PAU Mathematics II (Galicia) study guide
PAU Mathematics II (Galicia) · Work through your exam, one topic at a time.
The PAU Mathematics II examination (ABAU in Galicia) is the subject-specific university access test taken by students from the Science and Technology baccalaureate track who want Mathematics to count toward their admission score for engineering, mathematics, physics, computer science, health sciences and similar degrees. It is a written, constructed-response paper: you solve open problems and show your reasoning, rather than picking answers from a list. The PAU Mathematics II (Galicia) study guide has 6 sections and about 2,776 words.
01Matrices, determinants and systems of linear equations
This block opens the PAU Galicia paper almost every year: a matrix equation, a determinant depending on a parameter, or a discussion of a linear system with a parameter followed by its solution in the solvable cases. Products and inverses : matrix product is not commutative; (AB)^T = B^T A^T and (AB)^(-1) = B^(-1)A^(-1).
469 words, about 2 min02Vectors and analytic geometry in three-dimensional space
One full question per option is usually geometric: relative positions of lines and planes, a perpendicular line or plane, and a distance or an angle. The algebra is short, so marks are lost when the geometry is not justified.
514 words, about 3 min03Limits, continuity and differentiation of real functions of one variable
This is the largest block of the paper: a limit or continuity question with a parameter, and a full analysis of a function (domain, asymptotes, monotonicity, extrema, curvature) or a Rolle/mean value theorem proof. Indeterminate forms : L'Hopital applies only to 0/0 and infinity/infinity, differentiating numerator and denominator separately.
459 words, about 2 min04Integral calculus and applications to area and volume
Each option usually contains one integral question: a direct antiderivative (rational function, substitution, integration by parts) or an applied area or volume of revolution. Barrow's rule : the definite integral from a to b of f is F(b) - F(a) for any antiderivative F.
469 words, about 2 min05Probability and combinatorial counting
Probability supplies one of the statistics questions in the paper: typically a conditional probability or Bayes problem with urns, dice or diagnostic tests, or a counting problem leading to the binomial distribution. Laplace's rule : probability equals favourable outcomes divided by possible outcomes, valid only when the outcomes are equally likely.
390 words, about 2 min06Statistical inference: sampling, estimation and hypothesis testing
Inference is examined as a confidence interval or a hypothesis test, usually finishing with a decision expressed in the context of the problem. The arithmetic is routine; the interpretation is where marks are gained or lost.
475 words, about 2 min