiences. {j}
Probability. Tree diagram

Extension activities on the calculation of probabilities in dependent experiences using tree diagrams. {j}
Probability. Reinforce: Contingency tables

Activity on working with contingency tables. {j}
Combina, prueba, tantea... I

Actividad con la que practicar y reforzar diversas estrategias para resolver problemas matemáticos sin emplear conocimientos de la unidad.{j}
Combina, prueba, tantea... II

Actividad con la que practicar y reforzar diversas estrategias para resolver problemas matemáticos sin emplear conocimientos de la unidad.{j}
Tablas de contingencia

{j}

Mathematics for Academic Studies 4º ESO

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