Državna Matura Math A study plan
Državna Matura Math A · Give each week a clear focus.
8 weeks · About 6 hours per week
Numbers and algebra (real numbers, powers and roots, algebraic expressions, equations and inequalities)
Simplify expressions with integer and rational exponents and convert freely between radical and power notation without a calculator.
Factor and expand algebraic expressions, including difference of squares, sum and difference of cubes, and grouping.
Solve linear and quadratic equations in one variable, choosing between factoring, completing the square, and the quadratic formula.
Solve linear inequalities and quadratic inequalities, expressing solution sets in interval notation and checking boundary cases.
Your checkpoint
A one-page formula and error sheet plus 20 self-written mixed number-and-algebra problems solved with full working, scored at 80% or better.
Numbers and algebra (real numbers, powers and roots, algebraic expressions, equations and inequalities) & Functions (linear, quadratic, exponential, logarithmic, polynomial, rational; graphs and transformations)
Solve rational equations and equations containing radicals, identifying extraneous solutions explicitly.
Sketch linear and quadratic functions from their equations, stating intercepts, vertex, axis of symmetry, and range.
Apply vertical and horizontal shifts, reflections, and stretches to a parent graph and write the transformed equation.
Solve word problems that model real situations with linear or quadratic functions.
Your checkpoint
Ten function-sketching and transformation exercises with correct graphs and labelled key features, plus a short written summary of the three most common mistakes you made.
Functions (linear, quadratic, exponential, logarithmic, polynomial, rational; graphs and transformations)
Determine domain and range for polynomial, rational, exponential, and logarithmic functions.
Sketch exponential and logarithmic graphs and state their asymptotes and monotonicity.
Apply logarithm laws to combine and split logarithmic expressions and solve exponential and logarithmic equations.
Analyse rational functions, locating vertical and horizontal asymptotes and removable discontinuities.
Your checkpoint
A timed 45-minute set of 12 function problems covering all four function families, graded against the answer key with every error corrected in writing.
Geometry and trigonometry (plane and solid geometry, trigonometric ratios and identities)
Solve right triangles using sine, cosine, tangent, and the Pythagorean theorem in applied contexts.
Apply the sine rule and cosine rule to non-right triangles, including the ambiguous case.
Use trigonometric identities, including Pythagorean, double-angle, and sum identities, to simplify expressions and solve equations.
Compute areas and volumes of plane and solid figures, including prisms, pyramids, cylinders, cones, and spheres.
Your checkpoint
A geometry-and-trigonometry mock section of 15 problems completed in 60 minutes, with a written error log classifying each mistake as conceptual, procedural, or careless.
Geometry and trigonometry (plane and solid geometry, trigonometric ratios and identities) & Analytic geometry (lines, circles, conic sections, vectors in the plane)
Solve plane geometry problems involving similar triangles, circle theorems, and angle relationships.
Work with vectors in the plane: add, subtract, scale, compute magnitude, dot product, and the angle between vectors.
Write equations of lines in several forms and determine parallelism, perpendicularity, and intersection points.
Find the equation of a circle and solve problems on tangency and intersection of a line and a circle.
Your checkpoint
A two-part worksheet: 10 vector and line problems plus 5 circle problems, all fully justified, with a self-assessed score and a list of formulas you still need to memorise.
Sequences and series (arithmetic and geometric sequences, sums) & Analytic geometry (lines, circles, conic sections, vectors in the plane)
Identify arithmetic and geometric sequences and compute terms, common difference or ratio, and general formulas.
Compute sums of finite arithmetic and geometric series and interpret the sum of an infinite geometric series with ratio of absolute value below 1.
Apply sequences to real-world problems such as savings growth and depreciation.
Recognise and analyse the parabola and other conic sections from their equations, identifying vertex, focus, and directrix where relevant.
Your checkpoint
A mixed sequence-and-conic problem set of 12 items, including two applied word problems, completed under a 50-minute time limit.
Probability and statistics (combinatorics, probability, descriptive statistics) & Calculus (limits, derivatives, applications of derivatives, introductory integration)
Apply permutations and combinations to count arrangements with and without repetition and with restrictions.
Compute probabilities using classical definitions, complementary events, and the addition and multiplication rules.
Calculate and interpret mean, median, mode, range, variance, and standard deviation for a data set.
Compute limits of simple functions and apply the definition of the derivative to find derivatives of polynomial and rational functions.
Your checkpoint
A combined statistics-and-calculus worksheet of 15 problems with a one-paragraph interpretation of a data set you collect or simulate yourself.
Calculus (limits, derivatives, applications of derivatives, introductory integration) & Numbers and algebra (real numbers, powers and roots, algebraic expressions, equations and inequalities) & Functions (linear, quadratic, exponential, logarithmic, polynomial, rational; graphs and transformations)
Use derivatives to find tangents, stationary points, and intervals of increase and decrease, and solve simple optimisation problems.
Evaluate basic definite integrals and interpret them as areas under a curve.
Complete two full-length timed mock papers under exam conditions and mark them against the official-style key.
Review the error log and rebuild a final one-page summary sheet of formulas and recurring mistakes.
Your checkpoint
Two completed timed mock papers with scores recorded, plus a final review sheet covering your top ten recurring errors and the corrections.
Milestones
Week 2: Score at least 75% on a self-assembled 20-question set drawn only from Domains 1 and 2, with no unresolved conceptual errors in your notes.
Week 4: Complete the 15-problem geometry-and-trigonometry mock section within 60 minutes and score at least 70%, with an error log written for every missed item.
Week 6: Score at least 75% on a mixed set covering Domains 3, 4, and 5, and state from memory the general term and sum formulas for arithmetic and geometric sequences.
Week 8: Achieve at least 80% on both full-length timed mock papers, and confirm that every error in the final review sheet has a written correction and a matching practice example.