Maths Terminale Study Sheets 2026

Maths Spécialité Terminale — Complete Revision Guide 2026

The Bac maths exam lasts 4 hours (coefficient 16) with 3-5 independent exercises covering the full program.

Sequences

Arithmetic: u(n) = u(0) + nr, sum = (n+1)(u(0)+u(n))/2. Geometric: u(n) = u(0)×q^n, sum = u(0)(1−q^(n+1))/(1−q).

Proof by induction: initialisation, heredity (assume P(n), prove P(n+1)), conclusion.

Limits and Continuity

Key limits: e^x dominates x^n, x^n dominates ln(x). Intermediate Value Theorem: if f is continuous on [a,b] and k is between f(a) and f(b), then f(c) = k for some c in [a,b]. If f is strictly monotonic, the solution is unique.

Derivatives

Key derivatives: (x^n)' = nx^(n-1), (e^x)' = e^x, (ln x)' = 1/x, (sin x)' = cos x, (cos x)' = -sin x. Chain rule: (u∘v)' = v'×u'(v). Product: (uv)' = u'v + uv'. Quotient: (u/v)' = (u'v-uv')/v².

Applications: sign of f' gives variation table, f'(a) = 0 with sign change → extremum, tangent: y = f'(a)(x-a) + f(a).

Exponential Function

Unique function where f' = f, f(0) = 1. Properties: e^(a+b) = e^a×e^b, e^x > 0. Limits: e^x → +∞ (x→+∞), e^x → 0 (x→-∞).

Natural Logarithm

ln is the inverse of exp. ln(1) = 0, ln(e) = 1, ln(ab) = ln(a)+ln(b). Derivative: (ln x)' = 1/x. Limits: ln(x) → +∞ (x→+∞), ln(x) → -∞ (x→0⁺).

Integration

Integral from a to b of f = F(b) - F(a). Geometric meaning: area under curve. Integration by parts: ∫u'v = [uv] - ∫uv'. Mean value: μ = (1/(b-a))∫f.

Probability

Binomial distribution B(n,p): P(X=k) = C(n,k)p^k(1-p)^(n-k). E(X) = np, V(X) = np(1-p). Law of large numbers: observed frequency → theoretical probability as n → ∞.

3D Geometry

Parametric line: (x,y,z) = (x₀,y₀,z₀) + t(a,b,c). Plane equation: ax+by+cz+d = 0 with normal vector (a,b,c). Dot product: u·v = x₁x₂+y₁y₂+z₁z₂. Orthogonality: u·v = 0. Distance from point to plane: |ax₀+by₀+cz₀+d|/√(a²+b²+c²).