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)