turkey-yks

2024 yks-tyt

7 maths questions

Q3 Sequences and series, recurrence and convergence Applied/contextual sequence problem View
Selma designs a toy with identical clips in yellow and blue colors. In step 1, she places one clip on the ground. In each subsequent step, she attaches one clip to each blue part of all the clips she placed in the previous step as shown in the figure, and moves to the next step. Selma completes the first 3 steps of this toy using 7 clips.
Accordingly, after Selma completes step 12, how many more clips has she used in total compared to after completing step 10?
A) $3 \cdot 2^{10}$
B) $3 \cdot 2^{11}$
C) $7 \cdot 2^{9}$
D) $7 \cdot 2^{10}$
E) $2^{11}$
Q4 Indices and Surds Identifying Rational vs Irrational Numbers View
A note that Elif read in her mathematics book states that $\sqrt{a} + \sqrt{b} = \sqrt{c}$ for some values. Because water dripped on her book, Elif could not read the number $b$ in the example.
Accordingly, which of the following cannot be the number $b$?
A) $\sqrt{5}$
B) $\sqrt{20}$
C) $\sqrt{45}$
D) $\sqrt{60}$
E) $\sqrt{80}$
Q8 Inequalities Absolute Value Inequality View
In a store, the cost prices of a dishwasher, a washing machine, and a refrigerator are 18 thousand, 22 thousand, and $b$ TL, respectively. These products are sold together as a triple white goods package. This package is sold at twice the cost price of a refrigerator plus 30 thousand TL, the store makes a profit; when sold at three times the cost price of a refrigerator minus 20 thousand TL, the store makes a loss.
Accordingly, which of the following inequalities expresses all possible values of the cost price of a refrigerator?
A) $|b - 20000| < 10000$
B) $|b - 15000| < 5000$
C) $|2b - 15000| < 12000$
D) $|2b - 24000| < 17000$
E) $|3b - 16000| < 8000$
Q12 Curve Sketching Limit Reading from Graph View
In the rectangular coordinate plane, the graphs of functions $f$, $g$ and $h$ are given in the figure.
For functions $f$, $g$ and $h$
$$(f - g)(1) \cdot (f - h)(1) < 0$$
$$(g - h)(2) \cdot (g - f)(2) > 0$$
Given that the inequalities are satisfied, which of the following orderings is correct?
A) $f(3) < g(3) < h(3)$
B) $f(3) < h(3) < g(3)$
C) $g(3) < f(3) < h(3)$
D) $h(3) < f(3) < g(3)$
E) $h(3) < g(3) < f(3)$
Q16 Measures of Location and Spread View
When the numbers in a data set are arranged from smallest to largest, if the number of data is odd, the median (middle value) is the middle number; if the number of data is even, the median is the arithmetic mean of the two middle numbers.
Consisting of distinct integers and arranged from smallest to largest
$$9, 10, a, 13, 16, b$$
the arithmetic mean and median of the data set are consecutive integers.
Accordingly, what is the sum $a + b$?
A) 30
B) 36
C) 42
D) 48
E) 54
Q17 Arithmetic Sequences and Series Find Specific Term from Given Conditions View
Merve plans a 30-day walking program. On the first day, she walks for a certain duration, and plans to walk 1 minute longer each subsequent day than the previous day. Following this plan for the first 15 days, Merve began to struggle and reduced her walking time by 1 minute each day for the remaining days compared to the previous day.
After 30 days, Merve calculated her total walking time to be 1395 minutes.
Accordingly, how many minutes did Merve's first day walk last?
A) 30
B) 35
C) 40
D) 45
E) 50
Q29 Combinations & Selection Basic Combination Computation View
Duru observed that she was present in 45 of all three-person groups that could be formed from the students in her class.
Accordingly, in how many of all three-person groups that could be formed from the students in Duru's class is Duru not present?
A) 20
B) 35
C) 90
D) 105
E) 120