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100+ Free DIM Bakalavr Group I Practice Questions

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Key Facts: DIM Bakalavr Group I Exam

400 pts

Max Block Score

State Examination Center (DİM)

90

Total Questions

State Examination Center (DİM)

180 min

Exam Duration

State Examination Center (DİM)

50 AZN

Registration Fee

DİM Official Tariff

The DIM Bakalavr Group I exam is Azerbaijan's centralized Stage 2 undergraduate entrance test for engineering, IT, physics, and technical faculties. Administered by the State Examination Center (DİM), the test features 90 questions across Mathematics (30), Physics (30), and Chemistry/Informatics (30) for a maximum score of 400 points over 180 minutes, contributing to a 700-point total admission score alongside the Stage 1 Buraxılış exam. The official exam is administered in Azerbaijani or Russian; this bank is an English-language MCQ study adaptation.

Sample DIM Bakalavr Group I Practice Questions

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

1For what value of m does the quadratic equation x^2 - 6x + m = 0 have exactly one real root (a double root)?
A.m = 9
B.m = -9
C.m = 36
D.m = 3
Explanation: A quadratic equation ax^2 + bx + c = 0 has exactly one real root when its discriminant D = b^2 - 4ac equals 0. Here, a = 1, b = -6, and c = m. Setting D = (-6)^2 - 4(1)(m) = 36 - 4m = 0 yields 4m = 36, which gives m = 9.
2What is the exact simplified value of sin^4(x) - cos^4(x) in terms of cos(2x)?
A.-cos(2x)
B.cos(2x)
C.-sin(2x)
D.sin(2x)
Explanation: Using the difference of squares factorization, sin^4(x) - cos^4(x) = (sin^2(x) - cos^2(x))(sin^2(x) + cos^2(x)). Since sin^2(x) + cos^2(x) = 1, this simplifies to sin^2(x) - cos^2(x) = -(cos^2(x) - sin^2(x)) = -cos(2x).
3What is the domain of the real-valued function f(x) = sqrt(16 - x^2) / (x - 2)?
A.[-4, 2) U (2, 4]
B.[-4, 4]
C.(-4, 4) \ {2}
D.(-inf, -4] U [4, inf)
Explanation: For the square root in the numerator to be defined in real numbers, 16 - x^2 >= 0, which requires -4 <= x <= 4. The denominator requires x - 2 != 0, so x != 2. Combining these two restrictions gives the domain [-4, 2) U (2, 4].
4What is the local minimum value of the cubic polynomial function f(x) = 2x^3 - 9x^2 + 12x + 5?
A.9
B.10
C.5
D.8
Explanation: Find the critical points by differentiating: f'(x) = 6x^2 - 18x + 12 = 6(x^2 - 3x + 2) = 6(x - 1)(x - 2). Setting f'(x) = 0 yields critical points at x = 1 and x = 2. The second derivative is f''(x) = 12x - 18. At x = 2, f''(2) = 6 > 0, indicating a local minimum. Evaluating f(2) = 2(8) - 9(4) + 12(2) + 5 = 16 - 36 + 24 + 5 = 9.
5In a right triangle ABC with hypotenuse AB = 25 cm and leg AC = 15 cm, what is the length of the altitude drawn from the right angle C to the hypotenuse AB?
A.12 cm
B.10 cm
C.14 cm
D.9.6 cm
Explanation: First find the second leg BC using the Pythagorean theorem: BC = sqrt(25^2 - 15^2) = sqrt(625 - 225) = sqrt(400) = 20 cm. The area of triangle ABC can be computed as (AC * BC)/2 = (15 * 20)/2 = 150 cm^2. Equating this to (AB * h_c)/2 gives (25 * h_c)/2 = 150, so h_c = 300 / 25 = 12 cm.
6Given two vectors a = (3, -4) and b = (k, 6), for what value of k are vectors a and b perpendicular (orthogonal)?
A.k = 8
B.k = -8
C.k = 4.5
D.k = -4.5
Explanation: Two nonzero vectors are perpendicular if and only if their scalar (dot) product equals zero: a . b = (3)(k) + (-4)(6) = 0. This simplifies to 3k - 24 = 0, which yields 3k = 24, so k = 8.
7What is the solution to the equation log_2(x - 3) + log_2(x - 1) = 3?
A.x = 5
B.x = -1
C.x = 5 and x = -1
D.x = 7
Explanation: First establish the domain: x - 3 > 0 and x - 1 > 0, which requires x > 3. Using the product property of logarithms, log_2((x - 3)(x - 1)) = 3. Converting to exponential form gives (x - 3)(x - 1) = 2^3 = 8. Expanding yields x^2 - 4x + 3 = 8, so x^2 - 4x - 5 = 0. Factoring gives (x - 5)(x + 1) = 0, so x = 5 or x = -1. Since x = -1 is outside the domain, the unique valid solution is x = 5.
8A box contains 5 red balls and 7 blue balls. If 2 balls are drawn at random without replacement, what is the probability that both balls are red?
A.5/33
B.25/144
C.5/12
D.7/33
Explanation: Total number of balls is 5 + 7 = 12. The number of ways to choose 2 balls from 12 is C(12, 2) = (12 * 11) / 2 = 66. The number of ways to choose 2 red balls from 5 is C(5, 2) = (5 * 4) / 2 = 10. Thus, the probability is 10 / 66 = 5 / 33.
9A right circular cone has a base radius of 6 cm and a height of 8 cm. What is its total surface area?
A.96pi cm^2
B.60pi cm^2
C.36pi cm^2
D.120pi cm^2
Explanation: First find the slant height l of the cone using the Pythagorean theorem: l = sqrt(r^2 + h^2) = sqrt(6^2 + 8^2) = sqrt(36 + 64) = 10 cm. The lateral area is A_lat = pi * r * l = pi * 6 * 10 = 60pi cm^2. The base area is A_base = pi * r^2 = pi * 6^2 = 36pi cm^2. Total surface area is A_total = A_lat + A_base = 60pi + 36pi = 96pi cm^2.
10In an arithmetic progression, the third term is a_3 = 11 and the eighth term is a_8 = 31. What is the common difference d and the first term a_1?
A.d = 4, a_1 = 3
B.d = 4, a_1 = 5
C.d = 5, a_1 = 1
D.d = 3, a_1 = 5
Explanation: In an arithmetic progression, a_n = a_1 + (n - 1)d. Thus a_8 - a_3 = 5d. Substituting values: 31 - 11 = 20 = 5d, so d = 4. Then a_3 = a_1 + 2d = a_1 + 2(4) = 11, which gives a_1 = 11 - 8 = 3.

About the DIM Bakalavr Group I Exam

The DIM Bakalavr Group I Entrance Examination (I ixtisas qrupu üzrə qəbul imtahanı) is the official centralized subject examination for students seeking undergraduate university admission to technical, engineering, mathematics, computer science, and IT specialties in Azerbaijan. Administered by the State Examination Center (DİM), it constitutes Stage 2 (Blok imtahanı) of the undergraduate admission model.

Assessment

Centralized Stage 2 block test featuring 30 Mathematics questions, 30 Physics questions, and 30 Chemistry/Informatics questions

Time Limit

180 minutes (3 hours)

Passing Score

Competitive admission based on combined score (up to 700 points: 300 from Stage 1 Buraxılış + 400 from Stage 2 block exam); general eligibility minimum typically starts at 150-200 total points.

Exam Fee

50 AZN (State Examination Center (DİM) of Azerbaijan)

DIM Bakalavr Group I Exam Content Outline

35%

Mathematics

Algebraic transformations, equations and inequalities, functions and graphs, trigonometry, derivatives, plane and solid geometry, vectors, and combinatorics.

35%

Physics

Kinematics, dynamics, conservation laws, mechanical vibrations and waves, molecular physics, thermodynamics, electric circuits, magnetic fields, and geometric/wave optics.

30%

Chemistry & Technical Sciences

Atomic structure, periodic table properties, chemical bonding, reaction kinetics, solution equilibria, acids/bases, main-group chemistry, hydrocarbons, and functional organic compounds.

How to Pass the DIM Bakalavr Group I Exam

What You Need to Know

  • Passing score: Competitive admission based on combined score (up to 700 points: 300 from Stage 1 Buraxılış + 400 from Stage 2 block exam); general eligibility minimum typically starts at 150-200 total points.
  • Assessment: Centralized Stage 2 block test featuring 30 Mathematics questions, 30 Physics questions, and 30 Chemistry/Informatics questions
  • Time limit: 180 minutes (3 hours)
  • Exam fee: 50 AZN

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

DIM Bakalavr Group I Study Tips from Top Performers

1Prioritize high-yield mathematical problem solving: coordinate geometry, trigonometric identities, and derivative applications.
2Master dimensional analysis and unit conversions in physics mechanics and electrical circuit problems.
3Practice stoichiometry and chemical reaction balancing systematically to secure chemistry points quickly.

Frequently Asked Questions

What subjects are included in the DIM Bakalavr Group I block exam?

The Group I block exam includes Mathematics (30 questions), Physics (30 questions), and Chemistry (30 questions, or Informatics for the RK computer sub-track), totaling 90 questions.

How is the total admission score calculated for Group I?

The total admission score is out of 700 points: up to 300 points from the Stage 1 Buraxılış (School Leaving) exam, plus up to 400 points from the Stage 2 block exam (where subject scores are weighted by official coefficients).

In what language is the official DIM Bakalavr Group I exam delivered?

The official exam is administered in Azerbaijani or Russian, according to the candidate's language track. This practice bank is an English-language MCQ study adaptation.