European Baccalaureate Mathematics (3-period course) cheat sheet

The written Baccalaureate comprises five papers: L1, L2, Mathematics, plus two option-specific written papers; each paper is marked out of 100 and the mark counts directly toward the final percentage.

Mathematics (3-period course) written paper: 3 hours, marked out of 100, weighted at 3 periods in the final total; the 5-period course sits a longer paper weighted at 5 periods.

Written papers are marked out of 100 and then multiplied by the subject's period weighting; the weighted sum is divided by the total periods to give the written examination average.

The Mathematics paper tests the full 3-period syllabus: functions and graphs, limits and continuity, differentiation and its applications, integration, sequences and series, probability and statistics, vectors and analytic geometry.

Calculators: only non-programmable, non-graphing calculators without symbolic algebra (CAS) are permitted; a graphing or CAS calculator leads to confiscation and possible invalidation of the paper.

L1 and L2 written papers each carry two components: a language/literature section (text analysis, essay) and, for L2, a translation or comprehension element; both components must be answered.

Answer structure: show all working in Mathematics - method marks are awarded independently of the final answer; an unsupported correct answer can lose most of the marks for that item.

Time allocation rule of thumb: minutes available divided by number of marks gives minutes per mark; a 100-mark, 180-minute paper allows about 1.8 minutes per mark, so a 10-mark question deserves roughly 18 minutes.

Three oral papers in total: one in L1, one in L2 (or in History/Geography taught through L2), and one further oral drawn from the candidate's subject combination.

Each oral is examined by at least two examiners (typically one internal, one external) and lasts about 20 minutes including preparation time outside the room.

L1/L2 orals assess spoken fluency, pronunciation, range of vocabulary, grammatical accuracy, and the ability to sustain and defend an argument on an unseen text or topic.

History/Geography through L2: the candidate presents a document or source in L2, then answers questions; marks reward both subject content and the quality of the L2 expression.

Typical preparation time is 15-20 minutes with the unseen material; notes may be taken into the room but must not be read aloud verbatim.

Marking uses a rubric: content/subject knowledge, language accuracy, fluency and interaction, and structure of the presentation; each criterion is scored separately and combined out of 100.

The oral mark is weighted by the periods of the subject concerned and enters the final total on the same weighted scale as written papers.

The preliminary mark combines A marks (continuous formative assessment during S7) and B marks (the Pre-Baccalaureate examination taken in S7), each recorded out of 100 per subject.

A marks reflect class tests, homework, projects, and oral participation during the S7 year; B marks come from the single Pre-Baccalaureate written examination in each subject.

The preliminary mark is normally A and B combined, commonly weighted 50/50 or 40/60 depending on the school's approved internal rules; the exact weighting is fixed at the start of the year.

The preliminary mark counts for a defined share of the final Baccalaureate result (commonly 20% for the subjects concerned), with the written and oral papers providing the remaining share.

A marks must be based on a documented, dated record of assessments; candidates have the right to see their A and B marks before they are transmitted.

If the Pre-Baccalaureate examination is missed for a documented medical reason, the school applies its published procedure, usually a substitute assessment or a reweighting of the A marks.

The preliminary mark is reported to the examination board and combined with the written and oral results; it cannot be changed after the board's deadline except through a formal appeal.

Derivative rules: (x^n)' = nx^(n-1); (e^x)' = e^x; (ln x)' = 1/x; (sin x)' = cos x; (cos x)' = -sin x; product, quotient and chain rules apply for composites.

Integration: ∫x^n dx = x^(n+1)/(n+1) + C for n ≠ -1; ∫1/x dx = ln|x| + C; definite integrals give signed area, so split at zeros when the geometric area is asked.

Limits: use factorisation, rationalisation, or l'Hôpital's rule (0/0 or ∞/∞ forms only); the derivative definition is lim(h→0)[f(x+h)-f(x)]/h.

Sequences: arithmetic u_n = u_1 + (n-1)d with sum n(u_1+u_n)/2; geometric u_n = u_1·r^(n-1) with sum u_1(1-r^n)/(1-r) for r ≠ 1.

Probability: P(A∪B) = P(A)+P(B)-P(A∩B); conditional P(A|B) = P(A∩B)/P(B); independence when P(A∩B) = P(A)P(B).

Statistics: mean, median, quartiles, variance and standard deviation; for a binomial B(n,p), mean = np and variance = np(1-p).

Vectors: dot product a·b = |a||b|cos θ; perpendicular when a·b = 0; line equation r = a + t·d; plane normal from a cross product.

Function study routine: domain, parity, limits at boundaries, derivative sign table, extrema, asymptotes, then sketch; each step earns marks even if the sketch is imperfect.

Structure an oral in three moves: state the thesis or main finding, develop two or three supporting points with evidence, close with a synthesis - this maps directly onto the rubric.

Fluency is scored on continuity and pace, not speed; self-correction is acceptable, long silent gaps and reading from notes are penalised.

Language accuracy in L2 orals: target control of tense and agreement; occasional errors are tolerated if communication remains clear.

In History/Geography through L2, cite the document explicitly (author, date, nature, source) before analysing it - this is a required first step in the marking grid.

Examiners' follow-up questions test the ability to justify and extend; prepare a short justification for each claim made in the presentation.

Pronunciation and intonation are assessed separately from grammar; practise reading aloud the key vocabulary of the chosen topic.

The oral counts within the weighted total on the same period scale as written papers; a strong oral can offset a weaker written performance in the same subject.