turkey-yks

Q1 Indices and Surds Solving Exponential or Index Equations View

$$\frac { 2 ^ { - 2 } } { 4 ^ { - 1 } + \frac { 1 } { m ^ { - 1 } } } = 13 ^ { - 1 }$$
Given this, what is m?
A) 3
B) 4
C) 5
D) 6
E) 7

Q2 Indices and Surds Numerical Arithmetic with Fractions and Decimals View

$$2 \cdot ( 0,2 ) ^ { 3 } + ( 0,4 ) ^ { 3 }$$
What is the result of this operation?
A) 0,06
B) 0,08
C) 0,1
D) 0,12
E) 0,14

Q3 Indices and Surds Solving Equations Involving Surds View

$$\frac { 1 + \sqrt { a } } { 1 - a } - \frac { a } { 1 - \sqrt { a } } = \frac { 5 } { 3 }$$
Given this, what is a?
A) $\frac { 1 } { 2 }$
B) $\frac { 3 } { 2 }$
C) $\frac { 1 } { 4 }$
D) $\frac { 1 } { 9 }$
E) $\frac { 4 } { 9 }$

Q5 Solving quadratics and applications Evaluating an algebraic expression given a constraint View

Let $\mathbf { a }$ and $\mathbf { b }$ be real numbers such that
$$\begin{aligned} & a ^ { 2 } - a = b ^ { 2 } - b \\ & a \cdot b = - 1 \end{aligned}$$
Given this, what is the sum $a ^ { 2 } + b ^ { 2 }$?
A) 6
B) 5
C) 4
D) 3
E) 2

Q6 Laws of Logarithms Express One Logarithm in Terms of Another View

For real numbers x and y
$$2 ^ { x } = 6 ^ { x + y - 1 }$$
Given this, what is $3 ^ { \mathbf { x } }$ in terms of y?
A) $3 ^ { 1 - y }$
B) $6 ^ { 1 - y }$
C) $6 ^ { y }$
D) $9 ^ { - y }$
E) $9 ^ { 1 + y }$

Q7 Inequalities Ordering and Sign Analysis from Inequality Constraints View

For real numbers $x , y$ and $z$
$$x + y < 0 < x < y + z$$
Given this, which of the following orderings is correct?
A) $x < y < z$
B) $x < z < y$
C) $y < x < z$
D) $y < z < x$
E) $z < y < x$

Q8 Partial Fractions View

$$\begin{aligned} & a = \frac { x } { x - y } \\ & b = \frac { y } { x + y } \end{aligned}$$
Given this, what is the value of the expression $\frac { a + b - 1 } { a \cdot b }$?
A) $- 2$
B) $- 1$
C) $0$
D) $1$
E) $2$

Q9 Arithmetic Sequences and Series Find Specific Term from Given Conditions View

$$\frac { [ ( n + 1 ) ! ] ^ { 2 } + ( n ! ) ^ { 2 } } { [ ( n + 1 ) ! ] ^ { 2 } - ( n ! ) ^ { 2 } } = \frac { 61 } { 60 }$$
Given this, what is n?
A) 9
B) 10
C) 12
D) 13
E) 15

Q10 Modulus function Solving equations involving modulus View

For real numbers $\mathbf { x }$ and $\mathbf { y }$
$$\begin{aligned} & y - x = 1 \\ & y - | x - y | = 2 \end{aligned}$$
Given this, what is the sum $\mathbf { x } + \mathbf { y }$?
A) 5
B) 6
C) 7
D) 8
E) 9

Q11 Arithmetic Sequences and Series Counting or Combinatorial Problems on APs View

For integers $\mathrm { x } , \mathrm { y }$ and z
$$2 x = 3 y = 5 z$$
Given this, which of the possible values of the sum $x + y + z$ is closest to 100?
A) 93
B) 96
C) 98
D) 103
E) 105

Q12 Arithmetic Sequences and Series Compute Partial Sum of an Arithmetic Sequence View

$$A = 13 + 26 + 39 + \cdots + 169$$
Given this, what is the sum of the prime numbers that divide A?
A) 16
B) 18
C) 20
D) 22
E) 24

Q13 Arithmetic Sequences and Series Find Specific Term from Given Conditions View

The following are known about a set A.

It consists of 6 consecutive odd natural numbers.
The sum of the elements in the set equals 4 times the largest element.

Accordingly, what is the largest element of set $A$?
A) 21
B) 19
C) 17
D) 15
E) 13

Q21 Composite & Inverse Functions Custom Operation or Property Verification View

I. $f ( x ) = 2 x$ II. $f ( x ) = 2 ^ { x }$ III. $f ( x ) = x ^ { 2 }$ Which of these functions satisfy the equation $f ( a + b ) = f ( a ) \cdot f ( b )$ for every real number a and b?
A) Only I
B) Only II
C) I and II
D) I and III
E) II and III

Q22 Simultaneous equations View

If Ahmet's salary is increased by half of Deniz's salary, then the sum of their salaries becomes 2 times Ahmet's initial salary.
If Ahmet's salary is A TL and Deniz's salary is D TL, what is the relationship between $A$ and $D$?
A) $5A = 8D$
B) $5A = 6D$
C) $4A = 5D$
D) $3A = 4D$
E) $2A = 3D$

Q24 Simultaneous equations View

In a laboratory, the following are known about a drug experiment conducted on male and female guinea pig mice.

Male mice were given 1 tablet of medicine every 12 hours, and female mice were given 1 tablet every 8 hours.
Male mice were given 0.5 gram tablets, and female mice were given 1 gram tablets.
A total of 85 grams of medicine was given to these mice in one day, in the form of 95 tablets.

Accordingly, how many mice were used in the experiment?
A) 20
B) 25
C) 30
D) 35
E) 40

Q25 Simultaneous equations View

Stationery materials are to be distributed to students in a class. Enough materials are brought to the class so that each of the 36 students receives one pencil, one pencil sharpener, and one eraser. However, on the distribution day, since some students are absent, each student present in the class is given 3 pencils, 2 pencil sharpeners, and 1 eraser.
If a total of 42 items of these materials remain after distribution, how many pencil sharpeners are left?
A) 10
B) 11
C) 12
D) 13
E) 14

Q28 Combinations & Selection Distribution of Objects to Positions or Containers View

All 5 different marbles are to be distributed among 3 siblings of different ages.
In how many different ways can this distribution be made such that the oldest sibling gets 1 marble and the other two each get at least one marble?
A) 45
B) 50
C) 60
D) 70
E) 75

Q29 Conditional Probability Combinatorial Conditional Probability (Counting-Based) View

A bag contains 10 balls numbered from 1 to 10.
Given that the sum of the numbers on two balls randomly drawn from the bag is 15, what is the probability that ball number 7 was drawn?
A) $\frac { 2 } { 3 }$
B) $\frac { 2 } { 5 }$
C) $\frac { 2 } { 7 }$
D) $\frac { 1 } { 2 }$
E) $\frac { 1 } { 3 }$

Q31 Radians, Arc Length and Sector Area View

Below is a running park consisting of an isosceles right triangle and a semicircle with the hypotenuse of this triangle as its diameter. There are three running paths in this park. Ay\c{c}a, Bar\i\c{s}, and Cem start running from the starting point at the same time using paths A, B, and C respectively and reach the finish point.
Given that the speeds of Ay\c{c}a, Bar\i\c{s}, and Cem are 4 km, $\mathbf { 2 ~ km }$, and $\mathbf { 3 ~ km }$ per hour respectively, what is the order of arrival at the finish point?
A) Ay\c{c}a, Bar\i\c{s}, Cem
B) Ay\c{c}a, Cem, Bar\i\c{s}
C) Bar\i\c{s}, Cem, Ay\c{c}a
D) Bar\i\c{s}, Ay\c{c}a, Cem
E) Cem, Ay\c{c}a, Bar\i\c{s}

Q32 Measures of Location and Spread View

The graph below provides some information about the heights of five people.
The following are known about these people.

Ay\c{s}e and Kemal are the same height.
Bora is 2 cm shorter than Kemal.
Elif is 6 cm taller than Mehmet.
Mehmet is 3 cm taller than Ay\c{s}e.

Accordingly, what is the average height of these people in cm?
A) 164
B) 165
C) 166
D) 167
E) 168

Q34 Areas by integration View

A piece of paper in the shape of rectangle $ABCD$ has a point E marked on side $DC$ and a point F marked on side AB. When this paper is folded along line EF, AF and EC intersect perpendicularly as shown in the figure.
Given that the area of the figure obtained after the folding operation is $\mathbf { 18 }$ square units less than the area before the folding operation, what is the length |AD| in units?
A) 3
B) 4
C) 6
D) 8
E) 9

Q36 Circles Tangent Lines and Tangent Lengths View

The method of drawing a tangent to a circle with center O from an external point P is given below.

Line segment OP is drawn.
The midpoint M of line segment OP is determined.
A circle with center M and diameter [OP] is drawn.
The intersection points of the circles with centers O and M are marked. Let one of these points be T.
Ray [PT is tangent to the circle with center O at point T.

In this construction, if the radii of the circles with centers O and M are 4 cm and 3 cm respectively, what is the length $| PT |$ in cm?
A) $3 \sqrt { 3 }$
B) $2 \sqrt { 5 }$
C) $\sqrt { 7 }$

Q38 Circles Chord Length and Chord Properties View

$ABCDEF$ is a regular hexagon $|AL| = |LB|$ $| \mathrm { BC } | = 4 \mathrm {~cm}$ $| \mathrm { DK } | = 3 \mathrm {~cm}$ $|KE| = \mathrm { x }$ According to the given information above, what is x in cm?
A) $4 \sqrt { 3 }$
B) $3 \sqrt { 5 }$
C) $3 \sqrt { 7 }$
D) 6
E) 7

Q39 Straight Lines & Coordinate Geometry Geometric Figure on Coordinate Plane View

OABC is a parallelogram $\mathrm { A } = ( 5,0 )$ $\mathrm { C } = ( 3,4 )$
According to the given information above, what is the sum of the diagonal lengths of parallelogram OABC in units?
A) $5 \sqrt { 5 }$
B) $6 \sqrt { 5 }$
C) $7 \sqrt { 5 }$
D) $7 \sqrt { 3 }$
E) $8 \sqrt { 3 }$

Q40 Straight Lines & Coordinate Geometry Slope and Angle Between Lines View

In the right coordinate plane shown in the figure, lines d and e are perpendicular to each other.
Accordingly, what is the abscissa of the point where line d intersects the x-axis?
A) $\frac { 9 } { 2 }$
B) $\frac { 11 } { 2 }$
C) $\frac { 13 } { 3 }$
D) $\frac { 14 } { 3 }$
E) $\frac { 25 } { 6 }$

turkey-yks

Papers (30)

2013 ygs