100+ Free Bac Maths Spécialité Practice Questions

Pass your Baccalauréat Général — Spécialité Mathématiques (Terminale) exam on the first try — instant access, no signup required.

✓ No registration✓ No credit card✓ No hidden fees✓ Start practicing immediately

100+ Questions

100% Free

1 / 100

Question 1

Score: 0/0

The Terminale spécialité Mathématiques terminal written exam (épreuve écrite) lasts how long?

3 hours

2 hours

4 hours

5 hours

to track

Same family resources

Explore More French Baccalauréat

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

French Baccalauréat - Français (Épreuve Anticipée)

Practice Questions100 questions

French Baccalauréat Général - Histoire-Géographie, Géopolitique et Sciences Politiques (HGGSP)

Practice Questions100 questions

2026 Statistics

Key Facts: Bac Maths Spécialité Exam

A 4-hour written exam graded out of 20 with coefficient 16, made of 4 independent exercises spanning analysis, space geometry, probability and algorithmics; a new 2-hour anticipated Maths exam runs in Première from 2026.

Sample Bac Maths Spécialité Practice Questions

Try these sample questions to test your Bac Maths Spécialité exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1In the Terminale spécialité Mathématiques programme, the principle of reasoning by induction (raisonnement par récurrence) proves a property P(n) for all integers n greater than or equal to a starting value. Which two steps are required?

A.Show P is true for one large value of n

B.Differentiate P(n) and show the derivative is positive

C.Verify P at the starting value only

D.Initialisation (base case) and hérédité (inductive step P(n) implies P(n+1))

Explanation: A proof by recurrence has two parts: the initialisation, where you check P holds at the first integer, and the hérédité, where you assume P(n) and prove P(n+1). Both together guarantee P(n) for all n from the starting value onward.

2How many subsets (parties) of size 3 can be chosen from a set of 5 distinct elements? This is a combination, where order does not matter.

A.60

B.15

C.10

D.125

Explanation: The number of combinations is C(5,3) = 5! / (3! x 2!) = 10. Combinations count selections where order is irrelevant, which describes choosing a subset.

3A k-uplet (k-list) of elements chosen from a set with n elements, where repetition is allowed and order matters, can be formed in how many ways?

A.k^n

B.n! / (n-k)!

C.C(n,k)

D.n^k

Explanation: Each of the k positions can independently be any of the n elements, giving n x n x ... = n^k. This counts ordered lists with repetition allowed, as defined in the combinatoire section.

4Using Pascal's rule (la formule de Pascal), which identity relates binomial coefficients in the Terminale programme?

A.C(n,k) = n x C(n-1,k-1)

B.C(n,k) = C(n-1,k) x C(n-1,k-1)

C.C(n,k) = C(n,n-k)

D.C(n,k) + C(n,k+1) = C(n+1,k+1)

Explanation: Pascal's rule states C(n,k) + C(n,k+1) = C(n+1,k+1); it is the additive relation that generates Pascal's triangle (le triangle de Pascal). It lets each entry be built from the two above it.

5How many permutations (ways to order all elements) are there of a set of 4 distinct objects?

A.4

B.16

C.24

D.256

Explanation: The number of permutations of n distinct objects is n! For n = 4, 4! = 4 x 3 x 2 x 1 = 24.

6In the binomial theorem (formule du binome de Newton), the coefficient of a^k b^(n-k) in the expansion of (a+b)^n is:

A.n - k

B.k!

C.n^k

D.C(n,k)

Explanation: The binomial theorem states (a+b)^n = sum over k of C(n,k) a^k b^(n-k). The binomial coefficient C(n,k) is exactly the coefficient of each term.

7A set with n elements has how many subsets in total (the cardinal of its power set)?

A.n!

B.n^2

C.2^n

D.2n

Explanation: Each element is either in or out of a subset, giving 2 choices per element and 2^n subsets total. Equivalently, the sum of C(n,k) over all k equals 2^n.

8How many ways are there to arrange (order) 3 chosen objects taken from 7 distinct objects, with no repetition (an arrangement)?

A.343

B.21

C.35

D.210

Explanation: An ordered selection without repetition gives 7 x 6 x 5 = 210, which equals 7!/(7-3)!. Order matters, so this is larger than the number of combinations.

9Prove by induction that the sum 1 + 2 + ... + n equals n(n+1)/2. What is checked in the initialisation step for n = 1?

A.That the formula gives a positive value

B.That the derivative equals 1

C.That n(n+1)/2 is an integer for all n

D.That 1 = 1(2)/2 = 1, which holds

Explanation: Initialisation tests the base case n = 1: the left side is 1 and the right side is 1(1+1)/2 = 1, so P(1) is true. This anchors the induction before the inductive step.

10In set notation, if A and B are subsets of a universe, De Morgan's law gives the complement of (A union B) as:

A.A inter B

B.complement of (A inter B)

C.(complement of A) union (complement of B)

D.(complement of A) inter (complement of B)

Explanation: De Morgan's law states that the complement of a union is the intersection of the complements: not(A or B) = (not A) and (not B). This is part of the vocabulaire ensembliste et logique.

About the Bac Maths Spécialité Exam

The Spécialité Mathématiques is the most demanding mathematics course of the French baccalauréat général, studied 6 hours per week in Terminale and assessed by a 4-hour written exam graded out of 20 with coefficient 16. The Éduscol programme covers three thematic parts — Algèbre et géométrie, Analyse and Probabilités — plus two transversal parts: Vocabulaire ensembliste et logique, and Algorithmique et programmation (Python). The terminal exam presents 4 independent exercises drawn from analysis (suites, limites, dérivation, logarithme, primitives, intégration, équations différentielles), space geometry (vecteurs, droites, plans, produit scalaire), probability (loi binomiale, conditionnement, variables aléatoires, loi des grands nombres) and algorithmics. From the 2026 session a new anticipated written Mathématiques exam (2 hours, no calculator, coefficient 2) is also taken in Première. The spécialité is essential for science, engineering, economics and medical higher-education pathways.

Questions

100 scored questions

Time Limit

4 hours (terminal written exam)

Passing Score

Graded out of 20; the bac is awarded on a weighted average of 10/20 or more across all subjects, with this spécialité weighted coefficient 16.

Exam Fee

Free for enrolled lycée students and for candidats libres; no separate exam fee in France. (Ministère de l'Éducation nationale (France), via the académies)

Bac Maths Spécialité Exam Content Outline

35%

Analyse

Suites, limites, continuité, dérivation, convexité, logarithme, sinus/cosinus, primitives, équations différentielles, calcul intégral.

18%

Géométrie dans l'espace

Vecteurs, droites et plans, produit scalaire, orthogonalité et distances, représentations paramétriques et équations cartésiennes.

22%

Probabilités

Schéma de Bernoulli, loi binomiale, conditionnement et indépendance, variables aléatoires, concentration et loi des grands nombres.

12%

Algèbre et combinatoire

Combinatoire et dénombrement, triangle de Pascal, binôme de Newton, raisonnement par récurrence.

13%

Logique et algorithmique

Vocabulaire ensembliste et logique, et algorithmique/programmation en Python (boucles, seuil, dichotomie).

How to Pass the Bac Maths Spécialité Exam

What You Need to Know

Passing score: Graded out of 20; the bac is awarded on a weighted average of 10/20 or more across all subjects, with this spécialité weighted coefficient 16.
Exam length: 100 questions
Time limit: 4 hours (terminal written exam)
Exam fee: Free for enrolled lycée students and for candidats libres; no separate exam fee in France.

Keys to Passing

Complete 500+ practice questions
Score 80%+ consistently before scheduling
Focus on highest-weighted sections
Use our AI tutor for tough concepts

Bac Maths Spécialité Study Tips from Top Performers

1Master the named demonstrations the programme expects (récurrence, convergence of monotone bounded sequences, derivative of exp/ln) — they are regularly tested.

2Practise full written reasoning: in the bac, a justified method (property stated, hypotheses checked) earns marks even with a partial result.

3Drill the loi binomiale: know P(X=k) = C(n,k) p^k (1-p)^(n-k), E(X) = np and V(X) = np(1-p) until they are automatic.

4For géométrie dans l'espace, get fluent with the scalar product, normal vectors, Cartesian and parametric equations, and relative positions of lines and planes.

5Learn the croissances comparées limits (e^x/x to infinity, x ln x to 0) and the algebra of limits for suites and fonctions.

6Read and write short Python scripts: accumulation loops, threshold (seuil) searches and the dichotomy method are recurring exam items.

Frequently Asked Questions

How long is the Spécialité Mathématiques exam and how is it scored?

The terminal written exam lasts 4 hours and is graded out of 20. It is made of 4 independent exercises with progressive questions, and demonstrations are valued as much as the final result. The calculator is authorised in exam mode.

What coefficient does Spécialité Mathématiques carry in the bac général?

It carries coefficient 16, the heaviest weighting of the baccalauréat (tied with the candidate's second spécialité). The two spécialités together represent 32 of the 100 coefficient points.

What topics are on the Terminale spécialité programme?

The Éduscol programme covers Algèbre et géométrie (combinatoire, vecteurs/droites/plans, produit scalaire), Analyse (suites, limites, dérivation, logarithme, primitives, intégration, équations différentielles), Probabilités (loi binomiale, conditionnement, variables aléatoires, loi des grands nombres), plus logique ensembliste and Python algorithmics.

Are complex numbers in the spécialité programme?

No. Complex numbers (nombres complexes) are not in the Terminale spécialité Mathématiques programme; they belong to the option Mathématiques expertes taken in addition to the spécialité.

What is the new anticipated Maths exam in Première?

From the 2026 session, all Première students sit an anticipated written Mathématiques exam lasting 2 hours, graded out of 20, with coefficient 2 and no calculator. Spécialité maths students take a version aligned to their programme, plus their full Terminale spécialité exam the following year.

When are the bac 2026 spécialité exams held?

The spécialité written exams of the bac général 2026 are scheduled on 16, 17 and 18 June 2026; the Mathématiques exam takes place on one of these days, in the afternoon (14h–18h for the 4-hour paper).