turkey-yks

Papers (30)
2025
yks-ayt 36 yks-tyt 7
2024
yks-ayt 34 yks-tyt 7
2023
yks-ayt 24 yks-tyt 38
2021
yks-ayt 36 yks-tyt 13
2020
yks-ayt 35 yks-tyt 36
2019
yks-ayt 39 yks-tyt 9
2018
yks-ayt 39 yks-tyt 8
2017
lys1-math 56 ygs 18
2016
lys1-math 49 ygs 13
2015
lys1-math 50 ygs 13
2014
lys1-math 50 ygs 17
2013
lys1-math 50 ygs 25
2012
lys1-math 46 ygs 17
2011
lys1-math 49 ygs 19
2010
lys1-math 50 ygs 28
2020 yks-tyt

36 maths questions

Q2 Indices and Surds Number-Theoretic Reasoning with Indices View
For a project, 16 schools were selected from each of Turkey's 81 provinces, and a message was sent to each school's principal. Then, each school's principal sent this message to 35 teachers in their school.
Accordingly, what is the total number of principals and teachers to whom this message was sent?
A) $4^{6}$
B) $5^{6}$
C) $6^{6}$
D) $7 \cdot 5^{5}$
E) $8^{6}$
Q3 Indices and Surds Simplifying Surd Expressions View
When the numbers $\sqrt{5}, \sqrt{8}, \sqrt{12}, \sqrt{18}, \sqrt{20}$ and $\sqrt{27}$ are placed in the boxes below, with each box containing a different number, A, B, and C become whole numbers.
Accordingly, what is the sum $\mathrm{A} + \mathrm{B} + \mathrm{C}$?
A) 40
B) 44
C) 48
D) 52
E) 56
Q5 Inequalities Inequality Word Problem (Applied/Contextual) View
The difference between the heights of a building and a tree on flat ground is 8 meters. After some time, the tree's height doubled and this difference became 3 meters.
Accordingly, the building's height I. 13 meters II. 16 meters III. 19 meters which of these values could it be?
A) Only I
B) Only II
C) I and III
D) II and III
E) I, II and III
Q7 Number Theory Congruence Reasoning and Parity Arguments View
Where $a$ and $b$ are integers, $$a + 5b, \quad 2a + 3b \quad \text{and} \quad 3a + b$$ It is known that two of these numbers are odd and one is even.
Accordingly, I. (expression from figure) II. $2a + b$ III. $a \cdot b$ which of these expressions is an even number?
A) Only II
B) Only III
C) I and II
D) I and III
E) II and III
Q8 Inequalities Ordering and Sign Analysis from Inequality Constraints View
On the number line given below, the distance of K to 1 is equal to the distance of L to 2.
Accordingly, which of the following could be the value of the product $K \cdot L$?
A) A
B) B
C) C
D) D
E) E
Q9 Measures of Location and Spread View
Fatma and U\u011fur collected 10, 15, and 30 gram chocolates. Together they collected a total of 255 grams of chocolate.
When they returned home, after both of them gave some of their collected chocolates to their sister Nilay, each of the three siblings had an equal weight of chocolate.
Given that Nilay had no chocolate initially, how many chocolates does she have in the final situation?
A) 7
B) 6
C) 5
D) 4
E) 3
Q10 Number Theory Combinatorial Number Theory and Counting View
A three-digit natural number whose digits are different from each other and from zero is called a middle-divisible number if the digit in the tens place divides the digits in the other places. For example, 428 is a middle-divisible number. Accordingly, what is the difference between the largest middle-divisible number and the smallest middle-divisible number?
A) 723
B) 727
C) 736
D) 742
E) 745
Q11 Number Theory Properties of Integer Sequences and Digit Analysis View
Furkan measures his height against a wall every five years and marks it on the wall, writing it as a three-digit natural number in centimeters.
It is known that Furkan's height increased by 36 cm in the first five years and by 40 cm in the second five years. Given that $A$, $B$, and $C$ are non-zero digits, what is the sum $A + B + C$?
A) 15
B) 14
C) 13
D) 11
E) 10
Q12 Curve Sketching Limit Computation from Algebraic Expressions View
Some digits in the 11-digit phone numbers of Ayla and Berk are given as follows. $$\begin{aligned} & \text{Ayla} \longrightarrow 05{*}{*}{*}{*}{*}7235 \\ & \text{Berk} \longrightarrow 05{*}{*}{*}{*}{*}9415 \end{aligned}$$ Let $A$ be the set of digits in Ayla's phone number and $B$ be the set of digits in Berk's phone number, where $$\begin{aligned} & s(A) = 9 \\ & s(B) = 6 \end{aligned}$$ It is known that $A \cap B = \{0, 1, 4, 5, 6\}$. What is the sum of the values of elements in the set $A \setminus B$?
A) 18
B) 20
C) 21
D) 26
E) 27
Q13 Composite & Inverse Functions Graphical Interpretation of Inverse or Composition View
In the rectangular coordinate plane, parts of the graphs of functions $f$ and $g$ defined on the closed interval $[0, 7]$ are given in the figure.
On the closed interval $[0, 7]$:
  • For 4 different integers $a$, $f(a) < g(a)$,
  • For 3 different integers $b$, $f(b) > g(b)$
It is known that. Accordingly, which of the following could be the missing parts of the graphs of functions $f$ and $g$?
A) [Graph A]
B) [Graph B]
C) [Graph C]
Q14 Composite & Inverse Functions Recover a Function from a Composition or Functional Equation View
For functions $f$ and $g$ defined on the set of real numbers $$\begin{aligned} & (f \circ g)(x) = x^2 + 3x + 1 \\ & (g \circ f)(x) = x^2 - x + 1 \end{aligned}$$ the equalities are satisfied. Given that $f(2) = 1$, what is the value of $f(3)$?
A) 5
B) 6
C) 7
D) 8
E) 9
Q15 Measures of Location and Spread View
The number obtained by dividing the sum of the numbers in a data group by the number of terms in the group is called the arithmetic mean of that data group.
In a group consisting of people of different ages, the youngest person is 1 year old and the oldest person is 92 years old.
When the youngest person in the group is excluded, the arithmetic mean of the ages of the others is 45, and when the oldest person in the group is excluded, the arithmetic mean of the ages of the others is 38.
Accordingly, how many people are in the group?
A) 12
B) 14
C) 16
D) 18
E) 20
Q16 Inequalities Integer Solutions of an Inequality View
The appearance of an application used to adjust the sound level of a computer, consisting of 100 equal units with a speaker symbol at the bottom, is given below.
The sound level of the computer
  • when set to at least 1 and at most 32 units, the symbol appears as I)
  • when set to at least 33 and at most 65 units, the symbol appears as I\textbullet)
  • when set to at least 66 and at most 100 units, the symbol appears as I\textbullet))
On this computer, which is initially at a certain sound level, if the sound level is increased by 17 units, the symbol appears as I(\textbullet)), and if the initial sound level is decreased by 18 units, the symbol appears as I).
Accordingly, what is the sum of the integer values that the initial sound level can take in units?
A) 95
B) 96
C) 97
D) 98
Q17 Number Theory Linear Diophantine Equations View
Two friends sitting in a café drank 5 cups of tea, 1 cup of orange juice, and ate dessert. Part of the bill that the two friends paid is given in the figure.
Accordingly, if these two friends had drunk how many more cups of tea, would the total bill they would pay equal $\frac{2}{7}$ of the amount they paid for dessert?
A) 5
B) 7
C) 9
D) 11
E) 13
Q18 Number Theory Linear Diophantine Equations View
A stationery store sells red and blue colored pens with the same tag prices. In a campaign conducted at this stationery store, red pens are sold with the second one at 50\% discount, and blue pens are sold at 30\% discount from the tag price.
A person who bought 2 of each of the red and blue pens from this stationery store paid 4.5 TL less for the blue pens than for the red pens.
Accordingly, what is the tag price of one of these pens in TL?
A) 45
B) 40
C) 35
D) 30
E) 25
Q19 Number Theory Linear Diophantine Equations View
Two vehicles, one from city $A$ and one from city $B$, start moving towards each other at constant speeds on the road between these two cities and meet after some time. The vehicle starting from city $A$ reaches city $B$ 250 minutes after their meeting, and the vehicle starting from city $B$ reaches city $A$ 160 minutes after their meeting.
Accordingly, how many minutes after starting did these vehicles meet?
A) 170
B) 180
C) 190
D) 200
E) 210
Q20 Number Theory Linear Diophantine Equations View
For each person attending an event, either a meat or vegetable menu will be ordered for lunch. After the order was placed, 10 different people wanted to change their menu, and due to this change, the total amount to be paid increased by 80 TL.
Given that the price of the meat menu is 20 TL more than the price of the vegetable menu, how many people wanted to change their menu from vegetable to meat?
A) 5
B) 6
C) 7
D) 8
E) 9
Q21 Solving quadratics and applications Geometric or real-world application leading to a quadratic equation View
In a neighborhood with 95 buildings, each building is either 2 or 3 stories. Within the scope of urban renewal, 15 of these buildings are demolished and replaced with 5-story buildings each, and the total number of stories of the buildings in the neighborhood increases from 240 to 274.
Accordingly, by what percentage did the number of 3-story buildings in the neighborhood decrease as a result of urban renewal?
A) 16
B) 18
C) 20
D) 22
E) 24
Q22 Arithmetic Sequences and Series Find Specific Term from Given Conditions View
Ceyda plans to take an equal number of steps each day for a week. The graph below shows the difference between the number of steps Ceyda took daily and the number of steps she planned to take during this week.
For example, Ceyda took 50 more steps than planned on Monday and 100 fewer steps than planned on Tuesday.
On Friday, Ceyda took 165 more steps than on Thursday and 10 fewer steps than on Saturday, and after 7 days, the total number of steps she took was equal to the number of steps she initially planned to take.
Accordingly, how many more steps did Ceyda take on Friday than the number of steps she planned to take daily?
A) 85
B) 90
C) 95
D) 100
E) 105
Q23 Solving quadratics and applications Geometric or real-world application leading to a quadratic equation View
Duygu, who starts running on a running course, takes a break to rest after running a certain distance.
After the break, Duygu
  • if she runs 240 meters more, she will have run $\frac{7}{12}$ of the entire course,
  • if she runs $\frac{1}{3}$ of the distance she ran before, she will have run $\frac{3}{5}$ of the entire course.

Accordingly, what is the length of the entire course in meters?
A) 1440
B) 1620
C) 1800
D) 1980
E) 2160
Q24 Simultaneous equations View
Boxes A, B, C, and D contain a certain number of balls. The number of balls in box A is:
  • equal to 2 times the number of balls in box B,
  • equal to 3 times the number of balls in box C,
  • equal to 4 times the number of balls in box D.

If one of the boxes contains 8 balls, how many balls are there in total in these boxes?
A) 30
B) 36
C) 40
D) 44
E) 50
Q25 Simultaneous equations View
Districts A, B, and C and the roads between these districts are shown in the figure below.
The road distances of points D and E, which are on these roads, to some districts are given in the tables on the signs.
Accordingly, what is the difference between the road distance from district C to district B and the road distance from district C to district A in km?
A) 6
B) 8
C) 10
D) 12
E) 14
Q26 Simultaneous equations View
\c{C}\i{}nar has a total of 78 pens, some of which are blue. He distributed these pens among three pen holders as follows.
  • The number of pens in the pen holders is directly proportional to 3, 4, and 6.
  • The number of blue pens in each pen holder is equal to each other.
  • In one of the pen holders, the ratio of the number of blue pens to the total number of pens in that holder is $\frac{1}{2}$; in another pen holder, this ratio is $\frac{1}{3}$.

Accordingly, how many blue pens does \c{C}\i{}nar have in total?
A) 18
B) 24
C) 27
D) 30
E) 36
Q27 Simultaneous equations View
A group of students, each 7 years old, visited a botanical garden in 2015; another group of students, each 10 years old, visited in 2020. The official who guided the groups through the garden said about the same historical tree in the garden to both groups: ``The age of this tree is equal to the sum of all of your ages.''
From these two groups, if the number of students in the first group is 10 more than the number of students in the second group, how old is this tree in 2020?
A) 220
B) 230
C) 240
D) 250
E) 260
Q28 Permutations & Arrangements Linear Arrangement with Constraints View
Two students from each of three different schools will participate in a chess tournament. In the first round of the tournament, each student will be paired with a student who is not from their own school.
Accordingly, in how many different ways can the pairing in the first round be done?
A) 6
B) 8
C) 9
D) 12
E) 15
Q29 Combinations & Selection Combinatorial Probability View
Kerem randomly selects 3 numbers using the buttons shown in the figure to create the password for his locker, such that each is in a different row and different column.
Accordingly, what is the probability that all of the numbers Kerem selected are odd?
A) $\frac{1}{2}$
B) $\frac{1}{3}$
C) (from figure)
D) $\frac{5}{9}$
E) $\frac{4}{27}$
Q30 Sine and Cosine Rules Determine an angle or side from a trigonometric identity/equation View
A triangular ABC cardboard with vertices labeled with letters A, B, and C is shown as in Figure 1. 3 ABC cardboards can be assembled on a flat surface as shown in Figure 2 by overlapping the A vertices and leaving no gaps between the edges and without the cardboards overlapping.
The same process can be done using 9 ABC cardboards by overlapping the B vertices.
Accordingly, using how many ABC cardboards can this process be done by overlapping the C vertices?
A) 10
B) 12
C) 15
D) 18
E) 20
Q31 Straight Lines & Coordinate Geometry Geometric Figure on Coordinate Plane View
5 identical isosceles right triangles with right-angled side lengths of 1 unit are arranged as shown in Figure 1 such that their hypotenuses are on the same line and the vertices of adjacent triangles coincide.
Then triangle $ABC$ is rotated around point $A$ by some amount, and as shown in Figure 2, points B, C, and D become collinear.
Accordingly, what is the distance between points C and D in the final position in units?
A) 4
B) 5
C) 6
D) $3\sqrt{2}$
E) $4\sqrt{2}$
Q32 Sine and Cosine Rules Heights and distances / angle of elevation problem View
A seesaw on a flat ground as shown in Figure 1 consists of a straight segment 30 units long and a straight support 9 units long located at the exact center of this segment.
As shown in Figure 2, when the left end of the seesaw touches the ground, a shaded region in the shape of a right trapezoid is formed on the right side.
Accordingly, what is the perimeter of this trapezoid in units?
A) 54
B) 55
C) 56
D) 57
E) 58
Q33 Simultaneous equations View
A rectangular towel has one side blue and the other side white. This towel is hung on a straight rack such that the short sides of the towel are parallel to the rack. The length of the non-overlapping part of the towel's sides is 6 cm when the towel is hung as in Figure 1; and 12 cm when hung as in Figure 2.
The ratio of the area of the blue side of the towel visible in Figure 1 to the area visible in Figure 2 is $\frac{5}{4}$.
Accordingly, what is the length of the long side of the towel in cm?
A) 24
B) 28
C) 30
D) 36
E) 40
Q34 Simultaneous equations View
The front view of a cabinet consisting of five compartments shown in the figure is square-shaped. The door of each compartment is a rectangle with equal areas.
One compartment has been filled with only shirts as shown in the figure.
Accordingly, how many times is the long side of the lid of the compartment containing the shirts compared to its short side?
A) $\frac{4}{3}$
B) $\frac{5}{3}$
C) $\frac{7}{4}$
Q35 Sine and Cosine Rules Multi-step composite figure problem View
3 identical isosceles trapezoids are joined together such that any two of them share a vertex as shown below.
One side of the large triangle formed is 6 units, and one side of the small triangle is 3 units.
Accordingly, what is the perimeter of one of these isosceles trapezoids in units?
A) 10
B) 10.5
C) 11
D) 11.5
E) 12
Q36 Sine and Cosine Rules Multi-step composite figure problem View
In the square-shaped paper ABCD given in Figure 1, $|\mathrm{DE}| = 6$ and $|\mathrm{BF}| = 9$ units. When this paper is folded along the line segments $[\mathrm{CE}]$ and $[\mathrm{CF}]$ as shown in the figure, the BC side and DC side of the square coincide as shown in Figure 2.
Accordingly, what is the perimeter of square ABCD in units?
A) 64
B) 68
C) 72
D) 76
E) 80
Q37 Sine and Cosine Rules Determine an angle or side from a trigonometric identity/equation View
One interior angle of an $n$-sided regular polygon is calculated as $\frac{(n-2) \cdot 180^{\circ}}{n}$.
A triangular piece of paper is cut along the dashed lines as shown in the figure, 3 triangular pieces are removed, and a regular hexagon is obtained.
Given that the sum of the perimeters of the removed triangles is 36 units, what is the perimeter of the hexagon?
A) 18
B) 24
C) 30
D) 36
E) 42
Q38 Simultaneous equations View
A wooden piece in the shape of a square right prism with a square base has a base edge length equal to 2 times its height. When a cube with an edge length equal to the height of the wooden piece is removed from inside this wooden piece, the surface area of the resulting shape in the final state is 8 square units more than the surface area of the wooden piece in the initial state.
Accordingly, what is the volume of the wooden piece in the initial state in cubic units?
A) 32
B) 80
C) 108
D) 144
E) 256
Q39 Simultaneous equations View
The volume of a rectangular prism is equal to the product of its base area and height.
A closed glass container in the shape of a rectangular prism contains 360 cubic units of water. When the container is placed on a flat surface with different faces completely touching the surface, the height of the water is 2 units, 4 units, and 5 units respectively.
Accordingly, what is the volume of the container in cubic units?
A) 540
B) 720
C) 840
D) 960
E) 4080