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100+ Free ЦТ Mathematics Practice Questions

Prepare for the ЦТ/ЦЭ Mathematics (Belarus Centralized Testing / Centralized Exam) exam with instant access — no signup required.

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2026 Statistics

Key Facts: ЦТ Mathematics Exam

30

total tasks (10 Part A + 20 Part B)

РИКЗ Specification 2026

210 min

exam duration (3.5 hours)

РИКЗ

0–100

standardized score scale

Ministry of Education of Belarus

4.50 BYN

registration fee per subject (0.1 base amount)

РИКЗ 2026

20 / 10

admission threshold scores (1st / 2nd profile)

Ministry of Education Rules

The Belarus ЦТ/ЦЭ Mathematics exam features 30 tasks (10 Part A + 20 Part B) administered over 210 minutes. Scored on a 0–100 scale with admission thresholds of 20 points (1st profile) and 10 points (2nd profile), the registration fee is 0.1 base amount (4.50 BYN in 2026). Practice with 100 questions covering algebra, trigonometry, and geometry.

Sample ЦТ Mathematics Practice Questions

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

1Find the sum of the greatest common divisor (GCD) and the least common multiple (LCM) of the numbers 72 and 120.
A.384
B.360
C.432
D.288
Explanation: Prime factorizations: 72 = 2³ · 3² and 120 = 2³ · 3 · 5. GCD(72, 120) = 2³ · 3 = 24. LCM(72, 120) = 2³ · 3² · 5 = 360. Their sum is 24 + 360 = 384.
2Convert the repeating decimal 0.2(36) = 0.2363636... into an irreducible common fraction.
A.26/110
B.13/55
C.236/990
D.7/30
Explanation: Using the standard formula for mixed repeating decimals: (236 - 2) / 990 = 234 / 990. Dividing numerator and denominator by 18 gives 13 / 55, which is irreducible.
3A solution contains 12% salt by mass. How many grams of pure water must be added to 300 g of this solution to obtain an 8% salt solution?
A.120 g
B.180 g
C.150 g
D.200 g
Explanation: Mass of salt in the initial solution: 300 · 0.12 = 36 g. Let w be the mass of water added. In the new solution: 36 / (300 + w) = 0.08 ⇒ 300 + w = 36 / 0.08 = 450 g ⇒ w = 450 - 300 = 150 g.
4The price of an item was first increased by 20%, and subsequently the new price was decreased by 15%. What was the net percentage change in the item's price relative to the original price?
A.Decreased by 5%
B.Increased by 5%
C.Increased by 3.5%
D.Increased by 2%
Explanation: Let the initial price be P. After a 20% increase, the price becomes 1.20P. After a 15% decrease, the new price is 1.20P · (1 - 0.15) = 1.20P · 0.85 = 1.02P. This corresponds to an increase of (1.02 - 1) · 100% = 2%.
5Simplify the algebraic expression: ((a^(1/2) - b^(1/2)) / (a - b)) · (a^(1/2) + b^(1/2)) for a > 0, b > 0, a ≠ b.
A.1
B.a - b
C.a^(1/2) + b^(1/2)
D.a / b
Explanation: The denominator factors as a difference of squares: a - b = (a^(1/2) - b^(1/2))(a^(1/2) + b^(1/2)). Multiplying numerator terms gives (a^(1/2) - b^(1/2))(a^(1/2) + b^(1/2)) = a - b. Thus, (a - b) / (a - b) = 1.
6Compute the numerical value of the expression: √((3 - 2√2)²) + √((1 - 2√2)²).
A.4√2 - 4
B.2
C.4
D.2 - 4√2
Explanation: √(x²) = |x|. Since 3 = √9 > 2√2 = √8, 3 - 2√2 > 0, so |3 - 2√2| = 3 - 2√2. Since 1 < 2√2 = √8, 1 - 2√2 < 0, so |1 - 2√2| = -(1 - 2√2) = 2√2 - 1. Summing: (3 - 2√2) + (2√2 - 1) = 2.
7Calculate the exact value of: log₂(24) - log₂(3) + log_{√3}(9).
A.6
B.7
C.8
D.5
Explanation: log₂(24) - log₂(3) = log₂(24 / 3) = log₂(8) = 3. For log_{√3}(9), (√3)⁴ = (3^(1/2))⁴ = 3² = 9, so log_{√3}(9) = 4. Adding gives 3 + 4 = 7.
8Evaluate the value of the numerical expression: 25^(log₅(6)) + 4^(log₂(3)) - 10^(lg(7)).
A.42
B.38
C.31
D.29
Explanation: 25^(log₅(6)) = (5²)^(log₅(6)) = (5^(log₅(6)))² = 6² = 36. Similarly, 4^(log₂(3)) = (2²)^(log₂(3)) = 3² = 9. And 10^(lg(7)) = 7. Thus, 36 + 9 - 7 = 38.
9If x + y = 5 and xy = 6, find the numerical value of x³ + y³.
A.35
B.65
C.95
D.125
Explanation: Using the algebraic identity x³ + y³ = (x + y)³ - 3xy(x + y): x³ + y³ = 5³ - 3 · 6 · 5 = 125 - 90 = 35.
10Simplify the rational expression: ((x² - 9) / (x² + 6x + 9)) : ((2x - 6) / (x² - 9)) for all allowed values of x.
A.(x - 3) / 2
B.(x + 3) / 2
C.x - 3
D.(x - 3) / (2(x + 3))
Explanation: Factor every part: x² - 9 = (x - 3)(x + 3), x² + 6x + 9 = (x + 3)², 2x - 6 = 2(x - 3). The expression becomes: [(x - 3)(x + 3) / (x + 3)²] · [(x - 3)(x + 3) / (2(x - 3))] = [(x - 3) / (x + 3)] · [(x + 3) / 2] = (x - 3) / 2.

About the ЦТ Mathematics Exam

The Mathematics Centralized Testing (ЦТ) and Centralized Exam (ЦЭ) is the core STEM examination administered by RIKZ for secondary school graduation and university admission in Belarus. The paper consists of 30 tasks (10 closed-ended Part A items and 20 open-ended Part B items) completed over 210 minutes (3.5 hours). This practice bank offers 100 worked problem-solving questions across algebra, equations, geometry, and calculus.

Questions

30 scored questions

Time Limit

210 minutes

Passing Score

20/100 (1st profile) or 10/100 (2nd profile)

Exam Fee

4.50 BYN (Republican Institute for Knowledge Control (РИКЗ))

ЦТ Mathematics Exam Content Outline

~25%

Algebra & Expressions

Real numbers, fractions, powers, radicals, logarithms, and algebraic factoring.

~30%

Equations, Inequalities & Systems

Polynomial, rational, irrational, exponential, logarithmic, and trigonometric equations and systems.

~15%

Functions & Derivatives

Domain, range, monotonicity, graphing, derivative rules, critical points, and optimization.

~15%

Plane Geometry (Planimetry)

Properties of triangles, quadrilaterals, regular polygons, circles, and coordinate methods.

~15%

Solid Geometry (Stereometry)

Spatial figures, cross-sections, angles between lines/planes, surface areas, and volumes.

How to Pass the ЦТ Mathematics Exam

What You Need to Know

  • Passing score: 20/100 (1st profile) or 10/100 (2nd profile)
  • Exam length: 30 questions
  • Time limit: 210 minutes
  • Exam fee: 4.50 BYN

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

ЦТ Mathematics Study Tips from Top Performers

1Practice solving multi-step algebraic equations and inequalities using domain constraints (ODZ) methodically.
2Memorize key trigonometric identities and reduction formulas to simplify expressions rapidly.
3Draw accurate geometric sketches for both 2D and 3D geometry problems to identify right triangles and angles.
4Work through the 100 practice questions and review the step-by-step mathematical reasoning for every item.

Frequently Asked Questions

How many tasks are on the ЦТ Mathematics test and how long is it?

The official RIKZ examination has 30 tasks (10 in Part A and 20 in Part B) with a total time limit of 210 minutes (3 hours and 30 minutes).

What is the minimum passing score for ЦТ Mathematics?

The passing threshold is 20 points out of 100 when Mathematics is the 1st profile subject, and 10 points out of 100 when it is the 2nd profile subject.

Can I use a calculator on the ЦТ Mathematics exam?

No. Calculators are strictly prohibited on the ЦТ Mathematics exam in Belarus.

How much does registration cost for ЦТ Mathematics?

The fee for Centralized Testing (ЦТ) is 0.1 of a base amount (4.50 BYN in 2026) per subject. The Centralized Exam (ЦЭ) for secondary school graduates is free.

Is this bank the same language and format as the real ЦТ Mathematics paper?

No. The official RIKZ paper is sat in Belarusian or Russian and consists of 10 Part A items offering five answer options plus 20 Part B tasks whose answers must be written out as numbers. This bank is an English-language MCQ study adaptation with four options per question — a study aid for the official content, not an official translation or a format simulation.