Bulgaria DZI Mathematics study plan

Solve linear, quadratic, and fractional-rational equations in one variable, writing out each step and checking for extraneous roots

Solve linear and quadratic inequalities and express solution sets in interval notation

Apply absolute-value equations and inequalities and justify each case split

Classify real numbers and use basic set operations (union, intersection, complement) on number intervals

Identify and correct your own three most frequent algebraic sign errors by reworking missed problems

Solve systems of two and three linear equations and interpret the solution geometrically

Solve equation systems mixing linear and quadratic relations

State and apply the key triangle theorems (angle sum, congruence criteria, similarity) to compute unknown lengths and angles

Prove two triangles congruent or similar using an explicit criterion at each step

Set up and solve at least five word problems that translate into equations or systems

Sketch graphs of linear, quadratic, and rational functions from their defining parameters without a calculator

Determine domain, range, monotonicity, and extrema for each function family studied

Convert between exponential and logarithmic form and apply the laws of logarithms

Solve exponential and logarithmic equations and reject solutions outside the domain

Interpret function transformations (shifts, reflections, scalings) and match a graph to its formula

Solve exponential and logarithmic inequalities using monotonicity arguments

Solve real-world growth and decay problems by constructing exponential models

Compute terms of arithmetic and geometric progressions from given data and derive general-term formulas

Sum arithmetic and geometric series and apply the formulas to concrete problems

Distinguish convergent from divergent geometric series and compute the sum of convergent ones

Convert fluently among degrees and radians and place angles in the correct quadrant

Apply reduction formulas and fundamental identities to simplify trigonometric expressions

Solve basic trigonometric equations and list all solutions in a given interval

Apply the sine rule and cosine rule to non-right triangles and compute areas

Use circle properties (inscribed angles, tangents, chords) to compute unknown quantities

Apply the Pythagorean theorem, metric relations in right triangles, and area formulas for all standard plane figures

Compute coordinates, distances, midpoints, and slopes in the Cartesian plane

Derive and use equations of lines and circles, including parallel and perpendicular conditions

Determine relative positions of a line and a circle from the algebraic condition on the system

Solve analytic-geometry problems that require a planimetry insight before the algebra

Compute volumes and surface areas of prisms, pyramids, cylinders, cones, and spheres

Analyze cross-sections and use right-triangle relations inside solids to find unknown lengths

Count outcomes using permutations, variations, and combinations and identify which applies

Compute probabilities of events using the classical definition and complementary events

Calculate and interpret mean, median, mode, and standard deviation for a small data set

Complete two full-length timed mock exams under exam conditions and score them honestly

Categorize every error as conceptual, procedural, or careless and rank the categories by frequency

Re-teach your two weakest topics from earlier weeks using your own notes and re-solve representative problems

Memorize and reproduce a single consolidated formula sheet covering all ten domains

Build a final-week checklist of the five habits that most improved your accuracy