Official Mathematics Exam — BEPC Session 2019

This mathematics examination from the 2019 session of the Brevet d'Études du Premier Cycle (BEPC) in Cameroon is a rigorous test designed to assess the knowledge and skills of ninth-grade students. The document includes the official exam paper along with its answer key, making it an ideal resource for revision and practice.

Exam Structure:

The exam consists of two main parts:

• Part A — Resource Assessment, including numerical activities and geometric activities.
• Part B — Competency Assessment, featuring a real-world problem-solving scenario.

Numerical Activities:

Exercise 1 requires students to prove that an expression combining fractions and operations yields an integer, then to write a number in the form a√5 + b by manipulating radicals. Exercise 2 covers factoring a difference of squares, simplifying a rational expression with its existence condition, and computing a numerical value. It also includes a statistics exercise where students must solve a system of two linear equations to find missing frequencies, given the total number of students and the mean.

Geometric Activities:

Exercise 1 is set in an orthonormal coordinate system. Students must plot points, compute vector coordinates, prove orthogonality of two vectors, find a midpoint and construct a point's symmetric image. Exercise 2 deals with a cone of revolution: cross-section by a plane parallel to the base at half-height, volume ratio calculation between the original cone and the reduced cone, and numerical application with π = 3.14.

Competency-Based Problem:

Part B presents a recreational park development problem. The land is divided into three areas with different geometric shapes: a right-angled triangle (covered with grass), a trapezoid (covered with paving stones) and a half-disk (covered with concrete). Students must calculate the area of each space and then the corresponding material costs. This problem requires computing areas of various plane figures and applying proportional reasoning for costs.

Skills Assessed:

• Fraction and radical arithmetic
• Factoring (difference of squares) and rational expressions
• Systems of linear equations
• Descriptive statistics (frequencies, mean)
• Analytic geometry: vectors, orthogonality, midpoint, symmetry
• Three-dimensional geometry: cone cross-sections, volume ratios
• Area calculations and real-world problem solving

Target Audience:

This document is intended for ninth-grade students preparing for the BEPC exam, as well as mathematics teachers looking for an official exam paper with answer key to support their lessons and revision exercises.