THE SPANISH MATHS CURRICULUM OF BACHILLERATO16-18-year-old students
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
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
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
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.
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.
Mathematics IILinear Matrices. Operations. Inversion. EquationsAlgebra Determinants. Range of a matrix. Linear simultaneous equations. Discussion and resolution. Classification. Rouche- Frobenius Theorem. The Cramer rule.
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
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.
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.
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.
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
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
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.
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)