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Free Practice Questions for European Baccalaureate Mathematics (3-period course)

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Key Facts: European Baccalaureate Mathematics (3-period course) Exam

135 min

Total exam duration

OSGES European Schools Regulations

0–10

Grading scale

OSGES Marking Scheme

5.0 / 10

Minimum passing score

OSGES European Baccalaureate Rules

OSGES

Administering body

Office of the Secretary-General of the European Schools

S7 (Year 13)

Target education level

European Schools Secondary Cycle

100

Practice questions in this bank

OpenExamPrep

The European Baccalaureate Mathematics (3-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 (3-period course) Practice Questions

Try these sample questions to review concepts for the European Baccalaureate Mathematics (3-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 limit as x approaches infinity: lim_{x -> ∞} (6x^2 - 5x + 1) / (2x^2 + 3x - 4).
A.3
B.0
C.2
D.Infinity
Explanation: For rational functions where the degree of the numerator equals the degree of the denominator, the limit as x -> ∞ is the ratio of the leading coefficients. Dividing numerator and denominator by x^2 yields lim_{x -> ∞} (6 - 5/x + 1/x^2) / (2 + 3/x - 4/x^2) = 6 / 2 = 3.
2What is the derivative f'(x) of the polynomial function f(x) = 4x^3 - 5x^2 + 7x - 9?
A.12x^2 - 10x + 7
B.12x^2 - 5x + 7
C.4x^2 - 10x + 7
D.12x^3 - 10x^2 + 7x
Explanation: Applying the power rule d/dx(x^n) = n*x^(n-1) to each term gives: d/dx(4x^3) = 12x^2, d/dx(-5x^2) = -10x, d/dx(7x) = 7, and d/dx(-9) = 0. Combining these terms results in f'(x) = 12x^2 - 10x + 7.
3Find the derivative of the exponential function f(x) = e^(3x - 2).
A.e^(3x - 2)
B.3 * e^(3x - 2)
C.(3x - 2) * e^(3x - 3)
D.3 * e^(3x)
Explanation: Using the chain rule for exponential functions d/dx(e^u) = u' * e^u, where u = 3x - 2 and u' = 3, we get f'(x) = 3 * e^(3x - 2).
4If f(x) = ln(5x^2 + 2), what is f'(x)?
A.1 / (5x^2 + 2)
B.10x / (5x^2 + 2)
C.5x / (5x^2 + 2)
D.10x^2 / (5x^2 + 2)
Explanation: The derivative of ln(u) with respect to x is (1/u) * du/dx. Here u = 5x^2 + 2, so du/dx = 10x. Therefore, f'(x) = 10x / (5x^2 + 2).
5Find the slope of the tangent line to the curve y = x^3 - 3x + 2 at x = 2.
A.9
B.5
C.12
D.4
Explanation: The slope of the tangent line is given by the derivative dy/dx = 3x^2 - 3. Evaluating at x = 2 gives dy/dx|_(x=2) = 3(2)^2 - 3 = 12 - 3 = 9.
6What is the equation of the tangent line to y = x^2 - 4x + 5 at the point where x = 3?
A.y = 2x - 4
B.y = 2x - 1
C.y = 4x - 10
D.y = x - 1
Explanation: At x = 3, y = 3^2 - 4(3) + 5 = 2. The derivative is y' = 2x - 4, so at x = 3, slope m = 2(3) - 4 = 2. Using point-slope form: y - 2 = 2(x - 3) => y = 2x - 4.
7At what value of x does the quadratic function f(x) = x^2 - 6x + 8 achieve its local minimum?
A.x = 3
B.x = 6
C.x = 4
D.x = -3
Explanation: Setting the derivative f'(x) = 2x - 6 equal to zero gives 2x - 6 = 0 => x = 3. Since f''(x) = 2 > 0, x = 3 is a local minimum.
8Calculate the derivative of f(x) = (2x + 1) * e^x.
A.(2x + 1) * e^x
B.(2x + 3) * e^x
C.2 * e^x
D.(2x + 2) * e^x
Explanation: By the product rule d/dx(u * v) = u'v + uv', with u = 2x + 1 and v = e^x: f'(x) = 2 * e^x + (2x + 1) * e^x = (2 + 2x + 1)e^x = (2x + 3)e^x.
9Find f'(x) for the rational function f(x) = (3x - 1) / (x + 2).
A.7 / (x + 2)^2
B.5 / (x + 2)^2
C.(3x + 5) / (x + 2)^2
D.1 / (x + 2)^2
Explanation: Using the quotient rule d/dx(u/v) = (u'v - uv') / v^2: u = 3x - 1, u' = 3, v = x + 2, v' = 1. f'(x) = [3(x + 2) - (3x - 1)(1)] / (x + 2)^2 = (3x + 6 - 3x + 1) / (x + 2)^2 = 7 / (x + 2)^2.
10If f(x) = (3x^2 - 4)^4, what is the derivative f'(x)?
A.12x * (3x^2 - 4)^3
B.24x * (3x^2 - 4)^3
C.6x * (3x^2 - 4)^3
D.24x^2 * (3x^2 - 4)^3
Explanation: Applying the chain rule d/dx(u^4) = 4u^3 * u': u = 3x^2 - 4, so u' = 6x. Thus f'(x) = 4 * (3x^2 - 4)^3 * 6x = 24x * (3x^2 - 4)^3.

About the European Baccalaureate Mathematics (3-period course) Exam

The European Baccalaureate Mathematics (3-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.

35%

Functions & Differential Calculus

Polynomial, rational, exponential, and logarithmic functions, limits, derivative rules, tangent equations, monotonicity, local extrema, and optimization applications.

15%

Integral Calculus & Applications

Antiderivatives, indefinite and definite integrals, fundamental theorem of calculus, area under curves, area between curves, and average value of functions.

25%

Probability & Inferential Statistics

Descriptive statistics, conditional probability, Bayes' theorem, discrete random variables, binomial distribution, and normal distribution z-score calculations.

15%

Vectors, Geometry & Trigonometry

2D and 3D coordinate geometry, vector operations, scalar product, line equations, trigonometric ratios, sine/cosine rules, and radian measure.

10%

Sequences, Series & Financial Models

Arithmetic and geometric sequences and series, sum formulas, compound interest, exponential growth, decay, and financial applications.

Preparing for the European Baccalaureate Mathematics (3-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 (3-period course): Suggested Study Strategy

1Master the fundamental derivative rules (power, product, quotient, and chain rules) and practice finding equations of tangent and normal lines.
2Review optimization steps for economics and geometric problems by setting f'(x) = 0 and verifying extrema using the second derivative test.
3Practice probability tree diagrams, conditional probability P(A|B) = P(A ∩ B) / P(B), and Bayes' theorem applications.
4Familiarize yourself with standard normal z-score calculations Z = (X - μ) / σ and binomial distribution formulas B(n, p).
5Memorize sequence sum formulas S_n for arithmetic and geometric series, as well as compound interest A = P(1 + r)^n and exponential growth models.

Frequently Asked Questions

What is the European Baccalaureate Mathematics 3-period exam?

The European Baccalaureate Mathematics 3-period (MA3P) exam is the official mathematics assessment for secondary year 7 (S7) students in the European Schools system who take the 3-period standard course. It is set by the Office of the Secretary-General of the European Schools (OSGES).

What is the passing score for the EB Math 3P exam?

The European Baccalaureate uses a 0 to 10 scale (accurate to two decimal places). The passing score for the mathematics examination and the overall Baccalaureate diploma is 5.0 out of 10 (50%).

How long is the examination and what is its structure?

The exam lasts 135 minutes (2 hours 15 minutes). Part 1 is a 45-minute non-calculator section, while Part 2 is a 90-minute section where an approved technology tool (calculator) is permitted.

What calculator rules apply to the exam?

Part 1 does not allow any calculator or digital aids. In Part 2, standard scientific or graphing calculators approved by OSGES (without internet access or symbolic algebra / CAS capabilities unless explicitly authorized in exam regulations) are permitted.

What main topic areas are evaluated in Math 3P?

The syllabus covers five main areas: Functions & Differential Calculus (35%), Integral Calculus & Applications (15%), Probability & Inferential Statistics (25%), Vectors, Geometry & Trigonometry (15%), and Sequences, Series & Financial Models (10%).

In what language is the European Baccalaureate Math 3P exam written?

The European Baccalaureate exam papers are written in the student's L1/L2 working language (English, French, German, Spanish, Italian, Dutch, etc.). This OpenExamPrep question bank provides an English-language study adaptation.