100+ Free Matura Math Practice Questions

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The function f(x) = 2^x is defined for all real x. What is f(−3)?

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Key Facts: Matura Math Exam

The Polish Matura Mathematics basic level exam (Formuła 2023) is a compulsory 3-hour written exam comprising ~25 closed and 10 open tasks worth 46 points; the pass threshold is 30%, and the syllabus spans twelve core math topics.

Sample Matura Math Practice Questions

Try these sample questions to test your Matura Math exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Simplify the expression: (6^100 + 6^100 + 6^100 + 6^100 + 6^100 + 6^100).

A.6^99

B.6^100

C.6^101

D.6^600

Explanation: There are six terms each equal to 6^100, so their sum is 6 × 6^100 = 6^1 × 6^100 = 6^101. When multiplying powers with the same base, add the exponents: 1 + 100 = 101.

2Evaluate: log₇98 − log₇2.

A.1

B.2

C.7

D.49

Explanation: Using the logarithm quotient rule: log₇98 − log₇2 = log₇(98/2) = log₇49. Since 7² = 49, the value is 2.

3Which of the following is equal to √(48) − √(27) + √(12)?

A.√3

B.2√3

C.3√3

D.4√3

Explanation: Simplify each radical: √48 = 4√3, √27 = 3√3, √12 = 2√3. Then: 4√3 − 3√3 + 2√3 = (4−3+2)√3 = 3√3.

4Expand and simplify: (3 + 4a)² − (3 − 4a)².

A.24a

B.48a

C.16a²

D.32a²

Explanation: Use the difference of squares identity: (A+B)² − (A−B)² = 4AB. Here A = 3, B = 4a, so the result is 4 × 3 × 4a = 48a.

5How many three-digit natural numbers can be formed using the digits {0, 1, 3, 4, 5, 6, 7, 8, 9} (i.e., not containing the digit 2)?

A.504

B.576

C.648

D.729

Explanation: The hundreds digit has 8 choices (1–9 excluding 2). The tens digit has 9 choices (0–9 excluding 2). The units digit also has 9 choices. Total: 8 × 9 × 9 = 648.

6The line passing through points A(1, 3) and B(4, 9) has the equation:

A.y = x + 2

B.y = 2x + 1

C.y = 3x

D.y = 2x + 3

Explanation: Slope m = (9−3)/(4−1) = 6/3 = 2. Using point A: y − 3 = 2(x − 1) → y = 2x + 1. Check with B: 2(4) + 1 = 9 ✓.

7The first term of a geometric sequence is a₁ = 3, and the common ratio is r = 2. What is the 5th term?

A.24

B.36

C.48

D.96

Explanation: The nth term formula is aₙ = a₁ · rⁿ⁻¹. For n = 5: a₅ = 3 · 2⁴ = 3 · 16 = 48.

8What is the sum of the first 10 terms of the arithmetic sequence: 2, 5, 8, 11, …?

A.90

B.110

C.120

D.155

Explanation: Here a₁ = 2 and common difference d = 3. Sum formula: Sₙ = n/2 · (2a₁ + (n−1)d). S₁₀ = 10/2 · (4 + 9·3) = 5 · 31 = 155.

9Solve the equation: 2x² − 8 = 0.

A.x = ±1

B.x = ±2

C.x = ±4

D.x = ±√8

Explanation: Divide both sides by 2: x² = 4. Taking the square root: x = ±2. Both solutions satisfy the original equation.

10A bag contains 4 red balls and 6 blue balls. One ball is drawn at random. What is the probability it is red?

A.1/4

B.2/5

C.3/5

D.2/3

Explanation: Total balls = 10. Favorable outcomes (red) = 4. P(red) = 4/10 = 2/5.

About the Matura Math Exam

The Matura (egzamin maturalny) is the Polish secondary school leaving examination, administered by the Centralna Komisja Egzaminacyjna (CKE). Mathematics at the basic level (poziom podstawowy) is one of three compulsory written subjects alongside Polish Language and a Modern Foreign Language. Under Formuła 2023 — the version for students who began secondary school from 2019 onwards — the exam contains approximately 35 tasks (25 closed and 10 open) worth a total of 46 points, lasts 180 minutes, and requires a minimum of 30% to pass. Closed tasks include standard 4-option multiple-choice questions and true/false items; open tasks require full written solutions with calculations shown. The syllabus covers twelve topic areas: real numbers and logarithms, algebraic expressions, equations and inequalities, systems of equations, functions (linear, quadratic, exponential), sequences, trigonometry, plane geometry, analytic geometry, solid geometry, combinatorics, and probability and statistics. Rotating solids (braces obrotowe) are excluded from Formuła 2023. CKE publishes the official exam papers and marking schemes the same afternoon as the exam. Official results are released in early July.

Questions

35 scored questions

Time Limit

180 minutes (3 hours); candidates may use a ruler, compass, simple calculator, and the official CKE mathematical formula sheet.

Passing Score

30% of total points (approximately 14 out of 46 points). This threshold applies to all three compulsory basic-level Matura subjects.

Exam Fee

Free for current-year Polish secondary school graduates. Retakers sitting a subject for the third time or more pay 50 zł per subject (2026 rate); low-income exemptions are available upon application by February 9, 2026. (Centralna Komisja Egzaminacyjna (CKE), Warsaw, Poland)

Matura Math Exam Content Outline

18%

Functions

Linear, quadratic, exponential, and logarithmic functions; domain, range, transformations, composition, extrema, and even/odd parity.

11%

Equations and Inequalities

Linear, quadratic, polynomial and rational equations/inequalities; absolute value; discriminant and Vieta's formulas.

11%

Planimetry

Triangles, circles, regular polygons, quadrilaterals; area/perimeter; Pythagorean theorem; inscribed angles; similarity.

10%

Real Numbers, Powers and Logarithms

Operations in ℝ, integer and fractional exponents, roots, absolute value, logarithm rules and change-of-base.

Stereometry

Prisms, pyramids, cones, spheres — volumes and surface areas; space diagonals. Rotating solids excluded under Formuła 2023.

Sequences

Arithmetic and geometric sequences; term formulas; finite and infinite sums; compound interest applications.

Algebraic Expressions

Multiplication identities, polynomial factoring, simplification of rational expressions.

Analytic Geometry

Line and circle equations in the Cartesian plane; slopes; perpendicular/parallel lines; distance and midpoint formulas.

Trigonometry

Sine, cosine, tangent (0°–180°); key angle values; Law of Cosines; solving triangles; basic trig equations.

Systems of Equations

Linear systems with two unknowns solved by substitution or elimination; word-problem modelling.

Combinatorics

Counting principles, permutations, combinations C(n,k), digit-restriction problems.

Probability and Statistics

Classical probability, complementary events, mean, median, mode, standard deviation.

How to Pass the Matura Math Exam

What You Need to Know

Passing score: 30% of total points (approximately 14 out of 46 points). This threshold applies to all three compulsory basic-level Matura subjects.
Exam length: 35 questions
Time limit: 180 minutes (3 hours); candidates may use a ruler, compass, simple calculator, and the official CKE mathematical formula sheet.
Exam fee: Free for current-year Polish secondary school graduates. Retakers sitting a subject for the third time or more pay 50 zł per subject (2026 rate); low-income exemptions are available upon application by February 9, 2026.

Keys to Passing

Complete 500+ practice questions
Score 80%+ consistently before scheduling
Focus on highest-weighted sections
Use our AI tutor for tough concepts

Matura Math Study Tips from Top Performers

1Master the formula sheet CKE provides — know which formulas are given and which must be memorised, such as trigonometric identities and the quadratic formula.

2Practise closed tasks under timed conditions: each MCQ is worth 1 point and should take no more than 2–3 minutes.

3For open tasks, always show full working even if you make an arithmetic error — partial credit is awarded for correct method.

4Review past official CKE papers (arkusze maturalne) from 2023 onwards, as Formuła 2023 papers differ significantly from older exams.

5Focus on functions and planimetry, which together represent roughly 30% of the exam; ensure you can identify vertex form, graph transformations, and similarity ratios.

6The 30% pass threshold means strategic preparation — secure easy points in real numbers, statistics, and basic sequences before tackling harder optimisation and stereometry problems.

Frequently Asked Questions

What is the Polish Matura Mathematics exam?

The Matura (egzamin maturalny) is Poland's secondary school leaving examination. Mathematics at the basic level (poziom podstawowy) is one of three compulsory written subjects and must be passed to obtain the Matura certificate. The current version is Formuła 2023.

What is the passing score for Matura Mathematics?

Candidates must score at least 30% of the total available points. The exam is worth 46 points in total, so approximately 14 points are needed to pass.

How many questions are on the exam and what types are there?

The exam contains approximately 35 tasks grouped in about 31 thematic sets. Roughly 25 are closed tasks (4-option multiple-choice or true/false, worth 29 points) and 10 are open tasks requiring written calculations (worth 17 points).

How long is the Matura Mathematics exam?

The exam lasts 180 minutes (3 hours). Candidates may use a ruler, compass, simple (non-graphing) calculator, and the official CKE formula sheet.

What topics are covered under Formuła 2023?

The twelve topic areas are: real numbers and logarithms, algebraic expressions, equations and inequalities, systems of equations, functions (linear, quadratic, exponential), sequences, trigonometry, plane geometry, analytic geometry, solid geometry, combinatorics, and probability and statistics. Rotating solids are excluded.

When is the 2026 Matura Mathematics exam held?

The main (May) sitting of Matura Mathematics 2026 was held on 5 May 2026. A resit session (termin poprawkowy) is available in August for candidates who narrowly failed.