Armenia Mathematics Unified Exam case studies
Armenia Mathematics Unified Exam · Put your knowledge to work in context.
The Mathematics Unified Exam is the standardized mathematics assessment used in Armenia's unified university admissions system. Candidates finishing secondary school take it as part of the broader Unified State Examination battery, and results are used by higher-education institutions in Armenia when selecting and ranking applicants. Because scores feed directly into admission decisions, the exam rewards both accuracy and speed rather than isolated knowledge of any one topic. The content spans the full secondary mathematics curriculum: arithmetic and number theory, algebraic manipulation, equations and inequalities, functions and their graphs, sequences, trigonometry, plane and solid geometry, elementary combinatorics and probability, and a modest amount of calculus. The Armenia Mathematics Unified Exam case studies are 5 cases and about 2,344 words.
1The Mysterious Remainder
A number N leaves a remainder of 5 when divided by 7, a remainder of 3 when divided by 5, and a remainder of 2 when divided by 3. A student claims that the smallest positive integer satisfying these conditions is 68.
442 words, about 2 min2The Leaking Tank
A cylindrical tank with a radius of 2 meters and a height of 5 meters is filled with water. A small hole at the bottom causes water to leak out at a rate proportional to the square root of the depth of the water.
466 words, about 2 min3The Garden Gate
A rectangular garden is to be enclosed by a fence on three sides, with the fourth side being a wall. The fence material costs 10 dollars per meter, and the wall is already there.
386 words, about 2 min4The Tournament Schedule
In a round-robin chess tournament, each of the 6 players plays every other player exactly once. A win earns 1 point, a draw earns 0.5 points, and a loss earns 0 points.
577 words, about 3 min5The Trigonometric Identity
In a triangle ABC, angles A, B, and C satisfy A + B + C = π. A student is asked to prove that sin A + sin B + sin C = 4 cos(A/2) cos(B/2) cos(C/2).
473 words, about 2 min