PAU Applied Mathematics for Social Sciences II (Cantabria) study plan

Perform matrix addition, scalar multiplication, and multiplication, verifying dimension compatibility.

Compute determinants of 2×2 and 3×3 matrices using cofactor expansion and the rule of Sarrus.

Calculate the inverse of a square matrix using the adjoint method and the Gauss-Jordan method.

Determine the rank of a matrix by reducing it to row echelon form.

Solve systems of linear equations using Cramer's rule, matrix inversion, and Gaussian elimination.

Classify a linear system as consistent or inconsistent using the Rouché–Capelli theorem.

Solve systems with one or more parameters, expressing the solution in terms of the parameter.

Model a word problem (e.g., mixture, investment, or production) as a system of linear equations and solve it.

Interpret the solution of a system in the context of the original problem, checking for feasibility constraints.

Formulate a linear programming problem from a verbal description, identifying decision variables, objective function, and constraints.

Graph the feasible region for a two-variable problem, including finding the vertices algebraically.

Solve linear programming problems graphically, including cases with unbounded regions and multiple optimal solutions.

Apply the simplex method to standard maximization problems with slack variables.

Interpret the optimal solution and the meaning of slack variables in context.

Solve integer and mixed-integer linear programming problems by branch and bound for small cases.

Compute limits of polynomial, rational, exponential, and logarithmic functions at finite points and at infinity.

Identify and classify discontinuities (removable, jump, infinite) from a function's expression.

Apply the intermediate value theorem to prove the existence of roots.

Determine the domain and range of functions involving radicals, logarithms, and absolute values.

Compute derivatives using the product, quotient, and chain rules.

Differentiate implicit and logarithmic functions.

Find equations of tangent lines and normal lines at a given point.

Apply the first and second derivative tests to determine intervals of increase/decrease and concavity, and to locate extrema and inflection points.

Solve optimization problems (e.g., maximizing area or minimizing cost) by setting up and differentiating an objective function.

Compute indefinite integrals using standard formulas, substitution, and integration by parts.

Apply the fundamental theorem of calculus to evaluate definite integrals.

Calculate the area between two curves, including choosing the correct integration limits.

Use the mean value theorem for integrals and interpret the average value of a function.

Solve applied problems involving areas (e.g., consumer and producer surplus, or profit over time).

Apply the axioms of probability and the addition and multiplication rules to compute probabilities of events.

Use conditional probability, the law of total probability, and Bayes' theorem to solve problems.

Define discrete and continuous random variables, and compute their mean, variance, and standard deviation.

Work with the binomial and normal distributions, including standardization and use of tables.

Solve problems involving the normal approximation to the binomial distribution.

Complete a timed mock exam under conditions similar to the PAU (90 minutes) covering all six domains.

Identify and review the two weakest domains based on mock exam performance.

Re-solve incorrectly answered problems from the mock exam, writing out the correct reasoning.

Summarize key formulas and procedures for each domain on a single reference sheet.

Practice time management by allocating minutes per problem type.