Mathematics: method, justification and exact values
Mathematics is a compulsory written examination of the European Baccalaureate, set on a common syllabus across the language sections, so the content and the notation expected are the same whether you are taught in English, French or German. The paper mixes short technical questions with longer multi-part problems, and marks are awarded for method, justification and correct notation, not only for the final number.
Core content
- Analysis: limits and continuity, derivatives (product, quotient, chain rule), full curve study with sign tables, asymptotes and extrema, integration by substitution and by parts, areas between curves.
- Algebra and geometry: vectors, lines and planes in space, systems of equations, sequences, complex numbers where the section programme includes them.
- Probability and statistics: conditional probability, independence, binomial distribution, expected value, and interpretation of a result in the context of the problem.
Worked example
Compute the integral from 0 to 1 of x·e^(-x) dx.
Reasoning: integrate by parts with u = x and dv = e^(-x)dx, so du = dx and v = -e^(-x). Then the antiderivative is -x·e^(-x) + the integral of e^(-x) dx, that is -x·e^(-x) - e^(-x). Evaluate at 1: -1/e - 1/e = -2/e. Evaluate at 0: 0 - 1 = -1. Subtract: (-2/e) - (-1) = 1 - 2/e, approximately 0.264. Checks worth doing: choose u so that it becomes simpler on differentiation; track the minus signs from v; note that the integrand is positive on the interval, so a negative result signals an error.
Traps
- Stating a limit or an asymptote without algebraic justification; the justification is where the marks sit.
- Rounding inside the calculation. Give the exact value first, then the decimal approximation to the accuracy requested.
- Forgetting domain restrictions (denominators, square roots, logarithms) and units in applied questions.
- Ignoring 'hence' and 'deduce' parts, which are designed to use the previous result; a fresh independent calculation often earns nothing.
- Losing the constant of integration in indefinite integrals, or the sign of an area lying below the axis.