A square right prism with edge lengths 10, 10, 25 units is divided into unit cubes. Then, using all of these cubes, a square right prism with height 1 unit is formed with no gaps between them.
Accordingly, what is the surface area of this square right prism in square units?
A) 5200 B) 5400 C) 5600 D) 5800 E) 6000

A function $f$ defined on the set of real numbers satisfies the inequalities $$1 \leq f ( x ) \leq 2$$ for every $x$.
Accordingly,\ I. $\lim _ { x \rightarrow 1 } \frac { 1 } { f ( x ) }$ exists.\ II. $\lim _ { x \rightarrow 1 } \frac { f ( x ) } { x }$ exists.\ III. $\lim _ { x \rightarrow 1 } ( | f ( x ) | - f ( x ) )$ exists.
Which of the following statements are always true?\ A) Only I\ B) Only II\ C) Only III\ D) I and II\ E) II and III

ABCD rectangle, DEFG square\ $| \mathrm { DE } | = 6$ units\ $| \mathrm { AE } | = 3$ units\ $| \mathrm { AB } | = 12$ units\ $\mathrm { m } \widehat { ( \mathrm { BFC } ) } = \mathrm { x }$
Accordingly, what is $\cot ( x )$?\ A) $\frac { 1 } { \sqrt { 2 } }$\ B) $\frac { 1 } { 3 }$\ C) 1\ D) $\sqrt { 3 }$\ E) 2

$ABC$ triangle, AFD equilateral triangle, $[DE]$ // $[AB]$, $m ( \widehat { DFC } ) = x$
In the figure, $m \widehat { ( \mathrm { ACF } ) } = m \widehat { ( \mathrm { FCB } ) } = m \widehat { ( \mathrm { DEC } ) }$ and points $D$, $E$, $F$ lie on the sides of triangle ABC.
Accordingly, what is x in degrees?\ A) 20\ B) 25\ C) 30\ D) 35\ E) 40

ABC is a triangle $$\begin{aligned}& | \mathrm { AD } | = | \mathrm { CD } | = | \mathrm { BC } | \\& \mathrm { m } ( \widehat { \mathrm { BAD } } ) = 20 ^ { \circ } \\& \mathrm { m } ( \widehat { \mathrm { BCD } } ) = 60 ^ { \circ } \\& \mathrm { m } ( \widehat { \mathrm { ACD } } ) = \mathrm { x }\end{aligned}$$ Accordingly, what is x in degrees?\ A) 5\ B) 10\ C) 15\ D) 20\ E) 25

ABC isosceles triangle\ $AD \cap BC = \{ E \}$\ $AD \perp BC$\ $| \mathrm { AB } | = | \mathrm { BD } | = 6$ units\ $| AC | = | BC | = 9$ units\ $| CE | = \mathrm { x }$
Accordingly, what is x in units?\ A) 4\ B) 5\ C) 6\ D) 7\ E) 8

$ABC$ is a right triangle\ $\mathrm { AB } \perp \mathrm { AC }$\ $\mathrm { DE } \perp \mathrm { BC }$\ $| \mathrm { AD } | = | \mathrm { DB } | = 3$ units\ In triangle $ABC$, $D$ and $E$ lie on sides $AB$ and $BC$ respectively.\ If the area of triangle $ABC$ is 6 times the area of triangle $BDE$, what is $| AC |$ in units?\ A) $2 \sqrt { 3 }$\ B) $3 \sqrt { 2 }$\ C) $2 \sqrt { 6 }$\ D) 3\ E) 6

Aslı has divided her birthday cake into four equal slices as shown below.
Then, she shared one slice of this cake equally among Burcu, Cem, and Deniz.
Accordingly, what is the ratio of the amount that falls to Cem's share to the whole cake?
A) $\frac{1}{4}$
B) $\frac{1}{6}$
C) $\frac{1}{9}$
D) $\frac{1}{12}$
E) $\frac{1}{16}$

Melis, holding a piece of modeling clay, divides each piece of modeling clay she has into 2 pieces at each step, and after the 3rd step she has 8 pieces of modeling clay.
If Melis had divided each piece of modeling clay she had into 3 pieces instead of 2 at each step from the beginning, how many pieces of modeling clay would she have after the 4th step?
A) 12
B) 36
C) 51
D) 72
E) 81

Let $n$ and $k$ be positive integers. The value of $n _ { k }$ is defined as
- If $n$ is divisible by $k$, then $n _ { k } = \frac { n } { k }$ - If $n$ is not divisible by $k$, then $n _ { k } = 0$
Example: $$\begin{aligned} & 10 _ { 2 } = 5 \\ & 10 _ { 3 } = 0 \end{aligned}$$
Accordingly,
$$n _ { 2 } + n _ { 3 } = 10$$
what is the sum of the $n$ numbers that satisfy the equality?
A) 24 B) 28 C) 32 D) 36 E) 40

A two-compartment rectangular prism-shaped refrigerator has a lower compartment height of 1.5 meters and an upper compartment height of 0.5 meters. A decoration is attached to the top of the refrigerator's upper compartment as shown below.
Accordingly, the height of this attached decoration from the ground in meters could be which of the following?
A) $\sqrt{2}$
B) $\sqrt{3}$
C) $\sqrt{5}$
D) $\sqrt{6}$
E) $\sqrt{7}$

On a circular playground, five players named Ali, Büşra, Cem, Deniz, and Ekin are playing with a ball in positions shown in the figure. In each turn of this game; the player holding the ball passes it to the third player after them in the direction of the arrow.
Initially, the ball is in Ali's hands and the game starts when Ali passes the ball to Deniz. Deniz received the ball on the 1st turn, Büşra on the 2nd turn, and the game continued in this way.
Accordingly, who received the ball on the 99th turn?
A) Ali B) Büşra C) Cem D) Deniz E) Ekin

I. $-2 \square 25$ II. $2 \square \square -2$ III. $-2 \square -2$ In what order should the symbols for addition (+), subtraction (-), and multiplication (×) be placed in the empty boxes in the expressions so that the result of all three operations equals the same number?

	I	II	III
\cline{2-2} A)	+		$\times$
B)	-		+	-
C)	-		$\times$	+
D)	$\times$		+	-
E)	$\times$		-	+

Let $\mathrm { a }$, $\mathrm { b }$ and $c$ be non-zero real numbers,
$$\begin{aligned} & \mathrm { p } : \mathrm { a } + \mathrm { b } = 0 \\ & \mathrm { q } : \mathrm { a } + \mathrm { c } < 0 \\ & \mathrm { r } : \mathrm { c } < 0 \end{aligned}$$
the propositions are given.
$$( p \wedge q ) \Rightarrow r$$
Given that the proposition is false; what are the signs of $\mathbf { a }$, $\mathbf { b }$ and $\mathbf { c }$ respectively?
A) $+$, $-$, $+$ B) $+$, $-$, $-$ C) $-$, $-$, $+$ D) $+$, $+$, $-$

A natural number $a$ written inside an $n$-sided regular polygon is represented by a symbol that denotes the number $n \cdot a^{n}$.
For example, the symbol represents the number $3 \cdot 2^{3} = 24$.
Accordingly, which of the following symbols represents the value of the product?
A) [symbol A]
B) [symbol B]
C) [symbol C]
D) [symbol D]
E) $\square 4$

Let $a$ and $b$ be integers. The notation $\mathrm { a } \mid \mathrm { b }$ means that $a$ divides $b$ exactly.
A student wants to prove that the proposition "If integers $a$, $b$ and $c$ satisfy the conditions $a \mid c$ and $b \mid c$, then $(a + b) \mid c$ also holds." is false by using the counterexample method.
Accordingly, which of the following could be the example given by the student?

Let $a$, $b$, and $c$ be digits different from zero and from each other. Three numbers with decimal notations are given as:
$$\begin{aligned} K &= a,b \\ L &= b,c \\ M &= c,a \end{aligned}$$
Alican, who learned the ordering of numbers with decimal notation incorrectly, thought that the ordering of these three numbers should be done according to the magnitude of the value in the tenths place instead of the ones place, and obtained the ordering $\mathrm{K} < \mathrm{L} < \mathrm{M}$.
Accordingly, what is the correct ordering of these numbers?
A) $\mathrm{K} < \mathrm{M} < \mathrm{L}$
B) $\mathrm{L} < \mathrm{K} < \mathrm{M}$
C) $\mathrm{L} < \mathrm{M} < \mathrm{K}$
D) $\mathrm{M} < \mathrm{K} < \mathrm{L}$
E) $\mathrm{M} < \mathrm{L} < \mathrm{K}$

Below a 10 cm ruler with 0.8 cm distance on both sides, two identical 6 cm rulers with 0.2 cm distance on both sides are joined end to end without leaving a gap and aligned from the left as shown in the figure.
Accordingly, with which point on the 6 cm ruler is the right edge of the 10 cm ruler aligned?
A) 4
B) 4.5
C) 4.8
D) 5
E) 5.2

For positive integers $a$, $b$, and $c$,
$$a(b + c)$$
the expression equals an odd number.
Accordingly,
I. $a^{b} + c$ II. $b^{c} + a$ III. $c^{a} + b$
Which of these expressions always equals an odd number?
A) Only II
B) Only III
C) I and II
D) II and III
E) I, II, and III

Weights with their masses written on them are placed on the pans of an equal-armed balance as shown in the figure, balancing the scale.
When one of the weights given below is added to pan B of the scale and one of the weights on pan B is transferred to pan A, the scale remains balanced again.
Accordingly, how many grams is the weight added to pan B during this operation?
A) 10
B) 15
C) 30
D) 35
E) 40

When a square with side length $a$ units is divided into four regions as shown in the figure, region I represents a square with side length $b$ units.
For each $a$ and $b$ number satisfying this condition
$$a^{2} - 2ab + 2b^{2}$$
to which sum of areas of two regions is this expression equal?
A) I and II
B) I and IV
C) II and III
D) II and IV
E) III and IV

If 9 times a natural number $n$ equals a number that has the digit 3 in each of its digits, then $n$ is called a ternary number.
Accordingly, what is the sum of the digits of the smallest ternary number?
A) 7
B) 8
C) 9
D) 10
E) 11

In a project covering all 81 provinces in Turkey; first, $p$ parks are to be built in each province, and then $a$ trees are to be planted in each park built.
However, the number of parks to be built and trees to be planted in this plan was found to be insufficient, and first, one more park than the number of parks planned to be built in each province was built, and then one more tree than the number planned to be planted in each park was planted.
Accordingly, what is the difference between the total number of trees planted in the final situation and the total number of trees planned to be planted initially given correctly in which of the following?
A) 162
B) $81 \cdot a \cdot p$
C) $81 \cdot (a + p)$
D) $81 \cdot (a \cdot p + 1)$
E) $81 \cdot (a + p + 1)$

Let L be a real number. For functions f and g defined on the set of real numbers,
$$\lim _ { x \rightarrow 2 } f ( x ) = \lim _ { x \rightarrow 2 } g ( x ) = L$$
equality is satisfied.
Accordingly,
I. $f ( 2 ) = g ( 2 )$ II. $\lim _ { \mathrm { x } \rightarrow 2 } ( \mathrm { f } ( \mathrm { x } ) - \mathrm { g } ( \mathrm { x } ) ) = 0$ III. $\lim _ { x \rightarrow 2 } \frac { f ( x ) } { g ( x ) } = 1$
Which of the following statements are always true?
A) Only I B) Only II C) I and III D) II and III E) I, II and III

The unit prices used by Ali Bey, who conducts house and land buying and selling transactions in a certain region, are given in the table.

\cline{2-3} \multicolumn{1}{c|}{}	\begin{tabular}{ c } Purchase price
(TL)

&

Selling price

(TL)

\hline

House

$(1 \mathrm{~m}^{2})$

& 3000 & 3200 \hline

Land

(1 decare)

& 20000 & 25000 \hline \end{tabular}
Ali Bey bought a house for 450000 TL, and with all the money he obtained from the sale of this house, he bought a piece of land and then sold this land.
Accordingly, what is Ali Bey's profit from the sale of this land in TL?
A) 90000
B) 105000
C) 110000
D) 120000
E) 125000