Free Practice Questions for ÖABT İlköğretim Matematik

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Sample ÖABT İlköğretim Matematik Practice Questions

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

1Evaluate the limit: $\lim_{x \to 2} \frac{x^3 - 8}{x^2 + x - 6}$.

A.12/5

B.2

C.3/5

D.8/3

Explanation: Factoring the numerator yields $x^3 - 8 = (x - 2)(x^2 + 2x + 4)$, and the denominator factors as $x^2 + x - 6 = (x - 2)(x + 3)$. Canceling the common factor $(x - 2)$ for $x \ne 2$ gives $\lim_{x \to 2} \frac{x^2 + 2x + 4}{x + 3} = \frac{4 + 4 + 4}{2 + 3} = \frac{12}{5}$.

2Evaluate the trigonometric limit: $\lim_{x \to 0} \frac{1 - \cos(4x)}{x \sin(2x)}$.

A.4

B.2

C.8

D.1

Explanation: Using the half-angle identity $1 - \cos(4x) = 2 \sin^2(2x)$, the expression becomes $\frac{2 \sin^2(2x)}{x \sin(2x)} = \frac{2 \sin(2x)}{x}$. Applying the fundamental trigonometric limit $\lim_{x \to 0} \frac{\sin(2x)}{2x} = 1$, we get $2 \cdot 2 \cdot \lim_{x \to 0} \frac{\sin(2x)}{2x} = 4$.

3Find the limit at infinity: $\lim_{x \to +\infty} \left(\sqrt{x^2 + 6x + 2} - x\right)$.

A.3

B.6

C.0

D.+\infty

Explanation: Multiplying and dividing by the conjugate gives $\frac{(x^2 + 6x + 2) - x^2}{\sqrt{x^2 + 6x + 2} + x} = \frac{6x + 2}{\sqrt{x^2(1 + 6/x + 2/x^2)} + x}$. Factoring out $x$ from numerator and denominator yields $\lim_{x \to +\infty} \frac{6 + 2/x}{\sqrt{1 + 6/x + 2/x^2} + 1} = \frac{6}{1 + 1} = 3$.

4Let $f(x)$ be defined by $f(x) = \begin{cases} \frac{\sin(ax)}{x}, & x < 0 \\ b + 3, & x = 0 \\ x^2 + 5x + 4, & x > 0 \end{cases}$. If $f(x)$ is continuous at $x = 0$, what is the value of $a + b$?

A.5

B.4

C.7

D.1

Explanation: For continuity at $x = 0$, we must have $\lim_{x \to 0^-} f(x) = f(0) = \lim_{x \to 0^+} f(x)$. The right-hand limit is $\lim_{x \to 0^+} (x^2 + 5x + 4) = 4$. Thus $f(0) = b + 3 = 4 \implies b = 1$. The left-hand limit is $\lim_{x \to 0^-} \frac{\sin(ax)}{x} = a = 4$. Therefore, $a + b = 4 + 1 = 5$.

5Given $f(x) = x^2 \ln(3x + 1)$, what is the exact value of $f'(1)$?

A.2\ln(4) + 3/4

B.2\ln(4) + 1/4

C.\ln(4) + 3/4

D.2\ln(4) + 3

Explanation: By the product rule, $f'(x) = 2x \ln(3x + 1) + x^2 \cdot \frac{3}{3x + 1}$. Evaluating at $x = 1$, we obtain $f'(1) = 2(1) \ln(4) + (1)^2 \cdot \frac{3}{3(1) + 1} = 2\ln(4) + \frac{3}{4}$.

6Find the slope of the tangent line to the curve $x^3 + y^3 - 6xy = 0$ at the point $(3, 3)$.

A.-1

B.1

C.-2

D.0

Explanation: Differentiating implicitly with respect to $x$ gives $3x^2 + 3y^2 y' - 6(y + x y') = 0$. Grouping terms gives $(3y^2 - 6x)y' = 6y - 3x^2$, so $y' = \frac{6y - 3x^2}{3y^2 - 6x} = \frac{2y - x^2}{y^2 - 2x}$. Substituting $(3, 3)$ yields $y' = \frac{2(3) - 3^2}{3^2 - 2(3)} = \frac{6 - 9}{9 - 6} = \frac{-3}{3} = -1$.

7A rectangular garden is to be fenced on all four sides with a total perimeter of 48 meters. What is the maximum possible area of the garden?

A.144 m²

B.120 m²

C.196 m²

D.96 m²

Explanation: Let the dimensions be $x$ and $y$. The perimeter constraint is $2x + 2y = 48 \implies x + y = 24 \implies y = 24 - x$. The area function is $A(x) = x(24 - x) = 24x - x^2$. Taking the derivative, $A'(x) = 24 - 2x = 0 \implies x = 12$. Since $A''(x) = -2 < 0$, this yields a maximum area of $A(12) = 12(12) = 144\text{ m}^2$.

8According to the Mean Value Theorem for derivatives, there exists at least one value $c \in (0, 3)$ such that $f'(c) = \frac{f(3) - f(0)}{3 - 0}$ for $f(x) = x^3 - 3x$. What is $c$?

A.\sqrt{3}

B.1

C.\sqrt{2}

D.2

Explanation: First evaluate the average rate of change: $f(3) = 27 - 9 = 18$ and $f(0) = 0$, so $\frac{18 - 0}{3} = 6$. The derivative is $f'(x) = 3x^2 - 3$. Setting $f'(c) = 6$ yields $3c^2 - 3 = 6 \implies 3c^2 = 9 \implies c^2 = 3$. Since $c \in (0, 3)$, we have $c = \sqrt{3} \approx 1.732$.

9Find the x-coordinate of the inflection point of the cubic polynomial $f(x) = 2x^3 - 9x^2 + 12x - 5$.

A.3/2

B.1

C.2

D.5/2

Explanation: The first derivative is $f'(x) = 6x^2 - 18x + 12$, and the second derivative is $f''(x) = 12x - 18$. Setting $f''(x) = 0$ gives $12x = 18 \implies x = 18/12 = 3/2$. Since $f''(x)$ changes sign across $x = 3/2$ (from negative to positive), $(3/2, f(3/2))$ is the unique inflection point.

10A 10-meter ladder leans against a vertical wall. If the bottom of the ladder slides horizontally away from the wall at a rate of 2 m/s, how fast is the top of the ladder sliding down when the bottom is 6 meters from the wall?

A.1.5 m/s

B.2.0 m/s

C.1.2 m/s

D.2.5 m/s

Explanation: By the Pythagorean theorem, $x^2 + y^2 = 100$. When $x = 6$, $y = \sqrt{100 - 36} = 8$. Differentiating with respect to time $t$ gives $2x \frac{dx}{dt} + 2y \frac{dy}{dt} = 0$. Substituting $x = 6, y = 8$, and $\frac{dx}{dt} = 2$: $2(6)(2) + 2(8)\frac{dy}{dt} = 0 \implies 24 + 16\frac{dy}{dt} = 0 \implies \frac{dy}{dt} = -1.5\text{ m/s}$. Thus the top slides down at $1.5\text{ m/s}$.

About the ÖABT İlköğretim Matematik Exam

ÖABT İlköğretim 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 distinct İlköğretim Matematik paper. This ID represents İlköğretim Matematik, distinct from the upper-secondary Matematik paper.

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 İlköğretim Matematik, distinct from the upper-secondary Matematik paper.

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.
Multivariable 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.
Probability distributions · 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.

24% of official paper

Geometry

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

16% of official paper

Applied mathematics

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

Preparing for the ÖABT İlköğretim 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 İlköğretim Matematik, distinct from the upper-secondary Matematik paper.
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

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ÖABT İlköğretim 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.