Official Mathematics Exam — BEPC Session 2022

This mathematics examination from the 2022 session of the Brevet d'Études du Premier Cycle (BEPC) in Cameroon is a comprehensive test covering the entire ninth-grade curriculum. The document presents the complete official exam paper, with a rigorous structure and varied exercises.

Exam Structure:

The exam is divided into two parts:

• Part A — Resource Assessment, with numerical activities (3 exercises) and geometric activities (2 exercises).
• Part B — Competency Assessment, based on a contextualised problem-solving situation.

Numerical Activities:

Exercise 1 focuses on fraction arithmetic (operations and reduction to irreducible form) and rationalising the denominator of an expression containing a radical, followed by a second-order bound. Exercise 2 covers factoring a complex algebraic expression combining a difference of squares, expansion and factoring, then solving a product equation. Exercise 3 is a descriptive statistics problem with grouped data: students must complete a table (missing frequencies, class centres), identify the modal class and calculate the mean.

Geometric Activities:

Exercise 1 presents a plot of land shaped as a right-angled trapezoid. Students must determine missing dimensions from the area, calculate a length using the Pythagorean theorem, use trigonometry (tangent) to find an angle, and identify the image of a point under a translation. Exercise 2 takes place in an orthonormal coordinate system: computing vector coordinates, proving orthogonality, calculating distances, determining the nature of a triangle, matching lines to their Cartesian equations, and graphically representing the solution set of a system of inequalities.

Competency-Based Problem:

Part B features a public works company using a tanker truck with a cylindrical shape and hemispherical ends. Students must calculate the total volume of the tank (cylinder plus two hemispheres), convert to litres and determine the number of 1000-litre tanks needed. A second calculation involves a cylindro-conical water reservoir. This problem draws on volumes of composite solids and unit conversions.

Skills Assessed:

• Fraction arithmetic and denominator rationalisation
• Bounding real numbers
• Factoring and solving product equations
• Descriptive statistics: classes, modal class, mean
• Plane geometry: trapezoid, Pythagorean theorem, trigonometry, translation
• Analytic geometry: vectors, orthogonality, line equations, inequalities
• Volumes of composite solids (cylinder, sphere, cone)

Target Audience:

This document is designed for ninth-grade students preparing for the BEPC and teachers seeking a recent and comprehensive official exam paper for their assessments and revision sessions.