Official Mathematics Exam — BEPC Session 2018

This mathematics examination, administered during the 2018 session of the Brevet d'Études du Premier Cycle (BEPC) in Cameroon, is a comprehensive test assessing the core competencies of ninth-grade students. The document includes both the original exam paper and its detailed answer key, making it a complete pedagogical resource for exam preparation.

Exam Structure:

The exam is divided into two main parts:

• Part A — Resource Assessment, subdivided into numerical activities and geometric activities.
• Part B — Competency Assessment, consisting of a contextualised problem-solving situation.

Numerical Activities:

The numerical exercises cover several essential topics from the ninth-grade curriculum. Exercise 1 focuses on fraction arithmetic and simplification of expressions containing radicals. Students must demonstrate that a fractional expression yields an integer, then write an expression in the form a√3 + b. Exercise 2 covers expanding, simplifying and factoring algebraic expressions, as well as solving product equations in the set of real numbers. It also includes a descriptive statistics exercise: computing the mean from a frequency table of marks for 50 students.

Geometric Activities:

Exercise 1 in geometry is based on a real-world roof framing scenario. It involves applying the Pythagorean theorem to calculate lengths in a right-angled triangle, using properties of similar triangles formed by parallel lines, and trigonometry (tangent calculation and angle determination). Exercise 2 is set in an orthonormal coordinate system and requires plotting points, computing midpoint coordinates and verifying a Cartesian equation of a line.

Competency-Based Problem:

Part B presents a real-life problem: a municipality must choose between two models for a public artwork — a cone of revolution and a regular pyramid — and calculate the painting costs for the lateral surfaces. Students apply formulas for the lateral area of a cone and a pyramid, then perform cost calculations. A third calculation involves a cone of different dimensions belonging to a neighbouring municipality.

Skills Assessed:

• Fraction arithmetic and radical manipulation
• Algebra: expanding, factoring, solving equations
• Descriptive statistics (mean)
• Plane geometry: Pythagorean theorem, trigonometry, similar triangles
• Analytic geometry: coordinates, midpoint, equation of a line
• Three-dimensional geometry: lateral areas of cones and pyramids
• Real-world problem solving with cost calculations

Target Audience:

This document is intended for ninth-grade students preparing for the BEPC exam, as well as teachers seeking an official exam paper with answer key for review and practice sessions.