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Libro Digital
Audio: Unit 1. Real numbers
Vídeo: Real numbers
Audio: 1. Irrational numbers (I)
Interactive activity: Recognising irrational numbers
Key concepts: Irrational numbers
Audio: 1. Irrational numbers (II)
Interactive activity: Irrational numbers
Audio: 2. Real numbers: the real number line (I)
Interactive activity: The set of real numbers
Key concepts: Real numbers
Audio: 2. Real numbers: the real number line (II)
GeoGebra: Using Thales' theorem to represent fractional numbers
GeoGebra: Using the Pythagorean theorem to represent radicals
Interactive activity: Representing fractional numbers
Audio: 3. Sections of the real number line: intervals and half-lines (I)
Interactive activity: Open, closed and half-open intervals
Key concepts: Intervals
Audio: 3. Sections of the real number line: intervals and half-lines (II)
GeoGebra: Intervals on the real numbers line
Interactive activity: Intervals and half-lines
Interactive activity: Intervals on the real number line
Key concepts: Half-lines
Audio: 4. Roots and radicals (I)
Interactive activity: Activities for reviewing the properties of powers
Interactive activity: Radicals in exponential form
Key concepts: Roots and radicals
Audio: 4. Roots and radicals (II)
Interactive activity: Practise operations with radicals
Audio: 4. Roots and radicals (III)
Interactive activity: Activities to consolidate your knowledge of radicals
Interactive activity: Adding and subtracting radicals
Interactive activity: Operating with radicals
Audio: 4. Roots and radicals (IV)
Interactive activity: Consolidate your knowledge with some new rationalisation exercises
Interactive activity: Rationalising denominators
Interactive activity: Rationalising the denominator
Audio: 5. Approximate numbers. Errors
Interactive activity: Absolute and relative error
Key concepts: Approximations and errors
Interactive activity: Limit of absolute and relative error
Interactive activity: Practise calculating errors
Audio: 6. Numbers in scientific notation. Error control (I)
Interactive activity: Product and quotient with scientific notation
Key concepts: Scientific notation
Video: Scientific notation
Audio: 6. Numbers in scientific notation. Error control (II)
Interactive activity: Addition and subtraction with scientific notation
Interactive activity: Operations with numbers in scientific notation
Audio: 7. Logarithms (I)
Key concepts: Logarithms
Audio: 7. Logarithms (II)
Interactive activity: Logarithms
Interactive activity: Practise calculating logarithms
Audio: 7. Logarithms (III)
Key concepts: Outline
Learn by playing: Scientific notation
Answer key for the self-assessment (in Spanish)
SDG commitment. Target 4.6.
Libro Digital
Audio: Unit 2. Polynomials and algebraic fractions
Video: Polynomials and algebraic fractions
Audio: 1. Polynomials. Operations (I)
Interactive activity: Notable identities
Interactive activity: Polynomials
Interactive activity: Practise adding and subtracting polynomials
Audio: 1. Polynomials. Operations (II)
Interactive activity: Dividing polynomials
Interactive activity: Practise dividing polynomials
Key concepts: Division of polynomials
Videotutorial: Dividing polynomials
Audio: 2. Ruffini's rule (I)
Interactive activity: Activities for consolidating the application of Ruffini's rule
Interactive activity: Dividing polynomials. Ruffini's rule
Audio: 2. Ruffini's rule (II)
Interactive activity: Practise dividing using Ruffini's rule
Interactive activity: Remainder theorem
Spreadsheet: Applications of Ruffini's rule
Audio: 3. Root of a polynomial. Finding roots
Interactive activity: Integer roots of a polynomial
Interactive activity: Checking integer roots of a polynomials
Interactive activity: Practise finding the roots of a polynomial
Audio: 4. Factorising polynomials
Interactive activity: Factorising polynomials using Ruffini's rule
Interactive activity: Roots of a polynomial
Key concepts: Factorising polynomials
Video: Riffini's rule as a factoring tool
Interactive activity: Factorising polynomials
Interactive activity: Practise factorising polynomials
Audio: 5. Divisibility of polynomials (I)
Interactive activity: Dividing polynomials
Key concepts: Divisibility of polynomials
Audio: 5. Divisibility of polynomials (II)
Interactive activity: Calculating the GCD and LCM of polynomials
Interactive activity: Consolidating the GCD and LCM of polynomials
Interactive activity: GCD and LCM of two polynomials
Audio: 6. Algebraic fractions (I)
Interactive activity: Simplify algebraic fractions
Interactive activity: Simplifying algebraic fractions
Key concepts: Algebraic fractions
Audio: 6. Algebraic fractions (II)
Interactive activity: Operating with algebraic fractions
Interactive activity: Operations with algebraic fractions
Audio: 7. Decomposition of algebraic fractions into partial fractions (I)
Key concepts: Decomposition of algebraic fractions
Audio: 7. Decomposition of algebraic fractions into partial fractions (II)
Interactive activity: Decomposing algebraic fractions
Interactive activity: Decomposition of algebraic fractions into partial fractions
Key concepts: Outline
Learn by playing: Finding roots of a polynomial
Answer key for the self-assessment (in Spanish)
SDG commitment. Target 3.9b
Libro Digital
Audio: Unit 3. Equations, inequations and systems
Video: Equations
Interactive activity: Review solving first-degree equations
Audio: 1. Equations (I)
Interactive activity: Second-degree equations
Interactive activity: Second-degree equations and problems to practise methods for solving them
Interactive activity: Solving second-degree equations
Key concepts: Equations
Videotutorial: Second-degree equations
Audio: 1. Equations (II)
Interactive activity: Biquadratic equations
Interactive activity: Practise solving biquadratic equations
Interactive activity: Practise solving equations with x in the denominator
Interactive activity: Solving biquadratic equations
Audio: 1. Equations (III)
Interactive activity: Equations with radicals
Interactive activity: Practise solving equations with radicals
Audio: 1. Equations (IV)
Interactive activity: Exponential and logarithmic equations
Interactive activity: Solving exponential equations
Interactive activity: Solving logarithmic equations
Audio: 1. Equations (V)
Interactive activity: Factorised equations
Interactive activity: Practise solving problems with equations
Interactive activity: Practise using factorisation to solve equations
Audio: 2. Systrems of equations (I)
Interactive activity: Systems of linear equations
Key concepts: Systems of equations
Video: What is a system of equations?
Audio: 2. Systrems of equations (II)
Interactive activity: Systems of non-linear equations
Interactive activity: Systems of exponential equations
Interactive activity: Systems of logarithmic equations
Audio: 3. Inequations with one unknown (I)
Interactive activity: Integer solutions to an inequation
Key concepts: Inequations and systems of inequations
Audio: 3. Inequations with one unknown (II)
GeoGebra: Solving inequations by using graphs
Interactive activity: Solving inequations using graphs
Audio: 3. Inequations with one unknown (III)
Interactive activity: Reinforce your knowledge on how to solve inequations
Interactive activity: Using algebra to solve an inequation
Audio: 3. Inequations with one unknown (IV)
GeoGebra: Solving systems of inequations
Interactive activity: Solving systems of inequations
Key concepts: Outline
Learn by playing: Translating statements
Answer key for the self-assessment (in Spanish)
SDG commitment. Target 5.2.
Libro Digital
Audio: Unit 4. Functions. Characteristics
Video: Functions. Characteristics
Audio: 1. Basic concepts
Interactive activity: Basic concepts of functions
Interactive activity: Range of a function
Key concepts: Function
Audio: 2. How functions are presented (I)
Interactive activity: Functions presented as graphs
Interactive activity: Work on interpreting graphs
Key concepts: How a function is presented
Audio: 2. How functions are presented (II)
GeoGebra: Functions defined using tables of values
Audio: 2. How functions are presented (III)
Interactive activity: Functions presented as analytical expressions
Audio: 3. Domain of definition
Interactive activity: Domain of definition
Interactive activity: Domain of definition of a function
Interactive activity: Review calculating domains of definition of a function
Interactive activity: Work on calculating domains of definition
Key concepts: Domain and range
Audio: 4. Continuous functions. Discontinuities
GeoGebra: Continuous and discontinuous funtions
Interactive activity: Continuous functions
Key concepts: Continuity
Video: Continuity and discontinuity
Audio: 5. Increase, maximums and minimums (I)
Interactive activity: Increase, maximums and minimums
Key concepts: Increase, maximums and minimums
Videotutorial: Relative maximums and minimums
Audio: 5. Increase, maximums and minimums (II)
GeoGebra: Average rate of change
Interactive activity: Average rate of change (ARC)
Audio: 6. Tendency and periodicity (I)
Key concepts: Tendency and periodicity
Audio: 6. Tendency and periodicity (II)
GeoGebra: Periodic functions
Interactive activity: Periodic functions
Key concepts: Outline
Learn by playing: Graphs
Answer key for the self-assessment (in Spanish)
SDG commitment. Target 7.2.
Libro Digital
Audio: Unit 5. Basic functions
Video: Linear and quadratic functions
Audio: 1. Linear functions (I)
GeoGebra: Graphic representation of a straight line
Interactive activity: Graphing linear functions
Key concepts: Linear functions
Video: Equations of a line
Audio: 1. Linear functions (II)
GeoGebra: Calculating the slope of a line
Interactive activity: Review the point-slope equation
Audio: 1. Linear functions (III)
GeoGebra: Graphing piecewise linear functions
Interactive activity: Graphing piecewise linear functions
Audio: 2. The parabola, a very interesting curve
Interactive activity: Linear and quadratic functions
Audio: 3. Quadratic functions. Parabolas (I)
Interactive activity: Further theory and practice on the translation of parabolas
Interactive activity: Quadratic functions
Key concepts: Quadratic functions
Videotutorial: Parabolas and quadratic functions
Audio: 3. Quadratic functions. Parabolas (II)
GeoGebra: Graphing quadratic functions
Interactive activity: Graphing quadratic functions
Audio: 3. Quadratic functions. Parabolas (III)
Interactive activity: Lines and parabolas
Audio: 4. Absolute value functions
Interactive activity: Graphing absolute value functions
Key concepts: Absolute value functions
Audio: 5. Radical functions
Interactive activity: Radical functions
Key concepts: Radical functions
GeoGebra: Graphing radical functions
Interactive activity: Graphing radical functions
Audio: 6. Inversely proportional functions (I)
Interactive activity: Inversely proportional functions
Key concepts: Inversely proportional functions
Audio: 6. Inversely proportional functions (II)
GeoGebra: Graph inversely proportional functions
Interactive activity: Extension. Translation of hyperbolas
Interactive activity: Graphing inversely proportional functions
Audio: 7. Exponential functions (I)
GeoGebra: Graphing exponential functions
Interactive activity: Graphing exponential functions
Key concepts: Exponential functions
Audio: 7. Exponential functions (II)
Interactive activity: Exponential functions. Applications
Audio: 8. Logarithmic functions
GeoGebra: Graphing logarithmic functions
Interactive activity: Graphing logarithmic functions
Key concepts: Logarithmic functions
Key concepts: Outline
Learn by playing: Linear and quadratic functions. Memory game
Answer key for the self-assessment (in Spanish)
Interactive self-assessment
SDG commitment. Target 6.a.