1.

If 𝑎𝑏=500 and the product of noncommon factors of these numbers is 20, find
𝐿𝐶𝑀(𝑎;𝑏).

A) 180 B) 50 C) 90 D) 100 E) 250

2. What is the number of sides of a regular polygon if sum of the interior angles is
1620°?

A) 10 B) 11 C) 12 D) 13 E) 15

3. Two triangles, ΔABC and ΔDEF, are given. Which of the following is not a valid
criterion to prove that these two triangles are similar?
A) Corresponding angles are equal
B) The corresponding sides are proportional
C) Two sides are proportional, and the included angle is equal
D) Two angles and one side of one triangle are equal to two angles and one side of the
other triangle
E) The ratio of the areas of the two triangles is equal to the square of the ratio of their
corresponding sides.

4. Solve the equation ❑n C 2=21.

A) 8
B) 6
C) 7
D) 5
E) 3

5. To which point does point M ( 3 ,5 ) translate, given the translation formulas x '=x−1 and
y '= y+ 3?

A) (2, 8)
B) (4, 8)
C) (2, 5)
D) (3, 8)
E) (5, 3)

6. Find the reflection of point A ( 1 ,2 ,−3 ) across the Oxy plane.

 A) (−1 ,−2 ,−3 )
B) ( 1 , 2, 3 )
C) (−1 , 2,−3 )
D) (−1 ,−2 , 3 )
E.)( 1 ,−2 ,−3 )

7. The longer sides of two similar polygons are 20 cm and 15 cm, respectively, and the
difference between their perimeters is 20 cm. Find the perimeter of the larger polygon.

A) 60 cm
B) 20 cm
C) 80 cm
D) 35 cm
E) 5 cm

8. Twenty people will go on stage. Find the probability that Hasan will go on stage
either among the first three, or after the 12th, but before the 16th participant.

9. In triangle MNK , from point P, taken on the extension of side MK , a line, that intersects
side NK at point Q is drawn. Find PK , if MN =12, NK =30, PQ=8, and ∠ PQK =∠ NMK .

10.
CE 3
Find the length of FD if, in the parallelogram ABCD, BC = 5 and BD=14 .
11. There are t yellow marbles and n red marbles in a box. The probability that a
randomly drawn marble from the box is yellow is 0.3. Find the minimum value of the
product t · n.

12. There are 5 red marbles, 2 black marbles, and 3 yellow marbles in the bag.
Find the probability of selecting 3 marbles such that
a) one is red and two are yellow.
b) first marble is red and then next two are yellow.

13. In a group of 100 persons, 72 people can speak English and 43 can speak
French. a) How many of them can speak only English? b) How many of them can
speak only French and how many of them can speak both English and French? Note:
By using Euler-Venn diagram solve the given problem.

14. Ali completes a task in 8 days, Murad completes the same task in 12 days, and
Imran in 16 days when working individually.

i) When they began to work, Imran got sick. After Ali and Murad worked together
for 2 days Imran joined them to complete the task. How many days did it take to
complete the task?
ii) If they all worked together at the beginning, how many days would it take to
complete the task?

15. How many odd 4-digit numbers can be formed using the elements of the set
{0,1, 2, 3, 4, 5, 6}

a) without repeating any digits

b) with repeating digits?

16. How many even 4-digit numbers can be formed using the elements of the set
{0,1, 2, 3, 4, 5, 6}

a) without repeating any digits

b) with repeating digits?

17. Find the sum in a favorable way:

1 1 1 1
+ + +
10 40 88 154

18. How many fractions can be expressed as terminating (finite) decimal number?

9 4 9 10 6
; ; ; ;
36 5 2 15 8

A) 1 B) 2 C) 3 D) 4 E) 5

19. Which of the following is true for comparing the given numbers?
4
a= , b=0 , ( 4 ) , c=0 , ( 6 )
9

A) a=b< c B) a> b>c C) a=c <b

D) a=b> c E) a=b=c

20. Prove:

❑n C k =❑n−1 C k−1+❑n−1 C k
21.
AB−DC
If MN is a midline, then prove that PQ= 2

22. Express 1.2 as a percentage.

A) 20 % B) 12 % C) 120 % D) 140% E) 50%

23. In the given trapezoid, if AB/¿ CD, EF is a midline, DC=4 cm , AB=10 cm, then find
the length of KL.

24. Which quantities below are inversely proportional?

A) The distance and time spent on travelling with constant speed

B) Radius and the area of a circle
C) Perimeter and the side of a square
D) The number of farmers and hours spent on doing the task.
E) the number of pens and their price

25. How many pages does the book contain if Jama has read 60 pages, which
represents 40% of the total?

A) 120 B) 150 C) 180 D) 100 E) 160

26. If m=5 n then n is what percent of m ?

B) 24% B) 20% C) 30% D) 40% E) 50%

27. Mean terms of a proportion are 3 and 12. If the extreme terms of the proportion
are (x−2) and 4, find the value of x .
A) 10 B) 15 C) 20 D) 18 E) 11

28. 24% of a number is 18. What percent of that number is 125?

29. What percentage increase in the side of a square is required to achieve a 44%
increase in its area?

30. By what percent is the number of all natural divisors of 140 less than the
number of all natural divisors of 240?

31. Given a 1.25-liter of a 60% alcohol solution, find the concentration of the
solution under the following conditions:

i) If 0.25 liters of water is evaporated.

ii) If 0.75 liters of a 20% alcohol solution is added.

32. A bicycle is sold at the same price in Shop I and Shop II, and both shops offer
two discounts consecutively. Analyze the data in the table and answer the questions
below:
 № The first discount The second
discount
Shop I 40% 20%

Shop II 50% 10%

What is the total price reduction expressed as a percent in Shop I and Shop II, and
which shop offers the lower price after the double discount?

33. The diagonals of a rectangle form angle 250 with one of the sides of the
rectangle. The acute angle formed between the diagonals is

A) 250 B) 500 C) 550 D) 40 0 E) 1300

34. In the given rhombus ABCD ,if AC=12 cm , BD=16 cm, then find the perimeter of
the given rhombus.

A) 40 B) 42 C) 28 D) 36 E) 18

35. In the given parallelogram ABCD, if ∠ BCD=550 ,∠ ADE=α , DE=BC ,then find α .

36. If one of the internal angles of a regular polygon is 1350. Then find the number
of diagonals in the polygon.

37. In the given rectangle, DE=FE , CE=1 cm , FB=5 cm and ∠ BFE=45 0.

Find the area of the shaded region.