Bulgaria NVO Grade 7 Mathematics study guide
Bulgaria NVO Grade 7 Mathematics · Work through your exam, one topic at a time.
The National External Assessment (NVO) in Mathematics for Grade 7 is a standardized Bulgarian school-leaving-style examination taken at the end of lower secondary education. It is intended for Grade 7 students completing the primary/lower-secondary cycle, and results are commonly used in the admission process for secondary schools and language or mathematics-oriented gymnasiums, so the score can matter beyond the certificate itself. The Bulgaria NVO Grade 7 Mathematics study guide has 8 sections and about 2,536 words.
01Numbers and Operations: Naturals, Integers, Rationals, Powers and Roots
You need to move confidently between natural numbers (0, 1, 2, …), integers (… −2, −1, 0, 1, 2 …) and rational numbers (anything writable as a fraction of two integers, including terminating and repeating decimals). Master the order of operations: brackets first, then powers and roots, then multiplication and division left to right, then addition and subtraction left to right.
329 words, about 2 min02Algebraic Expressions and Polynomials: Monomials, Identities, Factorization
A monomial is a product of numbers and variables with whole-number exponents (e.g. A polynomial is a sum of monomials.
325 words, about 2 min03Equations and Inequalities: Linear Equations, Systems, Inequalities
Solve a linear equation by performing the same operation on both sides until the unknown stands alone. Clear denominators by multiplying by the least common multiple, expand brackets carefully, collect variables on one side and numbers on the other.
327 words, about 2 min04Functions and Coordinate Geometry Basics: Linear Functions and Proportion
In the coordinate plane, a point is written P(x, y): x is horizontal, y is vertical. Know all four quadrants and their sign patterns.
338 words, about 2 min05Geometry: Triangles, Quadrilaterals, Congruence and Similarity
Know the angle facts: angles on a straight line sum to 180°, angles around a point to 360°, vertically opposite angles are equal, and alternate and corresponding angles formed by a transversal of parallel lines are equal. For triangles: the interior angles sum to 180°; an exterior angle equals the sum of the two remote interior angles; the longest side faces the largest angle.
322 words, about 2 min06Measurement of Plane Figures: Perimeter, Area, Circles, Composite Shapes
Know the formulas: rectangle A = ab, P = 2(a + b); parallelogram A = a·h; triangle A = (a·h)/2; trapezoid A = ((a + b)/2)·h; rhombus A = (d₁·d₂)/2. For a circle, C = 2πr and A = πr²; a sector's arc length is (α/360)·2πr and its area (α/360)·πr².
280 words, about 1 min07Data, Statistics and Probability: Tables, Charts, Averages
Read and interpret tables, bar charts, line graphs, pie charts and histograms. For a data set, compute the mean (sum ÷ count), the median (middle value when ordered), the mode (most frequent value) and the range (maximum − minimum).
272 words, about 1 min08Mathematical Reasoning and Problem Solving: Word Problems and Modelling
Translate a word problem into an equation or expression. Identify the unknown, give it a letter, write down the relations stated in the text, and solve.
343 words, about 2 min