Mathematics and Physics from the Ground Up
PLEN

Matura in mathematics

Preparation for the Polish matura exam in mathematics, basic and extended level, following the 2024 core curriculum (sections I–XIII). Polish only.

0 Introduction

  1. 0.1How the maths matura works: the paper, scoring, the formula booklet draft

I Real numbers

  1. 1.1Operations, intervals and absolute value basicdraft Drill (42) · PDF
  2. 1.2Powers and roots basicdraft Drill (43) · PDF requires: 1.1
  3. 1.3Logarithms basicdraft Drill (36) · PDF requires: 1.2
  4. 1.4Percentages, compound interest, deposits and loans basicdraft Drill (35) · PDF requires: 1.2
  5. 1.5Divisibility and first proofs basicdraft Drill (32) · PDF requires: 1.1

II Algebraic expressions

  1. 2.1Special products and rational expressions basicdraft Drill (34) · PDF requires: 1.2
  2. 2.2Polynomials: division, factoring, integer roots extendeddraft Drill (43) · PDF requires: 2.1

V Functions

  1. 5.1Functions and graphs: reading properties basicdraft Drill (44) · PDF requires: 1.1
  2. 5.2The linear function basicdraft Drill (38) · PDF requires: 5.1
  3. 5.3The quadratic function: three forms and the graph basicdraft Drill (66) · PDF requires: 5.1
  4. 5.4The quadratic on an interval and optimisation basicdraft Drill (36) · PDF requires: 5.3
  5. 5.5Inverse proportionality basicdraft Drill (27) · PDF requires: 5.1
  6. 5.6Exponential and logarithmic functions basicdraft Drill (37) · PDF requires: 1.3, 5.1
  7. 5.7Graph transformations, composition, proving monotonicity extendeddraft Drill (31) · PDF requires: 5.3

III Equations and inequalities

  1. 3.1Linear equations and inequalities, equivalent transformations basicdraft Drill (30) · PDF requires: 2.1
  2. 3.2Quadratic equations and inequalities, factored polynomial equations basicdraft Drill (31) · PDF requires: 5.3, 3.1
  3. 3.3Polynomial inequalities and biquadratic equations extendeddraft Drill (25) · PDF requires: 2.2, 3.2
  4. 3.4Rational expressions, equations and inequalities extendeddraft Drill (23) · PDF requires: 3.3
  5. 3.5Equations and inequalities with absolute value extendeddraft Drill (23) · PDF requires: 3.2
  6. 3.6Vieta's formulas and equations with a parameter extendeddraft Drill (22) · PDF requires: 3.2

IV Systems of equations

  1. 4.1Linear systems and word problems basicdraft Drill (26) · PDF requires: 3.1
  2. 4.2Systems with a quadratic equation extendeddraft Drill (17) · PDF requires: 3.2, 4.1

VI Sequences

  1. 6.1Sequences: general term, recursion, monotonicity basicdraft Drill (31) · PDF requires: 5.1
  2. 6.2Arithmetic sequences basicdraft Drill (26) · PDF requires: 6.1
  3. 6.3Geometric sequences basicdraft Drill (26) · PDF requires: 1.4, 6.1
  4. 6.4Limits of sequences and geometric series extendeddraft Drill (25) · PDF requires: 6.3

VII Trigonometry

  1. 7.1Trigonometry of angles from 0° to 180° basicdraft Drill (27) · PDF requires: 1.2
  2. 7.2The law of cosines and the area of a triangle basicdraft Drill (24) · PDF requires: 7.1
  3. 7.3Radians, graphs, periodicity and reduction formulas extendeddraft Drill (20) · PDF requires: 5.7, 7.1
  4. 7.4Angle-sum formulas and trigonometric equations extendeddraft Drill (25) · PDF requires: 7.3
  5. 7.5The law of sines and solving triangles extendeddraft Drill (19) · PDF requires: 7.2

VIII Plane geometry

  1. 8.1Circles: chords, tangents, inscribed and central angles, sectors basicdraft Drill (20) · PDF requires: 7.1
  2. 8.2Triangles: types and special points basicdraft Drill (20) · PDF requires: 7.2
  3. 8.3Quadrilaterals and regular polygons basicdraft Drill (20) · PDF requires: 8.2
  4. 8.4Thales' theorem and similarity basicdraft Drill (17) · PDF requires: 8.2
  5. 8.5Trigonometry in figures and geometric proofs basicdraft Drill (16) · PDF requires: 8.1, 8.4
  6. 8.6Cyclic and tangential quadrilaterals, converse of Thales' theorem extendeddraft Drill (15) · PDF requires: 8.5

IX Analytic geometry

  1. 9.1Lines in the plane basicdraft Drill (18) · PDF requires: 5.2, 4.1
  2. 9.2Distance, the equation of a circle and symmetries basicdraft Drill (18) · PDF requires: 9.1
  3. 9.3Line and circle, two circles, tangents and perpendicular lines extendeddraft Drill (15) · PDF requires: 4.2, 9.2
  4. 9.4Vectors extendeddraft Drill (15) · PDF requires: 9.1

X Solid geometry

  1. 10.1Lines, planes and angles in space basicdraft Drill (16) · PDF requires: 7.1
  2. 10.2Volumes and surface areas, similar solids basicdraft Drill (15) · PDF requires: 10.1
  3. 10.3Cross-sections and the three perpendiculars theorem extendeddraft Drill (11) · PDF requires: 10.2

XI Combinatorics

  1. 11.1The multiplication and addition rules basicdraft Drill (25) · PDF
  2. 11.2Permutations, variations, combinations and binomial coefficients extendeddraft Drill (25) · PDF requires: 2.1, 11.1

XII Probability and statistics

  1. 12.1Classical probability basicdraft Drill (23) · PDF requires: 11.1
  2. 12.2Statistics: means, median, mode basicdraft Drill (24) · PDF
  3. 12.3Conditional and total probability, Bayes' formula extendeddraft Drill (19) · PDF requires: 12.1
  4. 12.4Bernoulli trials extendeddraft Drill (18) · PDF requires: 11.2, 12.3

XIII Differential calculus

  1. 13.1Limits and continuity of functions, the Darboux property extendeddraft Drill (18) · PDF requires: 5.7, 6.4
  2. 13.2The derivative: definition, meaning and computation extendeddraft Drill (21) · PDF requires: 13.1
  3. 13.3Monotonicity and extrema extendeddraft Drill (17) · PDF requires: 13.2
  4. 13.4Optimisation with the derivative extendeddraft Drill (10) · PDF requires: 5.4, 13.3

XIV Dress rehearsal

  1. 14.1Mock exam: basic level basicdraft Drill (24) · PDF requires: 5.4, 6.3, 8.5, 9.2, 10.2, 12.2
  2. 14.2Mock exam: extended level extendeddraft Drill (13) · PDF requires: 13.4, 14.1