Study by topic.
Five main topics, following the ministry curriculum's own strands, each opening into its subtopic courses. The weights are measured from every question of the real past papers on this site.
20 past papers · 980 questions measured
Algebra
Алгебр
The largest share of the exam: numbers and expressions, equations, sets, functions, logarithms, sequences, and complex numbers.
Numbers & Arithmetic
Тоо ба үсэгт илэрхийлэл
The number system as the exam uses it: rational vs irrational, exponent laws, scientific notation, roots, and the percent problems (interest, markup, error) that appear on nearly every paper. Short by design — at this level you are sharpening, not learning to count.
Algebra
Тэгшитгэл, тэнцэтгэл биш
The heaviest-weighted topic on the exam. Equations and inequalities, systems, polynomial identities and factoring, quadratics by every method, rational expressions with their forbidden values, and radical manipulation — each unit feeds the next, so the order matters.
Sets & Logic
Олонлог
Set operations, Venn counting, and interval notation — tested directly and used as the language of probability problems. Authored specifically for this course: nothing on the platform covered it before.
Functions
Функц ба график
The backbone of the paper: domain and range, graphs, transformations, composition and inverses — then the full family tour from linear through quadratic, piecewise, polynomial and rational.
Exponentials & Logarithms
Илтгэгч ба логарифм функц
Two sides of one coin, and three recurring exam shapes: growth-and-decay models, equation solving, and expression manipulation with the log laws.
Sequences & Series
Дараалал, цуваа
Arithmetic and geometric progressions, their sums, and recursive definitions. The exam rarely hands you the formula — it hands you conditions and expects you to rebuild it.
Complex Numbers
Комплекс тоо
Where a negative discriminant leads: arithmetic with i, conjugates and modulus, the complex plane, and the complete picture of quadratic roots.
Geometry & Trigonometry
Геометр ба тригонометр
Plane and solid geometry, trigonometry, and vectors and matrices — nearly a third of every paper.
Geometry
Геометр ба хэмжигдэхүүн
Plane geometry through solids: triangles and their centers, similarity, right-triangle trig, quadrilaterals, circles, areas, coordinate methods, and 3D measurement. Exam geometry chains two or three facts per problem — the order here builds those chains.
Trigonometry
Тригонометр
From right-triangle ratios to the unit circle, exact values, graphs, identities, trig equations, and the sine and cosine rules — nearly every ЭШ trig question lives inside these six units.
Vectors & Matrices
Вектор ба матриц
Vector arithmetic and coordinates, the dot product, 3D vectors, then matrix operations, determinants and inverses, geometric transformations as matrices, and systems in three unknowns — the exam connects vectors to geometry and matrices to systems.
Analysis
Анализын эхлэл
Limits, derivatives, and integrals. Concentrated in the hardest questions of both sections.
Probability & Statistics
Магадлал ба статистик
Probability theory and data analysis, from counting outcomes to reading distributions.
Probability
Магадлал
Probability models, conditional probability, random variables with expectation and variance, and the binomial distribution — in the order the exam escalates them.
Statistics
Өгөгдлийн шинжилгээ
Describing data, position and distribution (z-scores, the normal curve), two-variable data with regression, and inference — ЭШ statistics rewards interpretation over computation.
Combinatorics
Комбинаторик
A small but reliable slice of the exam — and the entry point to half of probability.
Not sure where to start?
Sit a past paper first — your results name the exact subtopics to fix.