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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-ayt

35 maths questions

Q1 Number Theory Combinatorial Number Theory and Counting View
When 6 of the integers from 1 to 9 are placed in the boxes below such that each box contains a different number, all equalities are satisfied.
$$\begin{aligned} & \square + \square = 5 \\ & \square - \square = 5 \\ & \square : \square = 5 \end{aligned}$$
Accordingly, what is the sum of the unused integers?
A) 23
B) 21
C) 19
D) 17
E) 15
Q2 Number Theory Prime Number Properties and Identification View
Let $a$, $b$, and $c$ be prime numbers,
$$a ( a + b ) = c ( c - b ) = 143$$
Given the equalities, accordingly, what is the sum $a + b + c$?
A) 22
B) 26
C) 30
D) 32
Q3 Indices and Surds Solving Exponential or Index Equations View
For integers $x$ and $y$
$$9 ^ { x } - 3 ^ { 2 x - 2 } = 2 ^ { y } \cdot 3 ^ { 6 }$$
the equality is satisfied. Accordingly, what is the sum $x + y$?
A) 3
B) 4
C) 5
D) 6
E) 7
Q5 Inequalities Ordering and Sign Analysis from Inequality Constraints View
For real numbers $a$, $b$, and $c$
$$a - b < 0 < c < c - b$$
the inequality is given.
Accordingly, I. $a \cdot b \cdot c > 0$ II. $( a + c ) \cdot b > 0$ III. $b - a + c > 0$ which of these statements are always true?
A) Only I
B) Only II
C) I and II
D) I and III
E) II and III
Q6 Modulus function Solving equations involving modulus View
For integers $x$ and $y$,
$$| x - 3 | + | 2 x + y | + | 2 x + y - 1 | = 1$$
the equality is satisfied. Accordingly, what is the sum of the values that $y$ can take?
A) $- 12$
B) $- 11$
C) $- 10$
D) $- 9$
E) $- 8$
Q7 Number Theory Congruence Reasoning and Parity Arguments View
The three-digit natural number ABA divided by the two-digit natural number A1 gives a quotient of 13 and a remainder of 19.
Accordingly, what is the sum $A + B$?
A) 8
B) 9
C) 10
D) 11
E) 12
Q8 Probability Definitions Set Operations View
Regarding sets $A$, $B$, and $C$
$$\begin{aligned} & \{ ( 1,2 ) , ( 2,3 ) , ( 3,4 ) \} \subseteq A \times B \\ & \{ ( 1,2 ) , ( 3,4 ) , ( 4,2 ) , ( 4,4 ) \} \subseteq A \times C \end{aligned}$$
it is known that.
Accordingly, I. The set $A \cap B$ has at least 3 elements. II. The set $A \cap C$ has at least 3 elements. III. The set $B \cap C$ has at least 3 elements. which of these statements are always true?
A) Only I
B) Only II
C) Only III
D) I and II
E) I and III
Q9 Probability Definitions Set Operations View
If the number of elements of a set whose all elements are positive integers is one more than the value of the smallest element of this set, this set is called a wide set.
Let $A$, $B$, and $C$ be wide sets,
  • $A \cup B \cup C = \{ 1,2,3,4,5,6,7,8,9 \}$
  • $A \cap B = \{ 3 \}$
  • $1 \in A$
  • $6 \in B$
it is known that. Accordingly, which of the following is set $C$?
A) $\{ 1,2 \}$
B) $\{ 3,4,8,9 \}$
C) $\{ 3,5,7,8 \}$
D) $\{ 4,5,6,7,8 \}$
E) $\{ 4,5,7,8,9 \}$
Q10 Complex Numbers Arithmetic Complex Division/Multiplication Simplification View
In the set of complex numbers
$$\frac { i \cdot ( 2 - i ) \cdot ( 2 - 4 i ) } { ( 1 - i ) \cdot ( 1 + i ) }$$
what is the result of the operation?
A) 2
B) 5
C) 10
D) $2 i$
E) $5 i$
Q11 Complex Numbers Arithmetic Solving Equations for Unknown Complex Numbers View
Let $\bar{z}$ be the conjugate of the complex number $z$,
$$\frac { 6 + 2 i } { z } = \bar { z } + i$$
the sum of the complex numbers $z$ that satisfy the equality is what?
A) $1 + 3 i$
B) $2 + i$
C) $3 + 2 i$
D) $4 + i$
Q13 Composite & Inverse Functions Recover a Function from a Composition or Functional Equation View
Let $a$ and $b$ be non-zero integers. A function $f$ is defined on the set of real numbers as
$$f ( x ) = a x + b$$
$$( f \circ f ) ( x ) = f ( x + 2 ) + f ( x )$$
According to this, what is the value of $f(3)$?
A) 7
B) 8
C) 9
D) 10
E) 11
Q14 Curve Sketching Limit Reading from Graph View
In the rectangular coordinate plane, the graph of a function $f$ defined on the closed interval $[-5,5]$ is given in the figure.
For distinct numbers $a, b, c$ and $d$ in the domain of this function
$$\begin{aligned} & f(a) = f(b) = 1 \\ & f(c) = f(d) = 3 \end{aligned}$$
the equalities are satisfied. Accordingly, regarding the ordering of $a, b, c$ and $d$ numbers I. $a < b < c < d$ II. $c < a < b < d$ III. $c < d < a < b$ Which of the following inequalities can be true?
A) Only I
B) Only II
C) I and II
D) II and III
E) I, II and III
Q15 Factor & Remainder Theorem True/False or Multiple-Statement Evaluation View
$P(x)$ and $Q(x)$ are non-constant polynomials, and $R(x)$ is a first-degree polynomial, where
$$P(x) = Q(x) \cdot R(x)$$
the equality is satisfied.
Accordingly, I. The constant terms of polynomials $P(x)$ and $R(x)$ are the same. II. If the graph of $P(x)$ is a parabola, then the graph of $Q(x)$ is a line. III. Every root of polynomial $Q(x)$ is also a root of polynomial $R(x)$. Which of the following statements are always true?
A) Only II
B) Only III
C) I and II
D) I and III
E) II and III
Q16 Factor & Remainder Theorem Polynomial Construction from Root/Value Conditions View
For third-degree real-coefficient polynomials $P(x)$ and $R(x)$ whose highest degree terms have coefficient 1, the numbers 2 and 6 are common roots. When the polynomial $P(x) - R(x)$ is divided by $x - 1$, the remainder is 10.
Accordingly, what is the value of $P(0) - R(0)$?
A) 24
B) 27
C) 30
D) 33
E) 36
Q17 Binomial Theorem (positive integer n) Find a Specific Coefficient in a Single Binomial Expansion View
Where $m$ and $n$ are integers,
$$\left(x^2 + 2y\right)^7$$
In the expansion of this expression, if one of the terms is $mx^ny^2$, what is the sum $m + n$?
A) 56
B) 64
C) 72
D) 86
E) 94
Q18 Solving quadratics and applications Quadratic equation with parametric or self-referential conditions View
Where $a$ and $b$ are positive real numbers,
$$2ax^2 - 5bx + 8b = a$$
the roots of the equation are $a$ and $b$. Accordingly, what is the sum $a + b$?
A) 5
B) 6
C) 10
D) 12
E) 15
Q19 Completing the square and sketching Sign analysis of quadratic coefficients and expressions from a graph View
Where $a, b$ and $c$ are real numbers,
$$y = ax^2 + bx + c$$
the parabola intersects the line $y = 1$ at points B and C, and intersects the line $y = 6$ at only point A. The locations of points A, B and C in the rectangular coordinate plane are shown in the figure below.
Accordingly, what are the signs of the numbers $a$, $b$ and $c$ respectively?
A) +, -, -
B) +, +, -
C) -, +, +
D) -, -, +
E) -, -, -
Q20 Laws of Logarithms Solve a Logarithmic Equation View
When a stick is divided into 4 equal parts, the length of each part is $\log_5(x)$ units, and when divided into 10 equal parts, the length of each part is $\log_5\left(\frac{x^2}{25}\right)$ units.
Accordingly, what is the length of the stick in units?
A) 5
B) 8
C) 10
D) 12
E) 15
Q21 Laws of Logarithms Solve a Logarithmic Equation View
Where $n$ is an integer and $1 < n < 100$,
$$\log_2\left(\log_3 n\right)$$
the value of this expression equals a positive integer. Accordingly, what is the sum of the values that $n$ can take?
A) 36
B) 45
C) 63
D) 72
E) 90
Q22 Laws of Logarithms Verify Truth of Logarithmic Statements View
Where $a$ and $b$ are positive real numbers different from 1,
$$\log_a 2 < 0 < \log_2 b$$
the inequality is satisfied. Accordingly, I. $a + b > 1$ II. $b - a > a$ III. $a \cdot b > 1$ Which of the following statements are always true?
A) Only I
B) Only II
C) I and II
D) I and III
E) II and III
Q23 Sequences and series, recurrence and convergence Direct term computation from recurrence View
The sequence $(a_n)$ of real numbers satisfies for every positive integer $n$
$$a_{n+1} = a_n + \frac{(-1)^n \cdot a_n}{2}$$
the equality. If $a_5 = 18$, what is $a_1$?
A) 4
B) 8
C) 16
D) 32
E) 64
Q24 Geometric Sequences and Series Finite Geometric Sum and Term Relationships View
For a geometric sequence $(a_n)$ with all positive terms and common ratio $r$
$$\begin{aligned} & a_1 + \frac{1}{2} + r \\ & a_7^2 = a_5 + 12 \cdot a_3 \end{aligned}$$
the equalities are given.
Q25 Permutations & Arrangements Selection and Task Assignment View
Between October 5, 2020 Monday and October 18, 2020 Sunday, including these two days, two meetings will be held on two different days within these 14 days.
If an arrangement is to be made such that at least one of the meetings is on a weekday, in how many different ways can this arrangement be made?
A) 70
B) 75
C) 80
D) 85
E) 90
Q26 Combinations & Selection Combinatorial Probability View
An exam consisting of a total of 8 questions, with 4 questions each in the verbal and quantitative sections, has the following statement in its booklet: ``To pass the exam, you must answer at least 5 questions correctly in total, with at least 2 questions from each of the verbal and quantitative sections.'' Sevcan, who read this statement incompletely, randomly selected 5 out of 8 questions on the exam and answered each question she selected correctly.
Accordingly, what is the probability that Sevcan passes the exam?
A) $\frac{3}{4}$
B) $\frac{4}{5}$
C) $\frac{5}{6}$
D) $\frac{6}{7}$
E) $\frac{7}{8}$
Q27 Trig Proofs Trigonometric Identity Simplification View
$$\frac{2\tan x - \sin(2x)}{\sin^2 x}$$
What is the simplified form of this expression?
A) $2\tan x$
B) $\tan(2x)$
C) $2\cos x$
D) $\cos(2x)$
E) 1
Q29 Quadratic trigonometric equations View
Where $0 < x < \frac{\pi}{2}$,
$$\frac{1 + \tan x}{\cot x} \cdot \frac{\sin x - \cos x}{\sin x} = 2$$
if this holds, what is the value of $\sin x$?
A) $\frac{1}{3}$
B) $\frac{3}{5}$
C) $\frac{\sqrt{2}}{2}$
D) $\frac{\sqrt{3}}{2}$
E) $\frac{\sqrt{5}}{3}$
Q31 Trig Proofs Triangle Trigonometric Relation View
In the figure, the line segments $[OA]$ and $[OD]$ intersect perpendicularly.
Accordingly, the ratio of the area of triangle OAB to the area of triangle OCD in terms of $\alpha$ is which of the following?
A) $\tan \alpha$
B) $\cot \alpha$
C) $\tan^2 \alpha$
D) $\cot^2 \alpha$
E) $\sec^2 \alpha$
Q33 SUVAT in 2D & Gravity View
A rectangular frame with side lengths 30 and 40 units is hung on a wall with nails at four corners as shown in Figure 1, with side AB parallel to the ground and at height $h$ units from the ground. Then, except for the nail at corner A, the other nails loosen and fall, and the frame rotating around corner A comes to rest as shown in Figure 2 with all corners touching the wall when corner C touches the ground.
If the heights of corners B and D from the ground are equal in this equilibrium position, what is $h$ in units?
A) 42
B) 48
C) 54
D) 60
E) 64
Q34 Sine and Cosine Rules Determine an angle or side from a trigonometric identity/equation View
In the figure, a regular hexagon and a square sharing one side are given. A regular polygon sharing one side with the regular hexagon and one side with the square is to be drawn as shown in the figure.
Accordingly, how many sides does the regular polygon to be drawn have?
A) 10
B) 12
C) 15
D) 16
E) 18
Q35 Circles Area and Geometric Measurement Involving Circles View
In the figure, a semicircle with center A and radius $[AC]$ and a semicircle with center B and radius $[BC]$ are given. Point B is on the circle centered at A, and point A is on the circle centered at B.
Accordingly, what is the area of the shaded region in square units?
A) $36\pi$
B) $42\pi$
C) $48\pi$
D) $54\pi$
E) $60\pi$
Q36 Radians, Arc Length and Sector Area View
In an amusement park, there is a circular Ferris wheel on flat ground consisting of identical cabins as shown in the figure, rotating in only one direction. A person boards one cabin when the cabin is closest to the ground.
Meryem boards a cabin and after the Ferris wheel rotates $48°$, Nisa also boards a cabin.
Accordingly, after Nisa boards her cabin, when the heights of the cabins where Meryem and Nisa are located are equal for the first time, how many degrees has the Ferris wheel rotated?
A) 130
B) 138
C) 144
D) 150
E) 156
Q37 Straight Lines & Coordinate Geometry Geometric Figure on Coordinate Plane View
In the rectangular coordinate plane, a square $ABCD$ with two vertices at $A(0, a)$ and $B(0, b)$ is given. The vertex $C$ of square $ABCD$ lies on the line $y = \frac{x}{3}$. If $a + b = 15$, what is the sum of the coordinates of point $D$?
A) 14
B) 18
C) 21
D) 24
E) 27
Q38 Straight Lines & Coordinate Geometry Line Equation and Parametric Representation View
In the rectangular coordinate plane, it is known that a line $d$ passes through point $A(-4, 1)$ and is perpendicular to the line $2x - y = 5$. If the point where line $d$ intersects the x-axis is $(a, 0)$ and the point where it intersects the y-axis is $(0, b)$, what is the sum $a + b$?
A) -3
B) -1
C) 0
D) 1
E) 3
Q39 Straight Lines & Coordinate Geometry Area Computation in Coordinate Geometry View
In the rectangular coordinate plane, points $A(2, 7)$ and $B(-1, 4)$ are translated 3 units in the positive direction along the x-axis to obtain points $D$ and $C$ respectively.
Accordingly, what is the area of the quadrilateral with vertices at points A, B, C, and D in square units?
A) 9
B) 10
C) 11
D) 12
E) 13
Q40 Simultaneous equations View
Irem has a cylindrical container completely filled with water and a marble block in the shape of a cylinder with height equal to half the height of this container. When the marble block is placed in the container so that it is completely submerged in water, $\frac{1}{32}$ of the water in the container overflows.
Accordingly, what is the ratio of the base radius of the container to the base radius of the marble block?
A) 2
B) 3
C) 4
D) $2\sqrt{2}$
E) $4\sqrt{2}$