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Exam Review

Key Facts: NMT Mathematics Exam

Official Tasks

UCEQA 2026 subject guidance

120 min

Shared Stage

UCEQA 2026 NMT structure

5/32

Raw Conversion Threshold

2026 admission rules, Appendix 5

NMT Mathematics: 22 official computer-based tasks, maximum 32 raw points. Stage 1: Ukrainian Language and Mathematics share 120 minutes. Candidates allocate time within the stage; there is no fixed 60-minute subject limit. Independent English-language four-option MCQ study adaptation by OpenExamPrep. These selected-topic exercises are supplementary, not an official translation, an official-format simulation, or a substitute for the full range of official tasks.

Sample NMT Mathematics Practice Questions

Try these sample questions to review concepts for the NMT Mathematics exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 93+ question experience with AI tutoring.

1Calculate the value of the numerical expression: $\frac{3.6 \times 10^{-2}}{1.2 \times 10^{-4}}$.

A.300

B.30

C.3

D.3000

Explanation: Divide the coefficients and subtract the exponents of ten: $\frac{3.6}{1.2} = 3$, and $\frac{10^{-2}}{10^{-4}} = 10^{-2 - (-4)} = 10^2 = 100$. Multiplying these gives $3 \times 100 = 300$.

2Simplify the algebraic expression: $\frac{a^2 - 9}{a^2 - 3a}$ for $a \neq 0$ and $a \neq 3$.

A.\frac{a+3}{a}

B.\frac{a-3}{a}

C.\frac{a+3}{a-3}

D.1 + \frac{3}{a^2}

Explanation: Factor the numerator as a difference of squares: $a^2 - 9 = (a - 3)(a + 3)$. Factor the denominator by taking out the common factor $a$: $a^2 - 3a = a(a - 3)$. Canceling the non-zero term $(a - 3)$ leaves $\frac{a + 3}{a}$.

3Find both roots of $3x^2 - 10x + 3 = 0$.

A.3 and 1/3

B.-3 and -1/3

C.1 and 3

D.3 and -1/3

Explanation: Factor the polynomial as $(3x-1)(x-3)$. Setting each factor equal to zero gives $x=1/3$ or $x=3$.

4Solve the linear inequality: $3 - 2(x - 4) \ge 5x - 3$.

A.x \le 2

B.x \ge 2

C.x \le -2

D.x \ge -2

Explanation: Expand the brackets: $3 - 2x + 8 \ge 5x - 3$, which gives $11 - 2x \ge 5x - 3$. Move $x$ terms to the left: $-2x - 5x \ge -3 - 11$, resulting in $-7x \ge -14$. Dividing by $-7$ reverses the inequality sign: $x \le \frac{-14}{-7} = 2$.

5Compute the value of the logarithmic expression: $\log_2 48 - \log_2 3$.

A.4

B.16

C.8

D.2

Explanation: Apply the quotient property of logarithms: $\log_a x - \log_a y = \log_a (\frac{x}{y})$. Here, $\log_2 48 - \log_2 3 = \log_2(\frac{48}{3}) = \log_2 16$. Since $2^4 = 16$, the value is $4$.

6Solve the exponential equation: $4^{x+1} - 4^x = 48$.

A.x = 2

B.x = 3

C.x = 1.5

D.x = 4

Explanation: Factor out $4^x$ on the left side: $4^x(4^1 - 1) = 48 \implies 4^x(3) = 48$. Dividing both sides by 3 yields $4^x = 16$. Since $16 = 4^2$, we have $x = 2$.

7What is the domain (область визначення) of the function $f(x) = \sqrt{6 - 2x} + \frac{1}{x - 1}$?

A.(-\infty; 1) \cup (1; 3]

B.(-\infty; 3]

C.[3; +\infty)

D.(-\infty; 1) \cup (1; +\infty)

Explanation: The expression under the square root must be non-negative: $6 - 2x \ge 0 \implies 2x \le 6 \implies x \le 3$. The denominator cannot be zero: $x - 1 \neq 0 \implies x \neq 1$. Combining these conditions yields $x \in (-\infty; 1) \cup (1; 3]$.

8Find the coordinates of the vertex of the parabola given by $y = x^2 - 6x + 5$.

A.(3; -4)

B.(-3; 32)

C.(3; 5)

D.(6; 5)

Explanation: For a quadratic function $y = ax^2 + bx + c$, the x-coordinate of the vertex is $x_v = -\frac{b}{2a} = -\frac{-6}{2(1)} = 3$. Substitute $x = 3$ into the equation to find $y_v$: $y_v = 3^2 - 6(3) + 5 = 9 - 18 + 5 = -4$. The vertex is $(3; -4)$.

9In an arithmetic progression $(a_n)$, the first term is $a_1 = 7$ and the common difference is $d = 4$. What is the sum of the first 15 terms ($S_{15}$)?

A.525

B.495

C.510

D.540

Explanation: The sum formula for an arithmetic progression is $S_n = \frac{2a_1 + (n - 1)d}{2} \times n$. For $n = 15$: $S_{15} = \frac{2(7) + (15 - 1)4}{2} \times 15 = \frac{14 + 56}{2} \times 15 = \frac{70}{2} \times 15 = 35 \times 15 = 525$.

10In a geometric progression $(b_n)$, $b_2 = 6$ and $b_5 = 162$. What is the common ratio $q$?

A.3

B.2

C.4

D.9

Explanation: The $n$-th term of a geometric progression is $b_n = b_1 q^{n-1}$. Dividing $b_5$ by $b_2$ eliminates $b_1$: $\frac{b_5}{b_2} = \frac{b_1 q^4}{b_1 q^1} = q^3$. Thus, $q^3 = \frac{162}{6} = 27$. Taking the cube root gives $q = 3$.

About the NMT Mathematics Exam

NMT Mathematics is a compulsory subject of Ukraine’s National Multi-Subject Test for higher-education admission. Independent English-language four-option MCQ study adaptation by OpenExamPrep. These selected-topic exercises are supplementary, not an official translation, an official-format simulation, or a substitute for the full range of official tasks.

Exam sponsor: Ukrainian Center for Educational Quality Assessment (УЦОЯО / UCEQA). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Computer-based subject component of Національний мультипредметний тест (НМТ / NMT). 15 single-choice tasks with five options each, 3 matching tasks, and 4 short numerical-answer tasks.

Time Limit

Stage 1: Ukrainian Language and Mathematics share 120 minutes. Candidates allocate time within the stage; there is no fixed 60-minute subject limit.

Passing Score

5 of 32 raw points is the minimum for a converted 100–200 result in 2026; it does not guarantee admission.

Exam / Certification Fees

Free participation; travel costs separate

Exam sponsor website

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

Official sources

UCEQA 2026 subject scope and task forms · Source checked 2026-10-23
UCEQA 2026 NMT structure and assessment languages · Source checked 2026-10-23
UCEQA 2026 candidate FAQ · Source checked 2026-10-23
2026 admission rules and score-conversion tables, Appendix 5 · Source checked 2026-10-23
UCEQA NMT participation procedure: no participation fee · Source checked 2026-10-23General participation procedure; the 2026 interview with the UCEQA director also discusses paid participation only as a possible future change.
UCEQA director interview, 19 May 2026 · Source checked 2026-10-23

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.