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100+ Free Czech Maturita Math Practice Questions

Prepare for the Czech Maturita — Mathematics Didaktický Test (CERMAT) exam with instant access — no signup required.

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2026 Statistics

Key Facts: Czech Maturita Math Exam

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 test your Czech Maturita Math exam readiness. 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.

Questions

25 scored 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 Fee

No exam fee; centrally funded state school-leaving examination in the Czech Republic. (CERMAT (Centrum pro zjišťování výsledků vzdělávání) under MŠMT ČR)

Czech Maturita Math Exam Content Outline

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.

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

Keys to Passing

  • 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 Study Tips from Top Performers

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.