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# The maths curriculum bachillerato

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### The maths curriculum bachillerato

1. 1. THE SPANISH MATHS CURRICULUM OF BACHILLERATO16-18-year-old students
2. 2. Bachillerato. 16-18- year-old studentsPost- compulsory secondary education Matemáticas IScience and Technology itineraries Matemáticas II Matemáticas Aplicadas a las Ciencias Sociales I Social studies itineraries Matemáticas Aplicadas a las Ciencias Sociales II
3. 3. Mathematics IArithmetics  The Reals. Abosute value. Inequalities. The numberand Algebra line. Distances and intervals  The Complex Numbers. Cartesian and polar forms. operations. Representation on the Plane.  Sequences. Limits. Number e. Logarithms.  The Binomial Theorem. Polynomials. Factoring polynomials. Algebraic fractions. Operations.  Equations and inequalities  Simultaneous linear equations. Gaussian elimination
4. 4. Mathematics IGeometry Trigonometry.- trigonometric ratios for any kind of angles. Trigonometric identities. Sine and cosine theorems. Solving triangles. Word problems. Use of variables to represent numbers in formulae Vectors on the plane. Operations. Distances on the plane. The dot product. The straight line on the plane. Forms. Parallel and perpendicular lines. Distances and angles Loci on the plane. The conic sections
5. 5. Mathematics IAnalysis Real functions. Polynomial, Rational, Trigonometric, exponential and logarithmic functions Domain, Image, monotony, and extremes. Composing functions. Reciprocal functions. Limits and continuity. Types of discontinuity. Asymptotes Derivatives. Local extremes Graphing functions. Studying function through its global characteristics  Interpreting functions that describe real situations.
6. 6. Mathematics IStatistics  Bivariate distributions. Correlation coefficients.and Regression line.Probability  Covariance.  Composed, conditioned and total probability.  Distribution of probability of discrete random variables. The binomial distribution  Distribution of probability of continuous random variables. The Standard distribution  Using the tables to solve problems of probability.
7. 7. Mathematics IILinear  Matrices. Operations. Inversion. EquationsAlgebra  Determinants.  Range of a matrix.  Linear simultaneous equations. Discussion and resolution. Classification. Rouche- Frobenius Theorem. The Cramer rule.
8. 8. Mathematics IIGeometry  Vectors on R3. The dot product. The cross product. The mixed product. Geometric meaning and analytic expression.  Equations of lines and planes on the 3D space  Incidence, parallelism and perpendicularity of lines and planes  Resolution of metric problems relates to angles, distances, areas and volumes
9. 9. Mathematics IIAnalysis  Limits of sequences and functions.  Continuity. Types of discontinuity  Derivative of a function at a point. Function derivative. Geometric view of the derivative.  Applying derivatives to the study of functions.  Primitive of a function. Definite integral of a function. The Barrow Theorem.  Applying integrals to calculate areas.
10. 10. Applied Mathematics IArithmetics  Rational and irrational numbers.and Algebra Rounding. Errors.  The Real line. Intervals. The standard form  Financial problems. Simple and compound interest. Annuity. Economical and financial indices  Polynomial equations.  Linear simultaneous equations. The Gaussian elimination method.
11. 11. Applied Mathematics IAnalysis  Real functions.  Interpolation and extrapolation.  Polynomial, inverse, exponential, and logarithmic, functions. Piece-wise functions.  Limits. Tendencies and continuity. Studying discontinuities  Derivative. Derivative of polynomial functions.
12. 12. Applied Mathematics IStatistics  Univariate data. Kind of variables. Graphs and tablesd.and Parameters.Probability  Bivariate data. Scatter-plot. Correlation. Linear regresion.  Random events. Probability.  Random variables.  Discrete random distributions. The binomial distribution.  Continuous random variables. The standard distribution
13. 13. Applied Mathematics IIAlgebra  Matrices. Operations. Inversion.  Using matrices to organize information and solve problems  Solving and discussing simultaneous equations by Gaussian elimination  Univariate and bivariate inequalities and simultaneous inequalitities.  Linear programming
14. 14. Applied Mathematics IIAnalysis  Limit of a function. Tendencies. Solving indeterminate forms of limits  Continuity. Types of discontinuity.  Derivative of a function at a point. Function derivative.  Applying derivatives to the local study of functions.  Optimization word problems  Studying and graphing functions  Introduction of the concept of Integral. Calculating areas by definite integrals.
15. 15. Applied Mathematics IIStatistics  Random events. Operationsand  Probability. Compound events. ConditionedProbability probability. Bayes’ formula  The central limit theorem. Approximating a binomial distribution as a standard. Law of Great Numbers.  Sampling. Population. Parameters.  Mean and proportion of a samples distribution.  Confidence intervals (for p in a binomial or m in normal distributions)  Hypothesis testing (for the proportion in a binomial and for the mean or difference of means in a standard distribution)