PAU Applied Math ACS II (Galicia) study guide
PAU Applied Math ACS II (Galicia) · Work through your exam, one topic at a time.
The PAU Applied Mathematics for Social Sciences II examination is the Galician university-access test taken by students on the social-science baccalaureate track who need a mathematics score for admission. It is also used by candidates improving their access grade or switching degree pathways. The PAU Applied Math ACS II (Galicia) study guide has 7 sections and about 3,185 words.
01Matrices, Determinants and Systems of Linear Equations
This domain covers matrix algebra (sum, product, transpose, powers, inverse), determinants up to order 3, rank, and the discussion and solution of linear systems. In the Galician PAU for Matemáticas Aplicadas ás Ciencias Sociais II the recurring items are a matrix equation such as AX + B = C, a system depending on a parameter a that must be discussed with the Rouché–Capelli theorem, and a 2×2 or 3×3 system solved by Cramer's rule or Gaussian elimination.
508 words, about 3 min02Functions: Limits, Continuity and Differentiation (Optimisation and Tangent Lines)
This domain tests limits, asymptotes, continuity (including piecewise functions with a parameter), derivative rules, the tangent line, monotonicity and extrema, and optimisation of functions taken from economic or social contexts. A 0/0 indeterminate form is resolved by factoring and cancelling, or by L'Hôpital's rule, which is valid only for 0/0 and ∞/∞.
450 words, about 2 min03Integral Calculus and Areas Under Curves
This domain covers antiderivatives (immediate integrals, linearity, simple substitution), the definite integral and Barrow's rule, and the computation of areas: between a curve and the x-axis and between two curves. Exam items almost always ask for the area of a region defined by a parabola and a line, or by a curve and the axes.
463 words, about 2 min04Probability: Conditional Probability, Independence, Bayes and Distributions
This domain tests the algebra of events, conditional probability, independence, the total probability theorem and Bayes' theorem (usually through a tree diagram or a contingency table), and the binomial and normal distributions with their parameters and tables. P(A ∪ B) = P(A) + P(B) − P(A ∩ B); the last term vanishes only for mutually exclusive events.
386 words, about 2 min05Descriptive Statistics: Univariate and Bivariate Data, Correlation and Regression
This domain tests summary measures for one variable (mean, median, mode, variance, standard deviation, coefficient of variation, quartiles), and for two variables the scatterplot, covariance, Pearson correlation coefficient and the least-squares regression line, together with their interpretation. Mean: x̄ = Σxᵢ/N, or Σxᵢfᵢ/N with frequencies.
483 words, about 2 min06Mathematical Modelling and Problem Solving in Social Science Contexts
This domain tests the translation of a statement in economic or social language into functions, equations and inequalities, and the interpretation of the result. Typical settings are costs, revenue and profit, price–demand functions, break-even analysis, tariffs, loans and populations.
414 words, about 2 min07Linear Programming and Feasible Regions (Graphical Method)
This domain tests the formulation and graphical solution of two-variable linear programming problems: objective function, constraints, feasible region, vertices and the fundamental theorem of linear programming, plus the interpretation of the optimum. Define x and y with units (quantities of two products, hours on two machines, hectares of two crops).
481 words, about 2 min