turkey-yks

2025 yks-tyt

4 maths questions

While teaching the topic of exponents, Teacher Kerem stated that the expression $a^{b^{c}}$ cannot be written without parentheses in this way, because the expressions $a^{\left(b^{c}\right)}$ and $\left(a^{b}\right)^{c}$ can have different values, and explained this situation with an example.
Accordingly, which of the following could be the example given by Teacher Kerem?
A) $a = 1, b = 2, c = 3$ B) $a = 2, \quad b = 1, \quad c = 3$ C) $a = 2, \quad b = 2, \quad c = 2$ D) $a = 3, \quad b = 0, \quad c = 3$ E) $a = 3, \quad b = 2, \quad c = 1$
Q3 Indices and Surds Simplifying Surd Expressions View
In a page of a mathematics textbook shown partially below, the result of the 1st operation is 12 more than the result of the 2nd operation.
$a = 2 \quad b = $
For the real numbers $a$ and $b$ given above, find the result of the following operations.
1. operation: $a\sqrt{b} + \sqrt{b} = $ 2. operation: $a\sqrt{b} - \sqrt{b} = $ 3. operation: $a\sqrt{b} \times \sqrt{b} = $ 4. operation: $a\sqrt{b} \div \sqrt{b} = $
Accordingly, the result of the 3rd operation is equal to how many times the result of the 4th operation?
A) 9 B) 16 C) 24 D) 30 E) 36
Q29 Permutations & Arrangements Combinatorial Counting (Non-Probability) View
Aras will complete all of the following activities on a Sunday: exercising, watching a movie, doing homework, doing household chores, and taking a bath. Aras does not start one activity before completing another. Aras must take a bath after exercising, and must complete his homework and household chores before watching a movie.
According to this, in how many different ways can Aras arrange these five activities?
A) 10 B) 15 C) 20 D) 25 E) 30
Q30 Probability Definitions Finite Equally-Likely Probability Computation View
Six friends, including Doğa and Duru, came to visit Defne's house. Defne randomly gave gifts to two of these friends.
According to this, what is the probability that Defne gave a gift to at least one of Doğa and Duru?
A) $\frac{2}{3}$ B) $\frac{3}{5}$ C) $\frac{4}{5}$ D) $\frac{8}{15}$ E) $\frac{11}{15}$