Brevet Maths Revision Sheets 2026

Brevet Mathematics — Complete Revision Guide 2026

The French Brevet maths exam lasts 2 hours and is scored out of 100 points. It covers the entire cycle 4 curriculum (Years 9-11 in the French system), with emphasis on the final year. The exam contains five to seven independent exercises spanning four domains: numbers and calculations, geometry, functions, and statistics-probability. An algorithmic exercise using Scratch is always included.

1. Numbers and Calculations

Fractions

Master all four operations with fractions:

• Addition/Subtraction: find a common denominator. Example: 2/3 + 5/7 = 14/21 + 15/21 = 29/21
• Multiplication: multiply numerators together and denominators together. Example: 3/4 × 2/5 = 6/20 = 3/10
• Division: multiply by the reciprocal. Example: 7/3 ÷ 2/5 = 7/3 × 5/2 = 35/6

Powers and Scientific Notation

Key rules: a^n × a^m = a^(n+m), a^n / a^m = a^(n−m), (a^n)^m = a^(n×m), a^0 = 1, a^(−n) = 1/a^n.

Scientific notation: write numbers as a × 10^n where 1 ≤ a < 10. Example: 0.00045 = 4.5 × 10^(−4).

Square Roots

Properties: √(a × b) = √a × √b, (√a)² = a, √(a²) = |a|.

Simplification: extract perfect squares. Example: √72 = √(36 × 2) = 6√2.

Warning: √(a + b) ≠ √a + √b.

Algebraic Expressions and Identities

Three essential identities (must know by heart):

• (a + b)² = a² + 2ab + b²
• (a − b)² = a² − 2ab + b²
• (a + b)(a − b) = a² − b²

Equations

• First-degree equations: isolate x. Example: 3x − 7 = 2x + 5 → x = 12
• Product equations: a product equals zero if and only if at least one factor is zero
• Inequalities: reverse the inequality sign when multiplying or dividing by a negative number

2. Geometry

Pythagorean Theorem

In a right triangle with hypotenuse BC: BC² = AB² + AC².

Use the direct theorem to calculate a missing side, the converse to prove a triangle is right-angled, and the contrapositive to prove it is not.

Thales' Theorem

When two parallel lines are cut by two secants meeting at point A: AB/AD = AC/AE = BC/DE.

Use it to calculate lengths (direct theorem) or prove lines are parallel (converse).

Trigonometry

In a right triangle, for an acute angle α:

• cos α = adjacent / hypotenuse
• sin α = opposite / hypotenuse
• tan α = opposite / adjacent

Mnemonic: SOH-CAH-TOA. Use trigonometry to find a missing side (when you know an angle and a side) or a missing angle (when you know two sides).

Transformations

Key transformations: reflection (axial symmetry), point symmetry (central symmetry), translation (shifts by a vector), rotation (turns around a center by a given angle), and enlargement/reduction (homothety with ratio k, where areas scale by k² and volumes by k³).

3D Geometry

Essential volume formulas:

• Prism/Cylinder: V = Base area × height (cylinder: V = πr²h)
• Pyramid/Cone: V = (1/3) × Base area × height
• Sphere: V = (4/3)πr³

3. Functions

Linear and Affine Functions

• Linear function: f(x) = ax — a straight line through the origin
• Affine function: f(x) = ax + b — a straight line with slope a and y-intercept b

To find the equation from two points A(x₁, y₁) and B(x₂, y₂): calculate slope a = (y₂ − y₁)/(x₂ − x₁), then solve for b.

4. Statistics and Probability

• Mean: sum of values / total count
• Median: middle value of an ordered dataset
• Quartiles: Q1 (25th percentile), Q3 (75th percentile), interquartile range = Q3 − Q1
• Probability: P(A) = favorable outcomes / total outcomes for equally likely events. P(complement of A) = 1 − P(A). In a probability tree, multiply along branches and add across paths.

5. Scratch Programming

Every Brevet exam includes a Scratch exercise. Know the key structures: variables, loops (repeat n times, repeat until), and conditionals (if...then...else). Common tasks include drawing regular polygons (repeat n times: move c steps, turn 360/n degrees) and computing sums or sequences.