11.. Three pipes can fill a pool in twelve hours. A drain can empty the full pool in eighteen hours.
How many hours will it take to fill a quarter of the pool if the three pipes and the drain are open?
A)9 B) C) D) 1
6 1
9 15
2
22.. Ayþe can work three times as fast as Zehra.
Working alone, Zehra can do a job in 36 days.
How many days would it take Ayþe to do one-third of the job alone?
A)12 B)9 C)4 D)3
33.. Mustafa and Ziya can do a job together in ten days. Mustafa can do it alone in fifteen days. How many days would it take Ziya to do the job alone?
A)30 B)15 C) D) 1
15 1
30
44.. Hakan can do a job in ten days and Hasan can do the same job in fifteen days. How many days will it take them to do the job if they work together?
A)3 B)6 C)12 D)24
66.. It takes Murat five hours to travel from city A to city B at a constant speed of 80 km/h. How many hours will it take Murat to complete the same journey if he drives at 50 km/h?
A)16 B)8 C)10 D)6
77.. Two cars begin traveling along the road at speeds of 70 km/h and 85 km/h respectively. What is the distance between the two cars after five hours?
A)350 km B) 425 km C)75 km D)35 km
88.. A car can travel x km in four hours. At the same speed it can travel x + 9 km in six hours. Find x.
A)6 B)8 C)12 D)18
55.. A pipe can fill a pool in six hours and a drain at the bottom of the pool can empty the full pool in eight hours. How many hours will it take to fill the empty pool if both the pipe and the drain are working?
A) 3 B)14 C)7 D)24
4
1111.. If the numerator and denominator of a fraction decrease by 20% and 60% respectively, what is the percentage increase in the fraction?
A)30% B)40% C)100% D)60%
1166.. Ahmet’s investment of $2800 earned $2520 in
three years. What was the annual simple interest rate?
A)30% B)40% C)50% D)60%
1177.. A certain amount of money was invested with a
monthly simple interest rate of 20%. After four months the amount was $5120. What was the initial principal?
A)$5000 B) $4800 C)$4600 D)$4200
1133.. 120 L of a salt solution contains 30 L of salt. What
is the percentage of salt in the solution?
A)20% B)25% C)75% D)50%
1144.. Ali added 60 L of a 40% alcohol solution to 20 L
of a 20% alcohol solution. What is the alcohol concentration of the new solution?
A)35% B)40% C)45% D)55%
1155.. A shopkeeper has a stock of clothes. He sells 30%
of his stock for 40% less than the wholesale price and the rest of the stock for 40% more than the wholesale price. What percentage profit the shopkeeper make from his stock?
A)15% B)16% C)18% D)32%
1122.. In a class of 92 students, 25% of the students are
girls. Find the number of boys in this class.
A)23 B)46 C)54 D)69
1100.. Two cities A and B are connected by a road. A car
leaves city A and begins traveling towards city B at (V + 20) km/h. At the same time, another car leaves city B and begins traveling towards city A at (V – 5) km/h. The cars pass each other after eight hours. Four hours after passing each other, the cars are 260 km apart. How long is the road from A to B?
A)540 km B)520 km C)500 km D)480 km 99.. It takes Fatma six hours to drive from city A to city B at a constant speed of (V + 10) km/h. She can cover the same distance driving at a speed of (2V – 6) km/h in four hours. Find V.
A)32 B)36 C)40 D)42
A. ANGLES AND DIRECTION
1. The Concept of Angle
The angle formed by the rays [OA and [OB is called angle AOB or angle BOA. [OA and [OB are called the sides of the angle.
We can write the angle AOB as [OA [OB, AéOB orAOB. We can also write [OA [OB = AOB.
The common endpoint O is called the vertex of the angle. If O is the vertex of one unique angle, we sometimes write O to or O the mean the angle with vertex O.
Definition angle
An angle is the union of two rays which have a common endpoint.
O
A
B side OB (vertex)
side OA
[OA È [OB = ÐAOB = ÐBOA =ÐO
2. Directed Angles
If we say that one of the two rays of an angle is the initial side of the angle and other side is the terminal side of the angle, then the corresponding angle is called a directed angle.
There are two different directions about the vertex of an angle from its initial side to its terminal side. If the angle is measured counterclockwise then the angle is called a positive angle. If it is measured clockwise then the angle is called a negative angle.
terminal side O
B
A initial side
ÐAOB is a positive angle (counterclockwise direction)
(+)
O
B
A ÐAOB is a negative angle
(clockwise direction) () terminal side
initial side
O
B
A
EXAMPLE
1
Determine the initial and terminal side of each angle and state its direction.Solution a. [OA is the initial side and [OB is the terminal side. AOB is a positive angle.
b. [OK is the initial side and [OL is the terminal side. KOL is a negative angle.
c. [OS is the initial side and [OR is the terminal side. SOR is a negative angle.
a. O
L
K
b.
S O
R
c.
3. Directed Arcs
Definition arc
The segment of a circle between the two sides of an angle AOB is called the arc corresponding to AOB. We write AïB to mean the arc corresponding to AOB.
A line which passes through a circle is called a secant line. A line segment AB which joins two different points on a circle is called a chord. Any secant or chord separates a circle into two arcs.
A chord which passes through the center of a circle is called a diameter. A diameter divides a circle into two equal arcs called semicircles.
B EF is a secant line F
E
diameter
A O B
AïB is a semicircle The length of every
diameter in a given circle is the same. For this reason, when we talk about ‘the diameter’ of a circle, we mean the length of any diameter in the circle.
In order to distinguish the two arcs formed by the line AB on the circle, we can plot two points C and D as shown in the figure below. We denote the positive arc AïB by AùCB and the negative arc AïB by AùDB.
The longer arc is called the major arc and the shorter arc is called the minor arc.