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2025
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2020
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2011
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2010
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2023 yks-tyt

38 maths questions

Q1 Arithmetic Sequences and Series Compute Partial Sum of an Arithmetic Sequence View
The table below shows some musical note symbols and the duration lengths of these note symbols.
Accordingly, what is the sum of the duration lengths of the musical note symbols given above?
A) $\frac{3}{2}$ B) $\frac{7}{4}$ C) $\frac{5}{4}$ D) $\frac{13}{8}$ E) $\frac{15}{8}$
Q2 Arithmetic Sequences and Series Find Specific Term from Given Conditions View
A flower bed with a height of 1.2 meters has five shelves at equal intervals in its left compartment and six shelves at equal intervals in its right compartment. The shelves at the bottom and top of these two compartments are at equal heights. A flower has been placed on the 4th shelf in the left compartment and on the 3rd shelf in the right compartment of the flower bed as shown in the figure.
Accordingly, what is the sum of the heights from the ground of the shelves where the flowers are located in meters?
A) 1.38 B) 1.36 C) 1.34 D) 1.32 E) 1.30
Q3 Geometric Sequences and Series Applied Geometric Model with Contextual Interpretation View
In a census conducted on January 1, 2015, a city with a population of 810,000 had population counts on January 1 each year from 2016 to 2023. In each of the first four years after 2015, the population increased by a ratio of $\frac{1}{10}$ compared to the previous year, and in each of the following four years, the population increased by a ratio of $\frac{1}{11}$ compared to the previous year.
Accordingly, what was the population of this city in the census conducted on January 1, 2023?
A) $2^{20}$ B) $3^{13}$ C) $5^{9}$ D) $6^{8}$ E) $10^{6}$
Q4 Indices and Surds Number-Theoretic Reasoning with Indices View
Let $A$ and $B$ be natural numbers. A square with side length $A\sqrt{B}$ units has an area of 720 square units.
Accordingly, which of the following cannot be the sum $A + B$?
A) 26 B) 49 C) 83 D) 127 E) 182
Q5 Partial Fractions View
Let $a, b, c$ and $d$ be positive real numbers; the value of the first notation equals the number $\frac{a+d}{b+c}$, and the value of the second notation equals the number $\frac{a \cdot d}{b \cdot c}$.
Given that the above holds, what is x?
A) 12 B) 16 C) 24 D) 36 E) 48
Q6 Inequalities Ordering and Sign Analysis from Inequality Constraints View
For real numbers $a, b$ and $c$,
$$a > a \cdot b > 2 \cdot a > a \cdot c$$
is known to hold.
Accordingly, which of the following could be the representation of the numbers $\mathbf{a, b}$ and $\mathbf{c}$ on the number line?
A) [number line A] B) [number line B] C) [number line C] D) [number line D] E) [number line E]
Q7 Probability Definitions Combinatorial Counting (Non-Probability) View
The figure below shows a lamp and the appearance of a string that operates this lamp. The lamp;
  • when closed, if the string is pulled and released, it gives dim light,
  • when giving dim light, if the string is pulled and released, it gives daylight,
  • when giving daylight, if the string is pulled and released, it gives bright light,
  • when giving bright light, if the string is pulled and released, it turns off.

Initially, this lamp was closed. The string was pulled and released A times and the lamp was observed to give bright light. Then, the lamp's string was pulled and released B more times and the lamp was observed to give daylight. Later, the lamp's string was pulled and released C more times and the lamp was observed to turn off.
Accordingly, which of the following is an even number?
A) $A \cdot B + C$ B) $B \cdot C + A$ C) $A \cdot (B + C)$ D) $B \cdot (A + C)$ E) $C \cdot (A + B)$
Q8 Arithmetic Sequences and Series Find Specific Term from Given Conditions View
Two balloons are hung on a string stretched between two walls as shown in the figure. Between these two balloons, 2 white balloons or 4 yellow balloons are to be hung such that the distance between the points where any two adjacent balloons are attached to the string is equal.
The distance between the points where any two adjacent balloons are attached to the string is 18 cm more when white balloons are hung compared to when yellow balloons are hung.
Accordingly, what is the distance in cm between the points where the two initially hung balloons are attached to the string?
A) 135 B) 144 C) 153 D) 162 E) 171
Q9 Probability Definitions Combinatorial Counting (Non-Probability) View
At the entrance of a hotel, there are three digital wall clocks showing the local times of cities $\mathrm{A}, \mathrm{B}$ and C. A customer looking at these clocks observed that the local time difference between cities A and B is 4 hours, and the local time difference between cities B and C is 3 hours.
When the clock showing the local time of city A reads 14.00, which of the following cannot be the time shown on the clock for city C?
A) 07.00 B) 13.00 C) 15.00 D) 17.00 E) 21.00
Q10 Principle of Inclusion/Exclusion View
In a friend group consisting of two girls and three boys, the girls' names are AYLIN and BENSU, and two of the boys' names are AKIN and KENAN.
The set of letters in the girls' names is set X, and the set of letters in the boys' names is set Y.
Given that $\mathbf{X} \cap \mathbf{Y} = \{\mathbf{A}, \mathbf{B}, \mathbf{E}, \mathbf{N}, \mathbf{U}\}$, which of the following could be the name of the other boy in the friend group?
A) BARIŞ B) BILAL C) BURAY D) BULUT E) BURAK
Q11 Probability Definitions Finite Equally-Likely Probability Computation View
Before the doctor's examination, Sibel Hanım's age, height, and weight are written on a card.
Age : 53
Height : .......
Weight : .......

Regarding this information,
$p$: Sibel Hanım's weight is more than 60 kilograms.
$q$: Sibel Hanım's height is in the range of 164 cm to 170 cm.
$r$: Sibel Hanım's age is in the range of 55 to 65.
propositions are given.
$$\left( p \Rightarrow q^{\prime} \right) \wedge r^{\prime}$$
Given that this proposition is false, which of the following could be Sibel Hanım's height and weight?
A) $160 \mathrm{~cm} - 56$ kilograms B) $165 \mathrm{~cm} - 58$ kilograms C) $166 \mathrm{~cm} - 62$ kilograms D) $171 \mathrm{~cm} - 59$ kilograms E) $172 \mathrm{~cm} - 64$ kilograms
Q12 Composite & Inverse Functions Evaluate Composition from Algebraic Definitions View
Let $a$ be a positive real number. The functions f and g are defined on the set of real numbers as
$$\begin{aligned} & f(x) = x + a \\ & g(x) = ax + 1 \end{aligned}$$
Given that $(\mathbf{f} \cdot \mathbf{g})(\mathbf{1}) = (\mathbf{f} + \mathbf{g})(\mathbf{2})$, what is $\mathbf{g}(\mathbf{7})$?
A) 8 B) 15 C) 22 D) 29 E) 36
Q13 Probability Definitions Combinatorial Counting (Non-Probability) View
The number of different digits in a natural number N is defined as shown in the figure.
Example: $4202 = 3$
Let A be a digit, and the equality shown in the figure holds.
What is the sum of different A values that satisfy the equality?
A) 8 B) 9 C) 10 D) 11 E) 12
Q14 Probability Definitions Combinatorial Counting (Non-Probability) View
Among the three-digit natural numbers $ABB$ and $BAB$, one is divisible by 11 and the other is divisible by 12.
Accordingly, what is the sum $\mathrm{A} + \mathrm{B}$?
A) 7 B) 8 C) 10 D) 11 E) 13
Q15 Probability Definitions Combinatorial Counting (Non-Probability) View
Let $A, B$ and $C$ be digits different from zero and from each other; the sum of the two-digit natural number AB and the two-digit natural number BC equals one less than the two-digit natural number CA.
Accordingly, how many different three-digit natural numbers ABC can be written using the digits A, B, and C that satisfy this condition?
A) 1 B) 2 C) 3 D) 5 E) 6
Q16 Measures of Location and Spread View
When the numbers in a data group are arranged from smallest to largest, if the number of terms in the group is odd, the median is the middle number; if it is even, the median is the arithmetic mean of the two middle numbers.
The mode is the value that appears most frequently among the data.
The average temperature values measured in a region over one week are given below.
Monday : $16^{\circ}\mathrm{C}$ Tuesday : $18^{\circ}\mathrm{C}$ Wednesday : $16^{\circ}\mathrm{C}$ Thursday : $20^{\circ}\mathrm{C}$ Friday : $20^{\circ}\mathrm{C}$ Saturday : $19^{\circ}\mathrm{C}$ Sunday : $20^{\circ}\mathrm{C}$
The mode of the data group formed by these average temperature values is found, and the days whose temperature values equal the mode of the data group are removed from the data group.
Accordingly, what is the median of the new data group formed by the temperature values of the remaining days?
A) 16 B) 17 C) 18 D) 19 E) 20
Q17 Proof Computation of a Limit, Value, or Explicit Formula View
A toy bear, a toy horse, and a cactus plant are placed on 3 wall shelves, each at a different height from the ground, first as shown in Figure 1, and then as shown in Figure 2. The heights that are equal in Figure 1 and Figure 2 are shown with dashed lines. It is known that the sum of the heights of the toy bear, toy horse, and cactus plant is 15 units.
Given that the height of the leftmost shelf from the ground is 18 units, what is the sum of the heights of the other two shelves from the ground?
A) 45 B) 48 C) 51 D) 54 E) 57
Q18 Probability Definitions Combinatorial Counting (Non-Probability) View
Boat trips are organized for visitors who want to visit a tourist island. The boat departs when there are at least 20 passengers and can carry a maximum of 35 passengers. On a particular day, 3 boat trips were organized and a total of 91 passengers were transported. The ratio of the number of passengers transported in the first trip to the number of passengers transported in the second trip is $\frac{4}{5}$.
Accordingly, how many passengers were transported in the third trip?
A) 21 B) 24 C) 28 D) 32 E) 35
Q19 Inequalities Inequality Word Problem (Applied/Contextual) View
A coffee machine detects the length of the cup placed in its cup holder. For the coffee machine to operate, the distance between the coffee reservoir and the top of the cup must be at least 11.5 cm and at most 12.4 cm, as shown in the figure.
When a cup of length $14.5 \mathrm{~cm}$ is placed in the cup holder of this coffee machine, the machine operates; when a cup of length $15.2 \mathrm{~cm}$ is placed, the machine does not operate.
Accordingly, when cups of the following lengths are placed in the cup holder of this coffee machine:
I. $14.2 \mathrm{~cm}$ II. $14.4 \mathrm{~cm}$ III. $14.6 \mathrm{~cm}$
For which of these will the machine definitely operate?
A) Only I B) Only II C) Only III D) I and II
Q20 Probability Definitions Combinatorial Counting (Non-Probability) View
Yeşim organized a poll on social media with a mosque photo she took in Edirne. After a certain period, the number of votes used for some cities and the ratio of the number of votes used for some cities to the total number of votes as a percentage are given. After this distribution, 5 more votes were cast in total, 4 of which were for Edirne and 1 for Istanbul.
Accordingly, what is the percentage of the number of votes cast for Edirne to the total number of votes in the final situation?
A) 36 B) 38 C) 40 D) 42 E) 44
Q21 Probability Definitions Combinatorial Counting (Non-Probability) View
The campaigns at stationery stores $A$ and $B$, which have the same prices for the same type of products, are as follows.
  • At stationery store A, when a backpack is purchased, a pen case is sold at half price.
  • At stationery store B, when 2 of the same type of product are purchased, a 40\% discount is applied to the 2nd product.

Ege and Deniz took advantage of stationery store A's campaign and each bought one backpack priced at 300 TL and one pen case priced at 120 TL.
If Ege and Deniz had each bought one backpack and one pen case of the same type from stationery store B, how much less would the total amount they paid be compared to what they paid to stationery store A?
A) 30 B) 36 C) 42 D) 48 E) 54
Q22 Travel graphs View
An athlete ran from point A in the direction of the arrow on a circular track divided into five equal-length sections at a constant high speed and reached point B in 60 seconds. Then this athlete ran from point B in the direction of the arrow at a constant low speed for 320 seconds.
Accordingly, what is the difference between the time it takes this athlete to run the entire track at low speed and the time it takes to run the entire track at high speed in seconds?
A) 80 B) 90 C) 100 D) 110 E) 120
Q23 Probability Definitions Combinatorial Counting (Non-Probability) View
A painter displayed all of his paintings at his first exhibition and sold some of them. In all subsequent exhibitions, this painter displayed the paintings that were not sold at the previous exhibition together with new paintings he created.
The painter sold $\frac{3}{5}$ of the paintings he displayed at each exhibition. Also, for each exhibition after the first, he created as many new paintings as the number of paintings remaining from the previous exhibition.
Given that the painter sold 96 paintings at his 3rd exhibition, how many paintings did he display at his first exhibition?
A) 100 B) 150 C) 200 D) 250 E) 300
Q24 Probability Definitions Combinatorial Counting (Non-Probability) View
Aras divides all of his marbles into groups of 3 and obtains a two-digit natural number AB, and divides them into groups of 8 and obtains a two-digit natural number BA.
According to this, if Aras divides all the marbles he has into groups such that each group has an equal number of marbles, which of the following could be the number of groups he obtains?
A) 40 B) 48 C) 54 D) 56 E) 60
Q25 Probability Definitions Combinatorial Counting (Non-Probability) View
Serkan's wardrobe contains three types of clothing: shirt ($G$), pants ($P$), and jacket (C). The numerical distribution of these clothes initially in the wardrobe is shown in the pie chart below.
Serkan takes a certain number of clothes from his wardrobe to dry cleaning. In the final situation, the numerical distribution of the clothes remaining in Serkan's wardrobe shown in the pie chart is the same as the initial one.
Given that Serkan initially had 5 jackets in his wardrobe and he took 1 of these jackets to dry cleaning, how many shirts are left in Serkan's wardrobe?
A) 8 B) 10 C) 15 D) 18 E) 20
Q26 Probability Definitions Combinatorial Counting (Non-Probability) View
When Ali dede, whose grandfather's restaurant was founded in 1949, came to the restaurant, he said the following sentence to his grandson.
``In the year this restaurant was founded, I was 11 years old, and in the year you were born, this place had been in service for 40 years.''
Accordingly, what is the sum of the ages of Ali dede and his grandson in 2022?
A) 101 B) 105 C) 109 D) 113 E) 117
Q27 Permutations & Arrangements Linear Arrangement with Constraints View
In a textile workshop, cardboard boxes arranged in a row will pass sequentially through two machines that perform labeling.
The first machine writes NORMAL CUT on the first two cardboards, NARROW CUT on the next two cardboards, and continues in this way, writing NORMAL CUT on two cardboards and NARROW CUT on two cardboards in sequence, labeling the cardboards and sending them to the second machine. The second machine labels the first cardboard with S, the second cardboard with M, the third cardboard with L, and continues in this way, labeling the cardboards sequentially with S, M, and L.
Accordingly, what is the label of the 175th cardboard coming out of the second machine?
A) NORMAL CUT M B) NARROW CUT M C) NORMAL CUT S D) NARROW CUT L E) NORMAL CUT L
Q28 Probability Definitions Combinatorial Counting (Non-Probability) View
A tour company has offered three different transportation options: train, bus, and airplane for a tour it will organize to Adana. The company's per-person fare information for this tour according to transportation vehicles and some information about the number of people who chose these transportation vehicles are given in the table below.
\cline{2-4} \multicolumn{1}{c|}{}TrainBusAirplane
Fare (TL)300750
Number of People108

Among the people who participated in this tour; the number of those who chose the bus for transportation is equal to 6 times the number of those who chose the airplane. Also, in this tour, the total fare paid by those who chose the train for transportation is equal to the total fare paid by those who chose the airplane.
Accordingly, what is the total number of people going to Adana with this tour?
A) 165 B) 171 C) 177 D) 183 E) 189
Q29 Combinations & Selection Selection with Arithmetic or Divisibility Conditions View
In a course, the weekly lesson durations of 7 lessons, each with different lesson times, are given in the table below.
LessonDuration (hours)
Lesson 15
Lesson 24
Lesson 34
Lesson 45
Lesson 53
Lesson 65
Lesson 75

Aslı, who enrolled in this course, wants to take four different lessons such that the total weekly lesson duration is 17 hours.
Accordingly, in how many different ways can Aslı select the lessons she will take?
A) 8 B) 10 C) 12 D) 16 E) 18
Q30 Probability Definitions Finite Equally-Likely Probability Computation View
A stove consisting of 1 large, 2 medium, and 1 small compartment with 4 ignition buttons, each of which activates a different compartment, is shown in the figure below.
Since the directions next to the buttons have been erased, it is not known which button activates which compartment.
Accordingly, when all compartments are closed and two buttons are randomly pressed, what is the probability that one of the medium compartments and the small compartment will activate?
A) $\frac{1}{2}$ B) $\frac{1}{3}$ C) $\frac{2}{3}$ D) $\frac{1}{4}$ E) $\frac{1}{5}$
Q31 Completing the square and sketching Determining coefficients from given conditions on function values or geometry View
Ayşe, who wants to set aside a portion of her notebook for history class, folds the page she wants to set aside more easily to find, as shown in the figure, from the upper right corner of the page.
In this notebook with rectangular pages, each line on the pages is parallel to the top edge of the page.
Accordingly, what is x in degrees?
A) 50 B) 52 C) 54 D) 56 E) 58
Q32 Completing the square and sketching Determining coefficients from given conditions on function values or geometry View
Three right triangles are positioned as follows: their hypotenuses lie on the same line and one vertex of each coincides.
Given that each of the blue angles measures $115^{\circ}$, what is the measure of the yellow angle in degrees?
A) 100 B) 105 C) 110 D) 115 E) 120
Q33 Sine and Cosine Rules Find a side length using the cosine rule View
In a triangle, one interior angle measure equals the average of the measures of the other two interior angles. The shortest and longest sides of this triangle are 10 and 16 units long, respectively.
Accordingly, what is the length of the third side of this triangle in units?
A) 11 B) 12 C) 13 D) 14 E) 15
Q34 Completing the square and sketching Determining coefficients from given conditions on function values or geometry View
A glazier using his extendable ladder to reach a window 6 meters high from the ground positions the ladder 4.8 meters away from a garden wall 3.6 meters high, as shown in Figure 1, and extends the ladder to touch the wall and reach the bottom of the window. The glazier then brings the ladder into the garden and, as shown in Figure 2, leans one end against the wall and extends it to the bottom of the window.
When the glazier positions the ladder as shown in Figure 2, he extends it 3.5 meters less than when he positions it as shown in Figure 1. Accordingly, what is the thickness of the wall in meters?
A) 0.5 B) 0.6 C) 0.7 D) 0.8 E) 0.9
Q35 Completing the square and sketching Determining coefficients from given conditions on function values or geometry View
In an application used to adjust the sound level of a music program, consisting of 100 equal units in the shape of a right triangle, the appearance of the application when the sound level is 60 units is given in Figure 1.
When the sound level is increased to 70 units as shown in Figure 2, the area of the green right triangle increases by 260 square units.
Accordingly, what is the height marked with ? in the appearance of the application in units?
A) 30 B) 35 C) 40 D) 45 E) 50
Q36 Completing the square and sketching Determining coefficients from given conditions on function values or geometry View
Three square-shaped tables with perimeters of 12, 16, and 28 units are given in Figure 1. These three tables are combined as shown in Figure 2 with no gaps between them to create a new table.
Accordingly, what is the perimeter length of the new table created in units?
A) 42 B) 46 C) 48 D) 52 E) 54
Q37 Completing the square and sketching Determining coefficients from given conditions on function values or geometry View
An isosceles trapezoid-shaped cardboard with a height of 30 units has an upper base length of 20 units. When this cardboard is cut along a line parallel to the lower base, reducing the height by 12 units, it is observed that the lower base length decreases by 6 units.
Accordingly, what is the area of the new cardboard obtained in square units?
A) 363 B) 385 C) 441 D) 450 E) 464
Q38 Completing the square and sketching Determining coefficients from given conditions on function values or geometry View
The interior angle measure of a regular n-sided polygon is calculated as $\frac{(n-2) \cdot 180^{\circ}}{n}$.
Six identical isosceles trapezoid-shaped mirrors, each with a perimeter of 28 units and shown in Figure 1, are combined as shown in Figure 2 with no gaps between them and all mirrors visible. In the resulting figure, the sum of the perimeter lengths of the red regular hexagon and the blue regular hexagon is 96 units.
Accordingly, what is the area of one of the mirrors used in square units?
A) $18\sqrt{3}$ B) $24\sqrt{3}$ C) $28\sqrt{3}$ D) $30\sqrt{3}$ E) $36\sqrt{3}$