PracticeVideosBlogFlashcardsEspañol
All Practice Exams

Free Practice Questions for European Baccalaureate Mathematics (5-period course)

Exam-style questions and explanations by OpenExamPrep.

✓ No registration✓ No credit card
Exam pass rate: 85-90%
100+ Questions
100% Free

Loading practice questions...

Same family resources

Explore More European Baccalaureate

Continue into nearby exams from the same family. Each card keeps practice questions, study guides, flashcards, videos, and articles in one place.

European Baccalaureate Ancient Greek

Practice Questions

European Baccalaureate Art

Practice Questions

European Baccalaureate Biology

Practice Questions

European Baccalaureate Chemistry

Practice Questions

European Baccalaureate Economics

Practice Questions

European Baccalaureate Geography

Practice Questions
Exam Review

Key Facts: European Baccalaureate Mathematics (5-period course) Exam

OSGES

Office of the Secretary-General of the European Schools

European Schools Governance

210 Mins

Total written exam duration (Part A + Part B)

OSGES EB Exam Regulations

Min 5.0

Minimum passing score out of 10.0

European Baccalaureate Marking Scale

5 Blocks

Analysis, Integrals/DEs, 3D Geometry, Probability, Complex Numbers

EB S6-S7 Math 5P Syllabus

100

Practice questions available in this OpenExamPrep bank

OpenExamPrep

The European Baccalaureate Mathematics (5-period course) is administered by the Office of the Secretary-General of the European Schools (OSGES). Official assessment involves written/oral components graded on a 0-10 scale (passing score 5.0). Local questions on OpenExamPrep are an English-language MCQ study adaptation designed for syllabus revision.

Sample European Baccalaureate Mathematics (5-period course) Practice Questions

Try these sample questions to review concepts for the European Baccalaureate Mathematics (5-period course) exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Evaluate the trigonometric limit: lim (x -> 0) [ sin(3x) / x ].
A.3
B.0
C.1
D.1/3
Explanation: Using the standard limit lim (u -> 0) [ sin(u) / u ] = 1, we rewrite sin(3x)/x as 3 * [ sin(3x) / (3x) ]. As x -> 0, 3x -> 0, so the limit equals 3 * 1 = 3.
2Find the derivative of the function f(x) = x^3 * e^(2x).
A.(3x^2 + 2x^3) * e^(2x)
B.6x^2 * e^(2x)
C.3x^2 * e^(2x)
D.(3x^2 + x^3) * e^(2x)
Explanation: By the product rule d/dx[u v] = u'v + uv', with u = x^3 and v = e^(2x), we get f'(x) = 3x^2 e^(2x) + x^3 (2e^(2x)) = (3x^2 + 2x^3) e^(2x).
3Find the equation of the tangent line to the curve y = x^2 - 4x + 5 at the point where x = 3.
A.y = 2x - 4
B.y = 2x - 1
C.y = 3x - 7
D.y = x - 1
Explanation: At x = 3, y = 3^2 - 4(3) + 5 = 2. Slope m = y'(3) = 2(3) - 4 = 2. Tangent line: y - 2 = 2(x - 3) => y = 2x - 4.
4Find the critical points of the function f(x) = 2x^3 - 9x^2 + 12x + 1.
A.x = 1 and x = 2
B.x = -1 and x = -2
C.x = 0 and x = 3
D.x = 3/2 and x = 2
Explanation: Setting f'(x) = 6x^2 - 18x + 12 = 6(x - 1)(x - 2) = 0 gives critical points x = 1 and x = 2.
5Determine the vertical asymptote of f(x) = (2x + 1) / (x - 4).
A.x = 4
B.x = 2
C.y = 4
D.y = 2
Explanation: Vertical asymptotes occur where denominator x - 4 = 0 and numerator 2(4)+1 = 9 != 0, giving line x = 4.
6Find the derivative of f(x) = ln(x^2 + 1).
A.2x / (x^2 + 1)
B.1 / (x^2 + 1)
C.x / (x^2 + 1)
D.2 / (x^2 + 1)
Explanation: By chain rule, d/dx[ln(u)] = u'/u with u = x^2 + 1 (u' = 2x), giving f'(x) = 2x / (x^2 + 1).
7Find the horizontal asymptote of f(x) = (3x^2 - 5) / (2x^2 + 1).
A.y = 3/2
B.y = -5
C.y = 0
D.x = 3/2
Explanation: Equal degrees in numerator and denominator mean horizontal asymptote is y = 3/2.
8Find the point of inflection of the curve f(x) = x^3 - 6x^2 + 9x.
A.(2, 2)
B.(1, 4)
C.(3, 0)
D.(2, 0)
Explanation: f''(x) = 6x - 12 = 0 => x = 2. f(2) = 8 - 24 + 18 = 2. Thus (2, 2) is the inflection point.
9Evaluate lim (x -> 0) [ (e^(2x) - 1 - 2x) / x^2 ] using L'Hôpital's rule.
A.2
B.1
C.4
D.0
Explanation: L'Hôpital once: lim (2e^(2x) - 2)/(2x). L'Hôpital twice: lim (4e^(2x))/2 = 4/2 = 2.
10Find the derivative of f(x) = arctan(3x).
A.3 / (1 + 9x^2)
B.1 / (1 + 9x^2)
C.3 / (1 + 3x^2)
D.1 / sqrt(1 - 9x^2)
Explanation: d/dx[arctan(u)] = u'/(1 + u^2) with u = 3x (u' = 3, u^2 = 9x^2) gives 3 / (1 + 9x^2).

About the European Baccalaureate Mathematics (5-period course) Exam

The European Baccalaureate Mathematics (5-period course) evaluates S6-S7 European Baccalaureate candidates on official OSGES syllabus learning outcomes. Note: Official examinations consist of written constructed-response papers and oral assessments; the 100 questions provided here are an English-language MCQ study adaptation for core concept revision.

Exam sponsor: Office of the Secretary-General of the European Schools (OSGES). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Official written paper and/or oral examination; 100 local practice MCQs for self-assessment.

Time Limit

180 minutes (3 hours)

Passing Score

5.0 out of 10.0 (50%)

Exam / Certification Fees

EUR 111.49 Baccalaureate registration fee

Exam sponsor website

Reported exam pass rate: 85-90%. This describes exam candidates, not OpenExamPrep users or results from using our resources. Exam sponsor website

Fees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.

Official sources

Our practice resources: topics covered

We aim to reflect publicly available exam outlines and topic information in our study resources. Coverage, format, and difficulty may differ from the actual exam, and we cannot guarantee that every detail is accurate or current. Confirm exam requirements, fees, and policies with the official exam sponsor.

25%

Analysis & Differential Calculus

Functions, limits, continuity, derivative rules, L'Hôpital's rule, implicit differentiation, tangent & normal lines, curve sketching, extrema, concavity, points of inflection, and optimization problems.

25%

Integral Calculus & Differential Equations

Indefinite & definite integrals, integration by substitution, integration by parts, partial fractions, areas bounded by curves, volumes of solids of revolution, arc length, separable and linear 1st order differential equations, and initial value problems.

20%

3D Vector Geometry & Analytical Geometry

3D Cartesian coordinates, vector operations, dot product, cross product, scalar triple product, parametric & symmetric line equations, Cartesian plane equations, distances, angles, relative positions, and spheres.

15%

Probability & Inferential Statistics

Combinatorics, permutations, combinations, conditional probability, Bayes' theorem, discrete random variables, Binomial distribution B(n,p), continuous random variables, and Normal distribution N(mu, sigma^2).

15%

Complex Numbers & Sequences/Series

Complex arithmetic, modulus and argument, polar/exponential forms, De Moivre's theorem, complex polynomial roots, transformations in the complex plane, arithmetic & geometric sequences, series sums, and sequence limits.

Preparing for the European Baccalaureate Mathematics (5-period course) Exam

What You Need to Know

  • Passing score: 5.0 out of 10.0 (50%)
  • Assessment: Official written paper and/or oral examination; 100 local practice MCQs for self-assessment.
  • Time limit: 180 minutes (3 hours)
  • Exam / certification fees: EUR 111.49 Baccalaureate registration fee Official sources

Using Our Practice Resources

  • Work through all 100 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
  • Use our AI tutor for tough concepts

European Baccalaureate Mathematics (5-period course): Suggested Study Strategy

1Master Part A non-calculator fundamentals: Practice exact arithmetic, logarithmic properties, exact trigonometric values, and basic calculus steps without relying on software.
2Flawless 3D vector algebra: Memorize distance formulas, cross-product matrix determinants, and the setup for point-to-plane and skew-line distance calculations.
3Integration technique recognition: Learn to immediately identify whether an integral requires substitution, integration by parts, or partial fractions decomposition.
4Stat & probability fluency: Practice Bayes' Theorem tree diagrams and standard normal z-score calculations with precision.
5Complex plane transformations: Fluently convert between rectangular (a + bi), polar r(cos theta + i sin theta), and exponential r*e^(i theta) forms.

Frequently Asked Questions

What is the passing mark for the European Baccalaureate Math 5P exam?

The European Baccalaureate grading system uses a scale of 0 to 10. The minimum passing mark is 5.0 out of 10.0 (equivalent to 50%).

How long is the written examination for Mathematics 5P?

The official written examination lasts 210 minutes (3 hours 30 minutes). Part A (non-calculator) is approximately 45–60 minutes, and Part B (with technological tool) is 150–165 minutes.

What technological tools are permitted during Part B of the exam?

Candidates are allowed to use approved Technological Tools such as GeoGebra (in official Exam Mode) or graphic display calculators (such as TI-Nspire CX CAS in Press-to-Test mode) compliant with OSGES regulations.

How is the final grade in Mathematics 5P calculated?

The final subject mark is composed of coursework internal assessments (S6 and S7 preliminary marks, class tests) combined with the final Baccalaureate written exam (and oral exam if chosen).

Is the European Baccalaureate Math 5P recognized by European and global universities?

Yes, the European Baccalaureate is fully recognized by universities across the EU, UK (UCAS), US, Canada, and worldwide as a premier pre-university diploma. Math 5P is accepted for competitive STEM, engineering, economics, and science degree programs.

How does this OpenExamPrep question bank help candidates prepare?

Our question bank translates the full OSGES Math 5P syllabus into 100 rigorous multiple-choice questions with step-by-step solutions and diagnostic wrong-answer explanations covering both non-calculator concepts and complex multi-step analytical problems.