Mert, who performs operations with radical numbers, instead of multiplying the number $\sqrt{10} + \sqrt{6}$ by its conjugate $\sqrt{10} - \sqrt{6}$, mistakenly divided it. Accordingly, how much greater is the number Mert found than the number he should have found? A) $\sqrt{12}$ B) $\sqrt{15}$ C) $\sqrt{18}$ D) $\sqrt{20}$ E) $\sqrt{30}$
An instructor at a parachute jumping course gives the following explanation to the trainees: "When jumping from an airplane at a height of 800 meters from the ground, you need to open your parachute 400 to 500 meters after jumping from the airplane in order to land safely on the ground." Accordingly, which of the following inequalities expresses the values that the height from the ground when the parachute opens can take in order to land safely? A) $|x - 350| \leq 50$ B) $|x - 300| \leq 100$ C) $|x - 250| \leq 150$ D) $|x - 200| \leq 200$ E) $|x - 150| \leq 250$
Let $a, b, c$ and $d$ be real numbers such that $$x + ay \leq b$$ $$x + cy \geq d$$ The solution set of the system of inequalities is shown in green on the coordinate plane below. Accordingly, what are the signs of the numbers $a, b, c$ and $d$ in order? A) $+, -, -, -$ B) $+, +, +, -$ C) $+, -, +, -$
In a data group, when the numbers are arranged from smallest to largest, if the number of terms in the group is odd, the median (middle value) is the middle number; if it is even, the median is the arithmetic mean of the two middle numbers. The ages and heights of the 9 players on a volleyball team, with the first component representing their ages and the second component representing their heights, are given as the sorted data group by height: $(18; 1.76), (17; 1.79), (18; 1.82), (19; 1.84), (20; 1.84)$, $(21; 1.88), (17; 1.90), (20; 1.92), (19; 1.96)$. One player left this 9-person team, but the median of both the ages and heights of the remaining players did not change. Accordingly, which of the following correctly gives the age and height of the player who left the team? A) $(17; 1.79)$ B) $(17; 1.90)$ C) $(19; 1.84)$ D) $(19; 1.96)$ E) $(21; 1.88)$
Let $a, b, c \in \mathbb{R}$ and $a \neq 0$. To factor the polynomial $ax^2 + bx + c$, we search for $m, n, r, s \in \mathbb{R}$ such that $a = m \cdot r$, $c = n \cdot s$, and $b = m \cdot s + n \cdot r$. If numbers satisfying these conditions can be found, the polynomial is factored as $ax^2 + bx + c = (mx + n)(rx + s)$. Using the method described above, Sude wants to factor the polynomial $2x^2 + bx - 21$ where $b \in \mathbb{R}$. After finding the real numbers $m, n, r$, and $s$ that satisfy the given conditions, she notices that these numbers are each integers. Later, she confuses the places where she should write the numbers $n$ and $s$, and mistakenly factors the polynomial as $(mx + s)(rx + n)$ instead of $(mx + n)(rx + s)$, and finds the factors of the polynomial $2x^2 + x - 21$. Accordingly, what is b? A) 11 B) 12 C) 13 D) 14 E) 15
Temperature conversions between Fahrenheit (${}^{\circ}\mathrm{F}$) and Celsius (${}^{\circ}\mathrm{C}$) are calculated using the formula $\mathrm{F} = \frac{9}{5} \cdot \mathrm{C} + 32$. Cem has been assigned to measure the classroom temperature in Celsius at the same time each day for five days they go to school and find the average temperature of these five days in Celsius. On one of these five days, Cem did not go to school, and his classmate Deniz took the measurement for that day. However, Deniz mistakenly recorded the F value instead of the C value for that day's temperature in the list. Based on the values in the list, Cem calculated the average temperature for these five days as $33.8^{\circ}\mathrm{C}$.
\cline{2-6} \multicolumn{1}{c|}{}
Monday
Tuesday
Wednesday
Thursday
Friday
Temperature (${}^{\circ}\mathrm{C}$)
23
27
25
20
26
After Deniz's measured temperature value is converted to Celsius and the five-day measurement has the values in the list as shown above, on which day did Cem not go to school? A) Monday B) Tuesday C) Wednesday D) Thursday E) Friday
In the graph below showing Fatih's time to reach work according to his departure time from home on a certain day, the graph representations between 07.00-08.00 and 08.00-09.00 are linear. Fatih, who left home at some time between 08.00 and 09.00, would have arrived at work at the same time if he had left home exactly one hour earlier. Accordingly, at what time did Fatih arrive at work? A) 09.12 B) 09.15 C) 09.18 D) 09.21 E) 09.24
In a mathematics class, the teacher asks Veli to calculate in how many different ways 3 students can be selected, Yasin to calculate in how many different ways 5 students can be selected, and Zeynep to calculate in how many different ways 11 students can be selected from the students in the class. All three students calculated the requested numbers correctly. Given that the numbers found by Yasin and Zeynep are the same positive integer, what is the number found by Veli? A) 364 B) 560 C) 688 D) 816 E) 960
To access an internet site, users must select all unit squares containing car parts from the photograph divided into 9 unit squares below and click the confirm button. Eda, who wants to access this site, randomly selected four different unit squares from this photograph and clicked the confirm button. Accordingly, what is the probability that Eda can access this site? A) $\frac{1}{15}$ B) $\frac{1}{36}$ C) $\frac{1}{56}$ D) $\frac{1}{84}$ E) $\frac{1}{126}$