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Exam Review

Key Facts: Czech Maturita Math Exam

Czech Maturita didaktický test z matematiky is administered centrally across the Czech Republic by CERMAT under MŠMT.

The examination duration is 135 minutes for standard test takers.

The spring 2026 test consisted of 25 tasks worth a total of 50 points.

The printed success threshold is 33 % of the maximum, i.e. at least 17 of 50 points.

Tasks 1–14 are open-response; tasks 15–25 are closed items with up to five alternatives.

Calculators without graphical or equation-solving modes and MFChT tables are permitted during the official sitting.

Test results are issued on a pass/fail basis with percentage scores, without letter grades on the school-leaving certificate.

Students may retake the test up to two times if unsuccessful on the first attempt.

Mathematics is an elective alternative to a foreign language in the common portion of the Czech Maturita.

The CERMAT Czech Maturita mathematics didaktický test is a 25-task, 135-minute paper worth 50 points covering algebra, functions, geometry, and probability; at least 17 points (33 % threshold) required to pass.

Sample Czech Maturita Math Practice Questions

Try these sample questions to review concepts for the Czech Maturita Math exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1A winter coat is initially discounted by 20%. During an end-of-season clearance, the already reduced price is further reduced by an additional 15%. If the final sale price of the coat is 1,224 CZK, what was its original full price before any discounts?
A.1,883 CZK
B.1,652 CZK
C.1,800 CZK
D.1,748 CZK
Explanation: Let P be the original price in CZK. After a 20% discount, the price becomes P * (1 - 0.20) = 0.80 * P. After a further 15% discount on this reduced price, the final price is (0.80 * P) * (1 - 0.15) = 0.80 * 0.85 * P = 0.68 * P. We are given 0.68 * P = 1,224 CZK. Solving for P: P = 1,224 / 0.68 = 1,800 CZK.
2What is the simplified exact value of the numerical expression sqrt(72) - sqrt(18) + sqrt(50)?
A.8*sqrt(2)
B.10*sqrt(2)
C.4*sqrt(2)
D.sqrt(104)
Explanation: Simplify each radical by factoring out perfect squares: sqrt(72) = sqrt(36 * 2) = 6*sqrt(2); sqrt(18) = sqrt(9 * 2) = 3*sqrt(2); sqrt(50) = sqrt(25 * 2) = 5*sqrt(2). Combining like terms gives: 6*sqrt(2) - 3*sqrt(2) + 5*sqrt(2) = (6 - 3 + 5)*sqrt(2) = 8*sqrt(2).
3For all real numbers x where the expression is defined (x not in {-3, 0, 3}), simplify the algebraic expression: ((x^2 - 9) / (2x^2 + 6x)) * ((4x) / (x - 3)).
A.2x / (x + 3)
B.(2x - 6) / (x + 3)
C.4
D.2
Explanation: Factor all numerators and denominators: x^2 - 9 = (x - 3)(x + 3); 2x^2 + 6x = 2x(x + 3). Substituting these factorizations into the product: [((x - 3)(x + 3)) / (2x(x + 3))] * [(4x) / (x - 3)]. Cancel the common factors (x + 3) and (x - 3): [1 / (2x)] * (4x) = 4x / (2x) = 2.
4Evaluate the following numerical expression and write the result in standard scientific notation: ((3.6 * 10^7) / (1.2 * 10^(-3))) * (2.0 * 10^(-5)).
A.6.0 * 10^9
B.6.0 * 10^5
C.6.0 * 10^(-1)
D.6.0 * 10^4
Explanation: Separate the decimal coefficients from the powers of 10: Coefficient: (3.6 / 1.2) * 2.0 = 3.0 * 2.0 = 6.0. Power of 10: 10^(7 - (-3) + (-5)) = 10^(7 + 3 - 5) = 10^5. Combining gives 6.0 * 10^5.
5For all real numbers a != 2 and a != -2, simplify the expression: ((a^3 - 8) / (a^2 - 4)) - ((a^2 + 2a + 4) / (a + 2)).
A.0
B.1
C.4 / (a + 2)
D.-4 / (a + 2)
Explanation: Factor the numerator and denominator of the first term using the difference of cubes and difference of squares formulas: a^3 - 8 = (a - 2)(a^2 + 2a + 4); a^2 - 4 = (a - 2)(a + 2). Thus, the first fraction becomes: [(a - 2)(a^2 + 2a + 4)] / [(a - 2)(a + 2)] = (a^2 + 2a + 4) / (a + 2). Now subtract the second fraction: (a^2 + 2a + 4)/(a + 2) - (a^2 + 2a + 4)/(a + 2) = 0.
6Rationalize the denominator of the fraction 6 / (sqrt(7) - 1) and simplify the expression completely.
A.sqrt(7) - 1
B.6*sqrt(7) + 6
C.sqrt(7) + 1
D.(sqrt(7) + 1) / 2
Explanation: Multiply both numerator and denominator by the conjugate of the denominator, which is (sqrt(7) + 1): [6 * (sqrt(7) + 1)] / [(sqrt(7) - 1)(sqrt(7) + 1)]. The denominator becomes (sqrt(7))^2 - 1^2 = 7 - 1 = 6. Dividing numerator and denominator by 6: [6 * (sqrt(7) + 1)] / 6 = sqrt(7) + 1.
7For any positive real number x > 0, simplify the radical expression: (x^(3/2) * (x^2)^(1/3)) / x^(1/6).
A.x^(7/6)
B.x^2
C.x^(5/3)
D.x^(8/3)
Explanation: Convert all components into fractional powers of x: x^(3/2) has exponent 3/2; (x^2)^(1/3) = x^(2/3); x^(1/6) has exponent 1/6. Apply the rules of exponents: x^(3/2 + 2/3 - 1/6). Find a common denominator for the exponents (common denominator is 6): 3/2 = 9/6; 2/3 = 4/6; 1/6 = 1/6. The exponent is (9 + 4 - 1)/6 = 12/6 = 2. Thus, the expression equals x^2.
8Given two intervals of real numbers A = (-4, 3] and B = [1, 6), determine the set difference A \ B (elements that belong to A but not to B).
A.(-4, 1]
B.[-4, 1)
C.(-4, 6)
D.(-4, 1)
Explanation: The set difference A \ B consists of all numbers x such that x in A and x not in B. A = {x in R: -4 < x <= 3} and B = {x in R: 1 <= x < 6}. Since B contains 1, 1 is excluded from the set difference. The elements remaining in A are all x satisfying -4 < x < 1. In interval notation, this is (-4, 1).
9For any real number x in the open interval (-3, -1), simplify the absolute value expression: |x + 3| - |2x - 4| + |x|.
A.2x - 1
B.4x + 7
C.-1
D.2x + 7
Explanation: Determine the sign of each argument when x in (-3, -1): 1) Since x > -3, x + 3 > 0, so |x + 3| = x + 3. 2) Since x < -1, 2x - 4 < 2(-1) - 4 = -6 < 0, so |2x - 4| = -(2x - 4) = -2x + 4. 3) Since x < -1 < 0, x is negative, so |x| = -x. Substituting these into the expression: (x + 3) - (-2x + 4) + (-x) = x + 3 + 2x - 4 - x = 2x - 1.
10Find the greatest common divisor (GCD / NSD) and the least common multiple (LCM / NSN) of the positive integers 84 and 126.
A.GCD = 14, LCM = 504
B.GCD = 21, LCM = 252
C.GCD = 42, LCM = 252
D.GCD = 42, LCM = 504
Explanation: Write the prime factorizations: 84 = 4 * 21 = 2^2 * 3^1 * 7^1; 126 = 2 * 63 = 2^1 * 3^2 * 7^1. GCD takes the lowest power of each common prime factor: GCD(84, 126) = 2^1 * 3^1 * 7^1 = 42. LCM takes the highest power of each prime factor: LCM(84, 126) = 2^2 * 3^2 * 7^1 = 4 * 9 * 7 = 252. Verify: GCD * LCM = 42 * 252 = 10,584 = 84 * 126.

About the Czech Maturita Math Exam

The Czech Mathematics Didaktický Test (didaktický test z matematiky) is the centralized written examination in mathematics administered by CERMAT for the common portion (společná část) of the Czech school-leaving maturitní zkouška. Upper-secondary students may choose between mathematics and a foreign language for their second compulsory state exam. The spring 2026 paper contains 25 tasks worth 50 points, completed in 135 minutes, with a printed success threshold of 33 % (at least 17 points). Permitted aids include the MFChT tables, a non-graphing calculator without equation solving, and drawing instruments. This practice bank is an English-language four-option multiple-choice study adaptation, not a simulation of the official paper: the real test is mostly open-response, including broadly-open tasks where the worked solution itself is marked, so use these items to drill the underlying principles, formulas, and calculation techniques rather than the exam format.

Exam sponsor: CERMAT (Centrum pro zjišťování výsledků vzdělávání) under MŠMT ČR. The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Questions

25 questions

Time Limit

135 minutes (standard); extended for approved accommodations and by 10 minutes under § 20(4) of the Education Act.

Passing Score

At least 17 out of 50 points; the booklet states the success threshold as 33 %. Results are reported as pass/fail (uspěl/neuspěl) with a percentage score.

Exam / Certification Fees

No exam fee; centrally funded state school-leaving examination in the Czech Republic.

Exam sponsor website

Fees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.

Our practice resources: topics covered

We aim to reflect publicly available exam outlines and topic information in our study resources. Coverage, format, and difficulty may differ from the actual exam, and we cannot guarantee that every detail is accurate or current. Confirm exam requirements, fees, and policies with the official exam sponsor.

20%

Ciselne obory a algebraicke vyrazy (Numbers and Algebra)

Operations with real numbers, powers, roots, factoring polynomials, rational expressions, percentages, and financial math.

20%

Rovnice a nerovnice (Equations and Inequalities)

Linear and quadratic equations, absolute value, rational inequalities, exponential/logarithmic equations, and systems.

20%

Funkce a jejich vlastnosti (Functions)

Linear, quadratic, rational, exponential, logarithmic, and trigonometric functions, domains, ranges, and graphical interpretations.

20%

Geometrie v rovine a prostoru (Geometry)

Planimetry (Pythagorean and Euclid theorems, similarity, circles), stereometry (solids, volume, surface area), and 2D/3D vectors and analytic geometry.

20%

Kombinatorika, pravdepodobnost a statistika (Probability and Statistics)

Combinatorics formulas (variations, permutations, combinations), classical probability, independent events, and statistical measures.

Preparing for the Czech Maturita Math Exam

What You Need to Know

  • Passing score: At least 17 out of 50 points; the booklet states the success threshold as 33 %. Results are reported as pass/fail (uspěl/neuspěl) with a percentage score.
  • Exam length: 25 questions
  • Time limit: 135 minutes (standard); extended for approved accommodations and by 10 minutes under § 20(4) of the Education Act.
  • Exam / certification fees: No exam fee; centrally funded state school-leaving examination in the Czech Republic. Official sources

Using Our Practice Resources

  • Work through all 100 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
  • Use our AI tutor for tough concepts

Czech Maturita Math: Suggested Study Strategy

1Familiarize yourself with the exact layout of the MFChT tables so you can locate formulas for trigonometry, analytic geometry, and stereometry in seconds.
2Practice multi-step algebraic manipulation carefully: sign errors in quadratic equations and rational expressions are the most common source of lost points.
3Master functional properties: practice sketching graphs of transformed rational functions and finding the domain of expressions involving fractions, roots, and logarithms.
4In analytic geometry, always write down direction and normal vectors first before attempting to find line intersections or distances.
5Work through past CERMAT spring and autumn tests under a strict 135-minute timer to build pacing and calculation endurance.

Frequently Asked Questions

What is the Czech Maturita didaktický test z matematiky?

It is the standardized national mathematics paper administered by CERMAT as part of the společná část (common portion) of the Czech school-leaving examination. Students who do not choose a foreign language take mathematics.

What is the passing score for Czech Maturita mathematics in 2026?

The test booklet prints a success threshold (hranice úspěšnosti) of 33 % of the 50-point maximum, which means you must score at least 17 points. The score is reported as pass/fail (uspěl/neuspěl) with an exact percentage.

How long is the test and what aids are allowed?

The test duration is 135 minutes. You may use standard secondary school mathematical, physical, and chemical tables (MFChT), drawing tools (ruler, triangle, compass), and a scientific calculator without CAS or graphing capabilities.

Is this practice bank an official CERMAT test?

No. This practice bank is an independent English-language MCQ study adaptation developed to help students practice and review the core mathematical principles, formulas, and problem types tested on the official CERMAT blueprint.