Bulgaria DZI Mathematics case studies
Bulgaria DZI Mathematics · Put your knowledge to work in context.
The Bulgarian State Matriculation Examination in Mathematics, known locally as ДЗИ по математика, is the national school-leaving examination taken by students completing secondary education in Bulgaria. A pass is one of the routes to a secondary school diploma, and the mathematics variant is chosen by candidates who need a mathematics result for university admission, most often for engineering, economics, informatics, and the natural sciences. It is a written examination combining multiple-choice items with constructed-response problems in which the working must be shown and is marked for method as well as answer. The syllabus spans the whole gymnasium mathematics course, from sets and real numbers through algebra, functions, exponentials and logarithms, trigonometry, sequences, combinatorics and probability, plane and solid geometry, and analytic geometry. The Bulgaria DZI Mathematics case studies are 5 cases and about 1,730 words.
1The Overlapping Survey
A school surveys 240 students about three optional activities: chess club (C), drama club (D), and debating club (B). The results show that 130 joined C, 110 joined D, and 90 joined B.
316 words, about 2 min2The Logarithm That Lost Its Domain
A student solves the equation log₂(x − 1) + log₂(x − 3) = 3 by combining the left side into log₂[(x − 1)(x − 3)] = 3, then writing (x − 1)(x − 3) = 8. Expanding gives x² − 4x + 3 = 8, so x² − 4x − 5 = 0, which factors as (x − 5)(x + 1) = 0.
340 words, about 2 min3The Rocket's Two Roots
A model rocket is launched vertically from a platform. Its height in metres after t seconds is modelled by h(t) = −5t² + 30t + 35 for 0 ≤ t ≤ 8.
330 words, about 2 min4The Tangent That Divides
A circle with centre O and radius 5 is given. Point P is outside the circle with OP = 13.
393 words, about 2 min5The Committee With Constraints
A club has 6 girls and 5 boys, all distinct. A committee of 4 must be formed.
351 words, about 2 min