Free Practice Questions for ÖABT Matematik

Exam-style questions and explanations by OpenExamPrep.

✓ No registration✓ No credit card

100+ Questions

100% Free

Loading practice questions...

Same family resources

Explore More ÖABT Öğretmenlik Alan Bilgisi Testi (Turkey)

Continue into nearby exams from the same family. Each card keeps practice questions, study guides, flashcards, videos, and articles in one place.

ÖABT İlköğretim Matematik (Turkey)

Practice Questions100 questions

ÖABT Kimya / Kimya Teknolojisi (Turkey)

Practice Questions100 questions

Sample ÖABT Matematik Practice Questions

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

1What is the value of the limit lim_{x -> 0} (e^x - 1 - x) / x^2?

A.1/2

B.1

C.0

D.1/6

Explanation: Applying Taylor expansion of e^x near x = 0, e^x = 1 + x + x^2/2 + O(x^3). Thus, e^x - 1 - x = x^2/2 + O(x^3), so dividing by x^2 yields 1/2 as x -> 0. Equivalently, applying L'Hopital's rule twice gives lim (e^x - 1)/(2x) = lim e^x / 2 = 1/2.

2For what value of the constant k is the function f(x) = { (sin(3x))/x if x != 0, 2k + 1 if x = 0 } continuous at x = 0?

A.1

B.3

C.0

D.2

Explanation: For continuity at x = 0, we must have lim_{x -> 0} f(x) = f(0). Since lim_{x -> 0} (sin(3x))/x = 3, we set 2k + 1 = 3, which solves to 2k = 2, hence k = 1.

3According to the Mean Value Theorem applied to f(x) = x^3 - 3x on the interval [0, 3], what is the value of c in (0, 3) satisfying f'(c) = (f(3) - f(0)) / (3 - 0)?

A.sqrt(3)

B.3/2

C.1

D.sqrt(6)

Explanation: We calculate f(0) = 0 and f(3) = 27 - 9 = 18. The average rate of change is (18 - 0)/3 = 6. The derivative is f'(x) = 3x^2 - 3. Setting 3c^2 - 3 = 6 gives 3c^2 = 9, so c^2 = 3. Since c must lie in (0, 3), c = sqrt(3).

4The function f(x)=x+ln(x), x>0, has inverse g. What is g′(1)?

A.1/2

B.2

C.1

D.−1/2

Explanation: Since f(1)=1, g(1)=1. The inverse-function derivative is g′(1)=1/f′(g(1)); with f′(x)=1+1/x, this gives 1/2. Positivity of f′ also verifies that f is strictly increasing on its domain.

5What is the exact value of the definite integral int_{0}^{1} x / (1 + x^2) dx?

A.(1/2) ln 2

B.ln 2

C.pi / 4

D.(1/2) ln(1/2)

Explanation: Let u = 1 + x^2, so du = 2x dx, which means x dx = du/2. When x = 0, u = 1; when x = 1, u = 2. Thus int_0^1 x/(1+x^2) dx = (1/2) int_1^2 (1/u) du = (1/2)[ln u]_1^2 = (1/2) ln 2.

6What is the value of the integral int_{0}^{pi} x sin(x) dx?

A.pi

B.2

C.0

D.2pi

Explanation: Using integration by parts: let u = x, dv = sin(x) dx, so du = dx and v = -cos(x). Then int_0^pi x sin(x) dx = [-x cos(x)]_0^pi - int_0^pi (-cos(x)) dx = (-pi cos(pi) - 0) + [sin(x)]_0^pi = (-pi)(-1) + (0 - 0) = pi.

7What is the value of the improper integral int_{0}^{infinity} x e^{-2x} dx?

A.1/4

B.1/2

C.1

D.1/8

Explanation: Recognizing the Gamma function or integrating by parts: int_0^infty x e^{-kx} dx = 1/k^2. With k = 2, this evaluates to 1/(2^2) = 1/4. Explicitly, [-x e^{-2x}/2]_0^infty + (1/2) int_0^infty e^{-2x} dx = 0 + (1/2)(1/2) = 1/4.

8Find the arc length of the parametrized curve r(t)=(3t²,2t³) for 0≤t≤1.

A.4√2−2

B.√13

C.2√2−1

D.4√2

Explanation: Differentiate to get r′(t)=(6t,6t²), whose speed on this interval is 6t√(1+t²). Its integral is [2(1+t²)^(3/2)]₀¹=4√2−2. This exceeds the endpoint distance √13, as an arc length should.

9The region 0≤x≤1, 0≤y≤x² is revolved about the horizontal line y=3. What is the resulting volume?

A.9π/5

B.π/5

C.36π/5

D.2π

Explanation: A vertical slice produces a washer with outer radius 3 and inner radius 3−x². Hence V=π∫₀¹[9−(3−x²)²]dx=π∫₀¹(6x²−x⁴)dx=π(2−1/5)=9π/5. The offset axis requires subtracting the inner disk.

10What is the sum of the infinite telescoping series sum_{n=1}^{infinity} 1 / (n(n + 1))?

A.1

B.1/2

C.2

D.3/2

Explanation: Using partial fractions, 1 / (n(n + 1)) = 1/n - 1/(n + 1). The partial sum is S_N = (1 - 1/2) + (1/2 - 1/3) + ... + (1/N - 1/(N + 1)) = 1 - 1/(N + 1). Taking N -> infinity, lim S_N = 1 - 0 = 1.

About the ÖABT Matematik Exam

ÖABT Matematik is a separately named ÖSYM field-knowledge assessment used in the MEB Academy selection system. Its published scope includes analysis, algebra, geometry and applied mathematics for the upper-secondary Matematik paper. This ID represents the official Matematik paper for upper-secondary candidates, distinct from İlköğretim Matematik.

Exam sponsor: ÖSYM / Milli Eğitim Bakanlığı (MEB). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

One written field test of 50 five-option MCQs in Turkish, lasting 90 minutes. No mandatory oral, practical, assignment or separate case-study submission occurs within this paper. The mandatory AGS session and subsequent Academy training and assessments are separate. This ID represents the official Matematik paper for upper-secondary candidates, distinct from İlköğretim Matematik.

Time Limit

90 minutes

Passing Score

No universal pass mark. Standardized scores support selection; at least 1 net in AGS and the relevant ÖABT test is required for score calculation.

Exam / Certification Fees

TRY 800 for ÖABT (late application TRY 1,200), plus the mandatory AGS session at TRY 800 (late TRY 1,200).

Exam sponsor website

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

Official sources

2026 ÖSYM MEB-AGS/ÖABT guide · Source checked 2026-10-21Identity, eligibility, language/format, fees, duration, scoring and Table 1 scope.
2026 results announcement · Source checked 2026-10-21Sitting held 26 July 2026; results released 26 August 2026.
Vector calculus · Source checked 2026-10-21Content reference for independent study; not an endorsement of this bank.
Linear algebra · Source checked 2026-10-21Content reference for independent study; not an endorsement of this bank.
Statistical inference · Source checked 2026-10-21Content reference for independent study; not an endorsement of this bank.

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.

36% of official paper

Analysis

Analysis. Published approximate weight in the 2026 guide, Table 1.

24% of official paper

Algebra

Algebra. Published approximate weight in the 2026 guide, Table 1.

20% of official paper

Geometry

Geometry. Published approximate weight in the 2026 guide, Table 1.

20% of official paper

Applied mathematics

Applied mathematics. Published approximate weight in the 2026 guide, Table 1.

Preparing for the ÖABT Matematik Exam

What You Need to Know

Passing score: No universal pass mark. Standardized scores support selection; at least 1 net in AGS and the relevant ÖABT test is required for score calculation.
Assessment: One written field test of 50 five-option MCQs in Turkish, lasting 90 minutes. No mandatory oral, practical, assignment or separate case-study submission occurs within this paper. The mandatory AGS session and subsequent Academy training and assessments are separate. This ID represents the official Matematik paper for upper-secondary candidates, distinct from İlköğretim Matematik.
Time limit: 90 minutes
Exam / certification fees: TRY 800 for ÖABT (late application TRY 1,200), plus the mandatory AGS session at TRY 800 (late TRY 1,200). 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

ÖABT Matematik: Suggested Study Strategy

1Use the 2026 guide and applicable MEB Academy notice to check the official field and current application conditions.

2Review the Turkish terminology and primary subject resources alongside these English explanations.

3Complete additional Turkish-language study across the published outline; this selected set does not exhaust the field.

Frequently Asked Questions

What are the eligibility and other assessment requirements?

The 2026 guide requires the statutory Academy-entry conditions. Graduation from a MEB-approved higher-education program for the intended field is required by the Academy application date. Check the applicable MEB recruitment notice for accepted programs and other conditions; test participation does not confer an appointment right. All candidates must take the morning AGS session; subsequent Academy training is separate.

How is the real examination scored?

Raw score is correct answers minus one-quarter of wrong answers. Scores are standardized and combined under the guide’s field-specific rules; there is no universal pass mark or automatic appointment.