Goals:

• Provide adapted, organized, and targeted material for new students.
• To offer, throughout the academic year, a study and learning platform that complements or corrects possible deficiencies in necessary knowledge, and that can be reviewed when detected and required.

This course is aimed at newly enrolled students who have identified gaps in the content of the 2nd year of Bachillerato curriculum. As a guide, we recommend taking this course if you meet any of the following conditions:

• You have obtained a score lower than 7 in the subject Mathematics II in the PAU or 2nd year of Baccalaureate.
• You have left unstudied some sections of the syllabus for the subject Mathematics II.
• Clearly identify that you have deficiencies in the management of the subject of mathematics.

Timing: Throughout the academic year (available from July 25, 2025).

Mode: Online

Registration: New students will be sent a message with registration instructions.

Organization and contentsThis course is completely voluntary and free of charge. It is offered online and has no time limit, but we recommend completing it before the official start of classes for the 2025-26 academic year.

It has a modular structure and can be completed sequentially (module by module in order, which is what we recommend) or selectively (only the modules of interest, for those who wish to address a specific knowledge gap).
The course content is organized into 5 blocks:

• Block 1: Numbers and operations
  Numbers, exponents, radicals, and scientific notation. Algebraic expressions, notable identities, and equations.
• Block 2: Geometry
  Plane figures. Solid bodies. Surfaces and volumes. Trigonometry. Vectors, lines, and planes in the plane and in space.
• Block 3: Algebra
  Matrices and systems of linear equations. Matrix algebra. Inverses of matrices and matrix equations. Determinants. Cramer's rule
• Block 4: Functions. Differential Calculus
  Basic functions. Elementary transformations. Rate of change. Limits. Derivatives. Applications
• Block 5: Integral Calculus
  Indefinite Integration: Primitives. Indefinite Integral. Immediate Integrals. Integration by Substitution. Integration by Parts. Integrals of Rational Functions.

You can access each block in any order you wish, but in each block you will have to complete questionnaires.

Methodology: Each block consists of the following teaching materials:

• PDF Notes: Very visual, very graphic, with definitions, properties, examples and exercises.
• Videos explaining the material in the notes.
• Videos with typical problem solving.
• Sheets of proposed problems.
• Progress quizzes: As you achieve the minimum score on your attempts, you'll be able to access subsequent content.

Evaluation and certificationTo obtain the certificate of completion, at least the 75% course quizzes must be completed and an average grade of at least 5 points obtained. Once these requirements are met, a certificate of completion worth 3 credits will be issued.

Credits: 3 ECTS

CommunicationThe course has a forum where you can ask questions about the course.
For any questions or individual queries regarding the organization of the course, you can contact the course coordinator at the following email address: cursoceromat@ull.edu.is