Madrid PAU Applied Mathematics for Social Sciences II

It tests applied mathematics for social sciences: matrices, determinants and systems; linear programming; limits, continuity, derivatives and function optimization; definite integrals and areas; probability and conditional probability; random variables and the normal distribution; and sampling with confidence intervals. Expect to justify each step rather than give only a final number.

It is a written paper where you choose among alternative questions within sections and must show working for full credit. The exact number of questions, the alternatives offered and the scoring breakdown are set by the official Madrid examination body, which publishes the current model and instructions; check its site before planning your timing.

Those figures change and are fixed by the official body, so no reliable number can be given here. The Comunidad de Madrid publishes the current duration, scoring criteria and any pass or grading rules on its official PAU/EuAv pages. Treat any number you hear second-hand as unverified.

Regional rules govern calculators, and they can change between sittings. The official instructions for your year state which models are allowed and which functions are prohibited. Practise with the calculator you will actually bring, and do not depend on it for algebraic steps that must be shown.

It is noticeably harder: the algebra becomes systems discussion, calculus adds optimization and areas, and probability moves into conditional probability, distributions and inference. The difficulty is less about exotic theory and more about applying standard techniques accurately and quickly under exam conditions.

Yes, Spanish university access allows repeated attempts in later sittings, and you normally keep your best valid mark for admission purposes. The number of sittings per year, the deadlines and how long marks remain valid are published by the official body and by the universities you apply to.

Start with matrices and systems, since the techniques recur and build confidence. Then do linear programming, which is largely graphical and quick to master. Move to calculus, then integration and areas, then probability and distributions, and finish with inference, which is short but conceptually dense.

Skipping working, not stating the method or the criterion used, arithmetic slips in determinants and integrals, forgetting to check feasible-region vertices in linear programming, ignoring the continuity condition in piecewise functions, and misreading whether a probability question asks for a conditional or a joint value.

Do full past papers under timed conditions, then mark them strictly against the official solutions and criteria. Keep an error log by topic and redo the questions you failed a week later. Aim to be able to start any question within a minute and to write a clean, complete solution without hesitation.