PAU Applied Mathematics for Social Sciences II - Canary Islands / ULPGC & ULL study guide
PAU Applied Mathematics for Social Sciences II - Canary Islands / ULPGC & ULL · Work through your exam, one topic at a time.
The PAU (Prueba de Acceso a la Universidad, widely still called Selectividad or EBAU) in Matemáticas Aplicadas a las Ciencias Sociales II is the university-entrance mathematics paper taken in the Canary Islands by students aiming at degrees in economics, business administration, law, sociology, tourism, accounting or similar social-science fields. It is set and coordinated by the public universities of the archipelago, principally the Universidad de Las Palmas de Gran Canaria and the Universidad de La Laguna, and it is one of the subjects that can count toward the admission score for those degrees. The PAU Applied Mathematics for Social Sciences II - Canary Islands / ULPGC & ULL study guide has 7 sections and about 2,880 words.
01Matrices and systems of linear equations
Matrices and systems of linear equations open the PAU Applied Mathematics for Social Sciences II paper in the Canary Islands. The exam asks you to multiply and invert matrices, compute a determinant and a rank, solve a matrix equation AX = B, and above all to discuss a linear system containing a parameter and then solve the consistent cases.
480 words, about 2 min02Linear programming in two variables
Linear programming in two variables is a certain exam question: translate a word problem into inequalities, draw the feasible region, optimise the objective at the vertices, and answer the duality or sensitivity part. Decision variables with x ≥ 0, y ≥ 0; each limited resource gives a ≤ inequality, each minimum requirement a ≥ inequality.
446 words, about 2 min03Limits, continuity and differentiation
Limits, continuity and differentiation form the calculus core of the paper: compute limits and remove indeterminacies, decide continuity (often with a parameter in a piecewise function), differentiate, and write the tangent line or interpret a rate of change. Indeterminacies 0/0, ∞/∞, ∞ − ∞, 0·∞ and 1^∞ are resolved by factorising, using a common denominator, multiplying by the conjugate, dividing by the highest power, or L'Hôpital when the form really is 0/0 or ∞/∞.
405 words, about 2 min04Applications of the derivative
The applications block turns derivatives into answers about shape and about economic decisions: intervals of increase and decrease, maxima and minima, concavity, inflection points, and the optimisation of cost, revenue and profit functions. f is increasing where f' 0 and decreasing where f' < 0; solve f' = 0 for the critical points and read the sign of f' on each subinterval.
408 words, about 2 min05Integration: antiderivatives, areas and accumulation
Integration in this paper is mainly computational and interpretive: find antiderivatives, apply Barrow's rule, compute the area between two curves, and explain the meaning of a definite integral of a marginal function. Standard antiderivatives: ∫x^n dx = x^(n+1)/(n+1) + C for n ≠ −1, ∫(1/x)dx = ln x + C, ∫e^x dx = e^x + C; linearity lets you split sums and pull out constants.
373 words, about 2 min06Probability: conditioning, total probability and Bayes
Probability questions combine counting with conditional reasoning: describe the sample space, count cases with the right combinatorial tool, then apply conditional probability, the total probability theorem and Bayes' theorem, usually through a tree or a two-way table. Laplace's rule P(A) = favourable/possible applies only when elementary outcomes are equiprobable.
352 words, about 2 min07Random variables, binomial and normal distributions
Random variables and distributions close the syllabus: model a discrete or continuous variable, compute expectation and variance, and use the binomial and normal models, including standardisation and the normal approximation to the binomial. Discrete X: P(X = x i) = p i with Σp i = 1; E[X] = Σx i p i; Var(X) = Σx i² p i − (E[X])²; σ = √Var.
416 words, about 2 min