Basque PAU Mathematics II

It is a written paper with open-response problems, answered by hand with full working shown. Questions are usually organised so that you choose among alternatives within a block. You must justify each step: an unsupported final answer earns little, while a correct method with an arithmetic slip still earns partial credit.

The duration and the scoring rules are set each year by the Basque education authority, and the weighting of the mathematics paper depends on the degree you are applying for. Those figures change, so consult the official body's website for the current values rather than relying on older information.

It is a demanding paper, but the difficulty lies in fluency and precision rather than in obscure theory. The syllabus is small and predictable. Candidates who lose marks usually do so through sign errors, unverified parameters, or skipped justifications, not because the problems are unfamiliar.

Resit arrangements are governed by the current regulations of the Basque Country, and the rules on how many times and when you may sit again are updated periodically. Check the official body's site for the applicable conditions in your year, and plan your preparation assuming you may need a second sitting.

Start with matrices and determinants, because linear systems and much of geometry depend on them. Then move to vectors and analytic geometry in space, which rewards careful formula work. Follow with limits and derivatives, then integrals, which build on differentiation. Leave probability and statistics last, as it is largely independent.

Most often from mixing up the different products, forgetting to check whether lines are parallel before using a distance formula, or failing to state the geometric condition being used. Write the formula first, substitute second, and always comment on what the result means - a distance, an angle, or a position.

Use Gaussian elimination and track the parameter carefully, then apply Rouché–Capelli to classify the system. State explicitly the values of the parameter that give no solution, one solution, or infinitely many, and solve the indeterminate cases. Examiners look for that complete discussion, not just a final answer.

Past papers are the best single resource, but only if you sit them under timed conditions and mark them against the published criteria. Doing five papers slowly is worth less than doing three properly timed and then rewriting the questions you got wrong. Keep an error log of recurring mistakes.

A scientific calculator is normally permitted, but the paper is designed so that the reasoning matters more than the arithmetic. Do not rely on it for algebraic manipulation, and check the current rules on permitted models with the official body before the exam day.

No. This is independent study material written for candidates preparing for the exam. It is not affiliated with or endorsed by the Basque education authority or any university, and the official regulations always take precedence over anything here.