Mathematics: Structured Reasoning for the Entrance Paper
What the paper tests
Burundi's Écoles d'Excellence mathematics paper rewards clean method, not lucky answers. Master these blocks: operations on whole numbers, fractions, decimals and percentages; proportionality and the rule of three; averages; perimeter, area and volume of squares, rectangles, triangles, circles and cuboids; unit conversion (length, mass, capacity, time, money in Burundian francs); simple equations and inequalities; and word problems about speed, work, mixture and sharing.
Traps that cost marks
- Unit mismatch: mixing metres and centimetres, or minutes and hours, before computing. Convert first, calculate second.
- Percentage direction: "price rises by 20% then falls by 20%" does not return to the start; compute on the new base.
- Division by a fraction: dividing by 1/2 doubles; dividing by 3/4 multiplies by 4/3. Invert and multiply.
- Perimeter versus area: fence questions need perimeter; paint or carpet questions need area.
- Reading the question twice: many items hide a second step ("then he gave away a third of the rest").
Rule of thumb: the three-line method
Write the given data, write what is asked, then write the formula linking them. Only then compute. Show every step; partial credit exists.
Worked example
A rectangular field is 45 m long and 30 m wide. A farmer fences it and then plants the whole surface. Fencing costs 2 000 FBu per metre, planting 1 500 FBu per square metre. Total cost?
- Perimeter = 2 × (45 + 30) = 150 m, so fencing = 150 × 2 000 = 300 000 FBu.
- Area = 45 × 30 = 1 350 m², so planting = 1 350 × 1 500 = 2 025 000 FBu.
- Total = 2 325 000 FBu.
Check plausibility: planting cost should exceed fencing cost here, which it does.