Bulgaria DZI Mathematics study guide
Bulgaria DZI Mathematics · Work through your exam, one topic at a time.
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. The Bulgaria DZI Mathematics study guide has 10 sections and about 2,801 words.
01Sets, Logic, and Real Numbers
A candidate must be fluent with set notation: union, intersection, difference, complement, subsets, and the number of subsets of an n-element set (2^n). Know the connectives (negation, conjunction, disjunction, implication, equivalence) and their truth tables, plus quantifiers and their negations.
287 words, about 1 min02Algebra: Equations and Inequalities
Candidates must solve linear, quadratic, rational, radical, and absolute-value equations and inequalities; use the discriminant Δ = b² − 4ac to classify quadratic roots; apply Vieta's formulas (sum −b/a, product c/a); and use sign charts for polynomial and rational inequalities. Systems of equations, including substitution and elimination, are also tested.
297 words, about 1 min03Functions and Graphs
Know domain, range, injectivity, monotonicity, parity (even/odd), periodicity, and inverse functions. Be able to sketch and transform graphs: shifts f(x ± a), scalings, reflections, and f(x) .
287 words, about 1 min04Exponential and Logarithmic Expressions and Equations
Master exponent laws, the definition log a b = c ⇔ a^c = b, logarithm laws (product, quotient, power, change of base), and the domains a 0, a ≠ 1, b 0. Solve exponential equations by equating exponents or taking logarithms, and logarithmic equations by combining logs and converting to exponential form.
310 words, about 2 min05Trigonometry
Know the unit circle, radian measure, the six trigonometric functions, exact values at 0, π/6, π/4, π/3, π/2, and the signs by quadrant (ASTC). Master the Pythagorean identities, double-angle and sum formulas, and solve equations like sin x = k and a sin²x + b sin x + c = 0.
306 words, about 2 min06Sequences and Progressions
Know the definitions of arithmetic and geometric progressions, their general terms, sums, and convergence conditions. Arithmetic: aₙ = a₁ + (n − 1)d, Sₙ = n(a₁ + aₙ)/2.
278 words, about 1 min07Combinatorics, Probability, and Statistics
Know the multiplication and addition principles, permutations (ordered), combinations (unordered), permutations with repetition, and the binomial theorem. For probability, master classical probability, complementary events, mutually exclusive events, independent events, and conditional probability.
238 words, about 1 min08Planimetry
Master triangle congruence and similarity, the Pythagorean theorem, Thales' theorem, the sine and cosine rules, area formulas (½ab sin C, Heron's formula), and properties of circles: inscribed angles, tangents, chord properties, and the power of a point. Know properties of parallelograms, trapezoids, and regular polygons, and the sum of interior angles of an n-gon (n − 2)·180°.
268 words, about 1 min09Stereometry
Know the volumes and surface areas of prisms, pyramids, cylinders, cones, and spheres; the relationships between similar solids; and the geometry of lines and planes in space, including dihedral angles and the angle between a line and a plane. Master the formulas V = (1/3)·B·h for pyramids and cones, V = (4/3)πr³ for spheres, and S = 4πr² for sphere surfaces.
244 words, about 1 min10Analytic Geometry
Know the distance formula, midpoint formula, slope, and equations of lines (slope-intercept, point-slope, general form). Master the equation of a circle (x − a)² + (y − b)² = r², the conditions for parallel (equal slopes) and perpendicular (product = −1) lines, and the distance from a point to a line.
286 words, about 1 min