Official Mathematics Exam — BEPC Session 2023

This mathematics examination from the 2023 session of the Brevet d'Études du Premier Cycle (BEPC) in Cameroon is a rigorous and comprehensive test assessing students' skills at the end of the lower secondary cycle. The document presents the complete official exam paper, including all sections of the test.

Exam Structure:

The exam comprises two main sections:

• Part A — Resource Assessment, with numerical activities (3 exercises) and geometric activities (3 exercises).
• Part B — Competency Assessment, in the form of a problem-solving situation.

Numerical Activities:

Exercise 1 covers advanced fraction arithmetic (multiple operations leading to an irreducible fraction), expanding an expression with radicals to prove an identity, and a multiple-choice question on simplifying nested square roots. Exercise 2 focuses on factoring algebraic expressions as products of first-degree factors, as well as simplifying a rational expression with its existence condition. Exercise 3 is a statistics exercise based on a histogram: students must read the graph to determine the class width, identify the modal class and calculate the mean age.

Geometric Activities:

Exercise 1 is set in an orthonormal coordinate system: computing vector coordinates, determining a Cartesian line equation, and checking the perpendicularity of two lines given by their equations (True/False). Exercise 2 involves a right-angled triangle with application of Thales' theorem to prove parallelism of two lines, trigonometric calculation (tangent and angle measurement), and identification of a homothety mapping one triangle onto another. Exercise 3 deals with the cross-section of a cone by a plane parallel to the base and computing volumes and areas using the similarity ratio.

Competency-Based Problem:

Part B presents a practical optimisation problem: ANGO owns a rectangular plot measuring 546 m by 510 m that he wishes to fence with regularly spaced posts. Students must use the GCD to determine the maximum spacing between posts (a whole number of metres), calculate the minimum number of posts required, then compare offers from two sellers (Alpha with a lower unit price but delivery fees, and Beta with a higher unit price but free delivery) to determine the most economical choice.

Skills Assessed:

• Fraction arithmetic and radical manipulation
• Factoring and rational expressions
• Statistics: reading histograms, modal class, mean
• Analytic geometry: vectors, line equation, perpendicularity
• Thales' theorem and trigonometry
• Homothety and similarity
• Cone cross-sections and volume/area ratios
• GCD and optimisation in a practical context

Target Audience:

This exam paper is intended for ninth-grade students preparing for the BEPC and for teachers seeking a recent official paper for practice, supervised tests or mock exams.