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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
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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
2017 ygs

18 maths questions

Q3 Indices and Surds Simplifying Surd Expressions View
$$\sqrt [ 3 ] { \frac { 32 } { \sqrt { 8 } - \sqrt { 2 } } }$$
What is the result of this operation?
A) $\sqrt { 2 }$ B) $2 \sqrt { 2 }$ C) $\sqrt [ 3 ] { 2 }$ D) 2 E) 4
Q6 Modulus function Solving equations involving modulus View
For non-zero real numbers $x$ and $y$
$$\begin{aligned} & | x \cdot y | = - 2 x \\ & \left| \frac { y } { x } \right| = 3 y \end{aligned}$$
the following equalities are given.
Accordingly, what is the sum $x + y$?
A) $\frac { 3 } { 2 }$ B) $\frac { 5 } { 2 }$ C) $\frac { 5 } { 3 }$ D) $\frac { 7 } { 3 }$ E) $\frac { 5 } { 6 }$
Q8 Exponential Functions Exponential Equation Solving View
$$\begin{aligned} & 4 ^ { x } + 4 ^ { y } = 10 \\ & 4 ^ { x } - 4 ^ { y } = 8 \end{aligned}$$
Accordingly, what is the value of the expression $\mathbf { 2 } ^ { \mathbf { x } + \mathbf { y } }$?
A) 2 B) 3 C) 4 D) 5 E) 6
Q11 Inequalities Integer Solutions of an Inequality View
For real number $x$
$$- 3 < 2 x < 7$$
Accordingly, what is the sum of the integer values that the expression $5 - x$ can take?
A) 5 B) 10 C) 15 D) 20 E) 25
Q13 Composite & Inverse Functions Evaluate Composition from Algebraic Definitions View
Let k be a real number. The functions f and g defined on the set of positive real numbers are
$$\begin{aligned} & f ( x ) = k x ^ { 2 } + 1 \\ & g ( x ) = \sqrt { x } + 2 \end{aligned}$$
defined in the form.
$$( f \circ g ) ( 9 ) = 6$$
Given that, what is the value of f(2)?
A) $\frac { 7 } { 5 }$ B) $\frac { 8 } { 5 }$ C) $\frac { 9 } { 5 }$ D) 2 E) 3
Q14 Factor & Remainder Theorem Remainder by Linear Divisor View
The polynomial $P ( x ) = ( x + 1 ) + ( x + 2 ) + \ldots + ( x + 9 )$
$$Q ( x ) = ( x + 1 ) + ( x + 2 ) + \ldots + ( x + 5 )$$
is divided by the polynomial.
What is the remainder obtained from this division?
A) 10 B) 12 C) 14 D) 16 E) 18
Q19 Permutations & Arrangements Handshake / Product Counting View
In a tournament with 8 teams, each team played against the other teams once. In the tournament, 3 referees were assigned from 4 available referees for each match, and all referees worked an equal number of matches.
Accordingly, how many matches did each referee work?
A) 14 B) 15 C) 18 D) 20 E) 21
Q30 Trig Proofs Triangle Trigonometric Relation View
ABC is an isosceles triangle $\mathrm { D } \in [ \mathrm { BC } ] , \mathrm { B } \in [ \mathrm { AE } ]$ $| \mathrm { AB } | = | \mathrm { BC } |$ $| \mathrm { AC } | = | \mathrm { AD } | = | \mathrm { DE } |$ $\mathrm { m } ( \widehat { \mathrm { ADB } } ) = 111 ^ { \circ }$ $m ( \widehat { B D E } ) = x$
Accordingly, how many degrees is $x$?
A) 15 B) 18 C) 21 D) 24 E) 27
Q31 Circles Area and Geometric Measurement Involving Circles View
Teacher Aslı created the number 3 on a piece of paper by painting identical equilateral triangles inside an equilateral triangle ABC as shown in the figure.
If the area of equilateral triangle ABC is 96 square units, what is the painted area in square units?
A) 22 B) 27 C) 33 D) 36 E) 44
Q32 Circles Area and Geometric Measurement Involving Circles View
Given two squares as shown; the area of square ABCD is equal to 2 times the area of square CEFG.
Accordingly, what is the ratio $\frac { | \mathrm { AF } | } { | \mathrm { AG } | }$?
A) $\frac { \sqrt { 5 } } { 2 }$ B) $\frac { 2 \sqrt { 2 } } { 3 }$ C) $\frac { \sqrt { 10 } } { 3 }$ D) $\frac { 2 \sqrt { 2 } } { 5 }$ E) $\frac { \sqrt { 10 } } { 5 }$
Q33 Circles Area and Geometric Measurement Involving Circles View
A rectangle ABCD with short side 12 units and long side 18 units is folded along AL and KC such that $| \mathrm { KB } | = | \mathrm { LD } | = 4$ units. Then, with M and N being the midpoints of the sides they are on, this resulting shape is folded again along the line MN as shown to form a trapezoid.
Accordingly, what is the area of this trapezoid in square units?
A) 108 B) 105 C) 102 D) 99 E) 96
Q34 Circles Chord Length and Chord Properties View
$ABCDEF$ is a regular hexagon $\mathrm { K } , \mathrm { L } \in [ \mathrm { AD } ]$ $| \mathrm { AB } | = 6$ units $| \mathrm { KL } | = \mathrm { x }$
In the figure, points $K$ and $L$ are on semicircles with diameters $AB$ and $DE$ respectively.
Accordingly, what is $x$ in units?
A) 5 B) 6 C) 9 D) $3 \sqrt { 3 }$ E) $6 \sqrt { 3 }$
Q35 Circles Circle Equation Derivation View
OAEF is a rectangle, ABCD is a square $| \mathrm { FE } | = 7$ units $| \mathrm { AB } | = 2$ units $| \mathrm { DE } | = x$
In the figure, points E and C are on a quarter circle with center O.
Accordingly, what is $x$ in units?
A) $\frac { 7 } { 2 }$ B) $\frac { 9 } { 2 }$ C) $\frac { 13 } { 4 }$ D) 3 E) 4
Q36 Circles Area and Geometric Measurement Involving Circles View
$$6 | \mathrm { AB } | = 3 | \mathrm { BC } | = 2 | \mathrm { CD } |$$
Above, three semicircles with diameters $[ \mathrm { AB } ] , [ \mathrm { BC } ]$ and $[ \mathrm { CD } ]$ with collinear centers are drawn inside a semicircle with diameter [AD], and the region between them is painted as shown in the figure.
If the perimeter of the painted region is $\mathbf { 24 \pi }$ units, what is its area in square units?
A) $44 \pi$ B) $48 \pi$ C) $52 \pi$ D) $56 \pi$ E) $60 \pi$
Q37 Volumes of Revolution Volume by Displacement or Composite Solid View
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
Q38 Volumes of Revolution Volume by Displacement or Composite Solid View
A right circular cone with height 10 units is placed inside a hollow right circular cylinder with height 10 units as shown in Figure 1. Water with volume $\mathrm { V } _ { 1 }$ cubic units is poured between this cylinder and cone, and the water height becomes 5 units. Then this object is inverted as shown in Figure 2, and after adding more water, the water volume becomes $\mathrm { V } _ { 2 }$ cubic units and the height becomes 5 units.
Accordingly, what is the ratio $\frac { \mathrm { V } _ { 1 } } { \mathrm {~V} _ { 2 } }$?
(During this process, water does not enter the cone.)
A) $\frac { 3 } { 7 }$ B) $\frac { 5 } { 11 }$ C) $\frac { 8 } { 15 }$ D) $\frac { 10 } { 21 }$ E) $\frac { 15 } { 31 }$
Q39 Straight Lines & Coordinate Geometry Geometric Figure on Coordinate Plane View
In the rectangular coordinate plane, a parallelogram whose vertices are the intersection points of the lines $y = 2$ and $y = 6$ with the line $y = 2x$ has diagonals intersecting at the point $(0,4)$.
What is the area of this parallelogram in square units?
A) 16 B) 18 C) 20 D) 22 E) 24
Q40 Vectors Introduction & 2D Magnitude of Vector Expression View
In the figure, squares OABC and ADEF are shown in the rectangular coordinate plane, each with one side on the x-axis. The vertex F is the midpoint of the side on which it lies in square OABC, which has a side length of 4 units.
Accordingly, which of the following is the vector $\overrightarrow { O B } + \overrightarrow { O E }$?
A) $( 4,6 )$ B) $( 8,6 )$ C) $( 10,4 )$ D) $( 10,6 )$ E) $( 10,8 )$