Official Mathematics Exam — BEPC Session 2020

This mathematics examination from the 2020 session of the Brevet d'Études du Premier Cycle (BEPC) in Cameroon provides a thorough assessment of ninth-grade students' mathematical skills. The document contains the complete official exam paper, structured according to the standard format of the Cameroonian national examination.

Exam Structure:

The exam is organised into two parts:

• Part A — Resource Assessment, with numerical activities (3 exercises) and geometric activities (3 exercises).
• Part B — Competency Assessment, centred on a real-life problem-solving situation.

Numerical Activities:

Exercise 1 involves solving a system of two linear equations in an applied context, followed by a descriptive statistics problem. Students must determine missing frequencies, express the mean as a function of variables and solve the corresponding system. Exercise 2 covers expanding and simplifying algebraic expressions, as well as factoring into products of first-degree polynomials, including recognition of notable identities. Exercise 3 requires computing the numerical value of a rational expression in irreducible form for different values of the variable.

Geometric Activities:

Exercise 1 takes place in an orthonormal coordinate system and focuses on writing a Cartesian equation of a line and identifying the slope of a parallel line (multiple choice). Exercise 2 concerns plane transformations applied to a parallelogram: translation, homothety and Chasles' relation on vectors, with True/False answers. Exercise 3 is a rich plane geometry problem: perpendicular and parallel lines, Thales' theorem, trigonometry (cosine), circumscribed circle and inscribed angles.

Competency-Based Problem:

Part B presents an original and concrete situation: NGONO must travel to a village without mineral water and considers buying spherical watermelons to stay hydrated. Students must calculate the volume of a sphere (watermelon with 14 cm diameter), determine the water content (85% of the volume), verify whether the total quantity covers daily needs (3 litres per day for 3 days), and solve questions related to the rectangular packaging of the watermelons. This problem draws on three-dimensional geometry, percentages and logical reasoning.

Skills Assessed:

• Systems of linear equations
• Descriptive statistics (frequencies, mean)
• Algebra: expanding, factoring, notable identities, rational expressions
• Analytic geometry: line equation, slope
• Plane transformations: translation, homothety, vectors
• Plane geometry: Thales' theorem, trigonometry, circumscribed circle
• Volume of a sphere and real-world application

Target Audience:

This exam paper is intended for ninth-grade students preparing for the BEPC and for teachers seeking a varied and comprehensive official exam paper for their revision sessions.