Armenia Mathematics Unified Exam study guide
Armenia Mathematics Unified Exam · Work through your exam, one topic at a time.
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. The Armenia Mathematics Unified Exam study guide has 10 sections and about 2,414 words.
01Number Theory and Arithmetic
Candidates must handle divisibility rules, prime factorization, greatest common divisor and least common multiple, remainders and modular arithmetic, and the distinction between rational and irrational numbers. Be fluent with the Euclidean algorithm and with converting repeating decimals to fractions.
234 words, about 1 min02Algebra and Algebraic Expressions
Master polynomial arithmetic, factoring patterns (difference of squares, sum/difference of cubes, perfect-square trinomials), rational expressions and their domains, exponent laws (including fractional and negative exponents), radicals, and logarithm rules. Know the binomial theorem and Pascal's triangle for expansion coefficients.
223 words, about 1 min03Equations and Inequalities
Solve linear, quadratic, rational, radical, exponential, logarithmic, and absolute-value equations, plus systems (substitution, elimination). For quadratics, use factoring, completing the square, or the quadratic formula; the discriminant b² − 4ac tells you the nature of the roots.
259 words, about 1 min04Functions and Graphs
Understand domain and range, function notation, composition, inverses, transformations, and the standard families (linear, quadratic, polynomial, rational, exponential, logarithmic, trigonometric). Know how shifts, stretches, and reflections change a graph, and how to read intercepts, asymptotes, and symmetry.
224 words, about 1 min05Sequences and Progressions
Distinguish arithmetic (constant difference d) and geometric (constant ratio r) sequences. Know formulas for the n-th term and partial sums, plus infinite geometric series when r < 1.
286 words, about 1 min06Trigonometry
Know the unit circle, radian–degree conversion, the six trig functions, fundamental identities (Pythagorean, reciprocal, quotient), sum/difference and double-angle formulas, and the laws of sines and cosines. Understand periodic graphs, amplitude, period, and phase shift.
194 words, under 1 min07Plane Geometry
Master triangle congruence and similarity, the Pythagorean theorem, angle properties of parallel lines, circle theorems (inscribed angle, tangent–chord, power of a point), area and perimeter formulas, and coordinate geometry (distance, midpoint, slope). Similarity ratio vs area ratio: areas scale by the square of the linear ratio; volumes by the cube.
216 words, about 1 min08Solid Geometry
Know formulas for volume and surface area of prisms, pyramids, cylinders, cones, and spheres. Understand cross-sections, similarity in 3D, and the relationship between linear, area, and volume scaling.
208 words, about 1 min09Combinatorics
Understand the multiplication and addition principles, permutations vs combinations, circular arrangements, and the pigeonhole principle. Know when order matters (permutation) and when it does not (combination).
178 words, under 1 min10Probability and Statistics
Know classical probability, conditional probability, independence, and the addition and multiplication rules. For statistics, understand mean, median, mode, range, variance, standard deviation, and how to read distributions.
392 words, about 2 min