The document describes the mathematics curriculum for 16-18 year old students in Spain. It is divided into 4 sections: Mathematics I, Mathematics II, Applied Mathematics I, and Applied Mathematics II. The courses cover topics such as algebra, geometry, analysis, statistics, probability, matrices, and functions. Students can choose either science and technology or social studies itineraries.

1. THE SPANISH MATHS
CURRICULUM OF
BACHILLERATO
16-18-year-old students

2. Bachillerato. 16-18- year-old students
Post- compulsory secondary education
Matemáticas I
Science and Technology itineraries
Matemáticas II
Matemáticas Aplicadas a
las Ciencias Sociales I
Social studies itineraries
Matemáticas Aplicadas a
las Ciencias Sociales II

3. Mathematics I
Arithmetics  The Reals. Abosute value. Inequalities. The number
and 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. Mathematics I
Geometry 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. Mathematics I
Analysis 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. Mathematics I
Statistics  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. Mathematics II
Linear  Matrices. Operations. Inversion. Equations
Algebra  Determinants.
 Range of a matrix.
 Linear simultaneous equations. Discussion
and resolution. Classification. Rouche-
Frobenius Theorem. The Cramer rule.

8. Mathematics II
Geometry  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. Mathematics II
Analysis  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. Applied Mathematics I
Arithmetics  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. Applied Mathematics I
Analysis  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. Applied Mathematics I
Statistics  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. Applied Mathematics II
Algebra  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. Applied Mathematics II
Analysis  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. Applied Mathematics II
Statistics  Random events. Operations
and  Probability. Compound events. Conditioned
Probability 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)