DO NOT OPEN THIS BOOKLET UNTIL ASKED TO DO SO Roll No. Total Questions: 50
Time: 1 hr hr.
CLASS
8
SOF INTERNATIONAL MATHEMATICS OLYMPIAD
Level-2
SET-1
Guidelines for the Candidate 1.
You will get additional ten minutes to ll up information about yourself on the OMR Sheet, before the start of the exam.
2.
The Question Paper comprises two sections : Mathematics (45 Questions) and Achievers Section (5 Questions) Each question in Achievers Section carries 3 marks, whereas all other questions carry one mark each.
3.
All questions are compulsory. compulsory. There There is no negative marking. Use Use of calculator is not permitted.
4.
Write your Name, Roll No. and Class clearly on the OMR Sheet and do not forget to sign it.
5.
There is only ONE correct answer. answer. Choose only ONE ONE option for an answer.
6.
To mark your choice of answers by darkening the circles in the OMR Sheet, use an HB Pencil or a Blue / Black ball point pen only. E.g.
Q.16: A number has nine ones, six tens and eight hundreds. What is the number? A. 869
B. 896
C. 968
D. 986
As the correct answer is option A, you must darken the circle corresponding to option C.
16. A
B
C
7.
Rough work should be done in the blank space provided in the booklet.
8.
Return the OMR Sheet to the invigilator invigilator at the end of the exam.
D
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MATHEMATICS
1.
Simplify:
9.
−6 × 28 + −11 × 65 − −3 ÷ 9 ÷ −1 7 18 13 22 29 87 7 A. C. 2.
10 6
5
B.
6
7
D.
10
−10 −6
5
Step-I
Draw AB = 8 cm.
6
Step-II
Draw
Step-III Draw
7
Step-V
C.
a b
is 12. B.
D.
70 90
B. D.
12 years Data inadequate
B. D.
b a
34 38
B. D.
56.2 58.5
B. D.
b2 13.
80 100
Step-III
C.
Step-IV
D.
Step-V
If 2 men each working 5 hours per day can nish a job in 12 days, then how long will 4 men each working 2 hours per day take to nish the same job? 14 10
15.
15 18
250 450
B. D.
225 550
If A's expenditure is 20% more than B's expenditure and B's expenditure is 30% less than C's expenditure, then by what percentage A's expenditure is less than C's expenditure? 16% 14%
B. D.
If S.P. of an article is
12% 18%
5
of its C.P., then the prot 4 percentage in the transaction is
C.
14.
B. D.
If x varies inversely as y 3 and x is 16 when y is 5, then nd x when y is 2.
1
%
B.
1 20 % 4
25%
D.
1 25 % 2
A.
36 40
55.4 59.7
B.
A. C.
a2
24 years None of these
Step-II
A. C.
99 + 97
What is the number which multiplied by itself gives 3158.44? A. C.
2
a
2
99 − 97
11.
How many non-perfect square numbers are there between 19 2 and 20 2? A. C.
8.
2
a b
12 5
= 120° at D so that its arm
A.
A. C.
The total age of A and B is 12 years more than the total age of B and C. C is how many years younger than A? A. C.
7.
b
B. D.
One-third of a number is as much less than 33 as 48 is greater than half the number. Find the number. A. C.
6.
10.
14 10
The value of
A.
5.
(a – b) (a + b – 2) (a – b + 2) (2a – b – 1)
∠ADM
DM cuts BN at C.
The sum of the interior angles of a polygon is 1440°. Find the number of sides of the polygon. A. C.
4.
Draw
Which of the following is the factor of A. B. C. D.
∠BAY = 45° at A. ∠ABN = 105° at B.
Step-IV Cut off a length AC = 5 cm from AY.
10
4a 2 + b 2 – 4ab + 2b – 4a + 1 ?
3.
The steps of construction of a quadrilateral ABCD are given below in which AB = 8 cm, AD = 5 cm, ∠A = 45°, ∠B = 105° and ∠D = 120°. Which of the following is a wrong step?
4
If x +
1 x
= 4, then x −
1
x
=
A.
2 3
B.
3 2
C.
2 6
D.
3 6
What is the probability that you randomly choose a ball that is not red from a bag of 6 black , 8 yellow, 4 red and 5 white balls? A. C.
19/21 4/23
B. D.
19/23 14/23 Class-8 | Set-1 | Level-2
16.
A train of length 600 m moving with the speed 144 km/hr crosses another train moving in opposite direction at the speed 240 km/hr in 15 seconds. Find the length of second train. A. C.
17.
B. D.
700
700 m 1200 m
600
se lc yc i b f o . o N
21.42% 22.42% 20.42% 23.40%
500 400 300 200 100 0
2 3
, we get
40 9
C.
se M
T
ir sr
de u
F u h
W
. What
3 11
D.
9
11
A. C.
13 15 13
23.
5:7 7:5
–
B. D.
4:5 5:4
If ABCD is a rectangle, then nd the area of the shaded region of the gure given below. D
5 cm
J
I
4 cm
c m c 2
C 9 D 6
3
K
m
In a class, boys. If
2
5
A. C. 24.
of the girls and
1
25.
C.
30 27 30
Class-8 | Set-1 | Level-2
4 cm
E
B.
D.
7 30 29 36
54.5 cm 54.5 cm2
F
5 cm
B
1
B. D.
545 cm2 5.45 cm2
A sum of ` 2200 is in the denominations of ` 50 and ` 10 notes. If the total number of notes be 100, then (a)
The number of 10-rupee notes is _____.
(b)
The number of 50-rupee notes is _____.
(a) A. 40 B. 50 C. 30 D. 70
of the students are girls and rest are
19
m
12 cm
of the boys are absent, 4 9 what part of the total number of students is absent?
A.
6 c
A
True False Sometimes true and sometimes false None of these 3
c
G
2
‘If a number is divisible by any number p, then it is also divisible by each of the factor of p’. The statement is A. B. C. D.
21.
c
4 3 3 4
m
H
L
1 9 9 0 B
20.
C
m
A 3 B 5 4
3, 4, 8, 3,
S
sold in a whole week. B.
2, 8, 4, 8,
u
T
Mon and Tues to the average number of bicycles
5
8, 2, 2, 2,
n S
Find the ratio of the number of bicycles sold on
Find the missing values of A, B, C and D respectively
A. B. C. D.
ta
Week
is the fraction? A.
n o
In a fraction, numerator is 2 more than denominator. If we multiply the fraction by 2
19.
The given graph shows the number of bicycles sold in a whole week.
The largest possible circle is cut out from a square cardboard. What percent of the card board will be 22 left? (Use p = ) 7 A. B. C. D.
18.
1000 m 900 m
22.
(b) 60 50 70 30
Find the divisor, given that the dividend is 2200, remainder is 14 less than the divisor and the divisor is one-third of the quotient. A. C.
25 24
B. D.
27 None of these 3
26.
1 By selling an article, a person made a loss of 2 % . 2 If he would sell the article at ` 6 more, then he would have made a prot of 5%. Find the cost price of the article. A. C.
27.
` `
` `
a2
D.
2
3 7
B. D.
If SP is x 2 y
A. C.
+
x
`
x, CP is
`
A.
` 180
C. 35.
` 0.32 ` 1.12
36.
2
a
37.
2 a
y and profit is 20%. Then
15
−10
2 15
2
D.
−3
17 60
39.
17
10, 15, 7 8, 12, 7 4, 6, 4 6, 9, 5 41. 27 − 48 + 75 − 128 + 98 + 18
33.
A.
4 3−2 2
B.
2 2 −4 3
C.
4 3+2 2
D.
4 2 +2 3
What least number must be subtracted from each of the numbers 14, 17, 34 and 42, so that the remainders will be proportion? A. C.
4
3 4
B. D.
5 2
12, 21, 15, 18,
16, 28, 20, 24,
12
20 35 25 30
126 136
B. D.
–126 –136
Directly Inversely Data Inadequate None of these
2p : l 2 : l
B. D.
5:4 5:2
` `
l : p 4 : 3l
B. D.
7:4 13 : 7
7985 7995
B. D.
` 9795 ` 7800
If n is a perfect cube, then every prime factor of ' n' occurs A. one time B. 2 times C. 3 times D. 4 times c
42.
11
The simple interest on a sum of money for 2 years at 13% p.a. is ` 2028. What will be the compound interest on ten times the s ame sum at 5% p.a. compound interest for the same period? A. C.
Simplify:
D.
If x : y = 2 : 5, then (10 x + 3 y) : (5 x + 2 y) is A. C.
40.
12
11
A wire of length l units is bent to form a circle. Then ratio of radius of the circle to the area of the circle so formed is _____. A. C.
15
B.
The number of vertices , edges and faces of the given gure are respecively. A. B. C. D.
38.
14
14
The number of persons varies _________ with the number of days required to consume a given quantity of food. A. B. C. D.
10 5
B.
The cube roots of 1372 × (–1458) is A. C.
2
11
Three numbers are in the ratio of 3 : 4 : 5. The sum of their cubes is 74088. The numbers are _____. A. B. C. D.
− 13 = ____.
13
If
−1
The value of x is
5( x – y) = 125 and 343 = y 3, then the value of x is
y
32.
B.
2
A. C.
31.
B. D.
a
C.
30.
2 2.16
34.
` 100
The diagonal of a square is 'a' units. Then the area of the square is ______ square units. A.
29.
B. D.
If given ` 200 becomes ` 216 at the rate of 4% p.a. simple interest in T years, then nd the difference between compo und inter est and simple interest in T years. A. C.
28.
80 150
−1
x − 2 + 3x − 5 = 5x − 7 − 1 4 2 5 10
a
x a xb x c xb × x c × x a A. C.
x 0
b
equals B. D.
xa + b + c 1 Class-8 | Set-1 | Level-2
43.
If ABCD is a parallelogram , then the values of x, y and z respectively are
44.
C
D
t
28°
56°
Find the value of 1 + (0.09)−1/ 2 − (64)5/ 6 × 70 16 A. C.
128°
O
45.
z
x
y
B
A.
56°, 30° and 72°
B.
56°, 28° and 74°
C.
28°, 72° and 58°
D.
56°, 28° and 72°
B. D.
–341/12 –341/6
Which of the following statements is incorrect? A.
t
A
341/12 341/6
B. C. D.
A line graph displays data that changes continuously over periods of time. A pie graph can not be use to compare parts of a whole. A histogram is a bar graph that shows data in intervals. A bar graph is used to show comparison among categories.
ACHIEVERS SECTION 46.
Find the values of p, q, r and s.
48.
(i)
Prime numbers differing by __ p __ are called twin primes.
(ii)
The number of prime numbers between 0 and 4 is __ q__ .
A. C.
(iii) The greatest common factor of relatively prime numbers is __ r__ . (iv) Least common multiple of rst two prime number is __ s__ .
47.
A. B. C. D.
p 2 2 2 1
q 1 2 1 2
r 1 1 2 1
50.
Principal (in `)
Time (in years)
Rate % (p.a.)
C.I. (in `)
A.
5000
3
6%
9550.8
B.
2500
3
15%
805.25
C.
7500
2
5%
766.75
D.
1500
2
8%
249.60
Class-8 | Set-1 | Level-2
49.
40% 20%
B. D.
The value of value of z is A. C.
s 2 6 1 2
Select the correct match.
The price of a refrigerato r, P is 5 times that of price of a cooler, Q. If P increases by 20% and that of Q decreases by 40%, then what is the change in the total price of the refrigerator and cooler put together?
(20 +
5 10
30% 10%
20 + 20 +… B. D.
4 20
In the given gure, PQRS is a rectangle. Diagonals PR and QS intersect at O such that ∠ POQ = 60°. D SRM is an isosceles triangle with SR = RM and ∠RMS = 30°. Find the value of angles e, g , h and j respectively.
S
A. B. C. D.
P
30°, 30°, 30°, 90°,
30°, 90°, 30°, 30°,
90°, 60°, 30°, 30°,
30° 30° 90° 30°
) = z , then the R
a j b
c N
g
d e h 3 0 °
T
M
O 60°
i
f Q
5
SPACE FOR ROUGH WORK
6
Class-8 | Set-1 | Level-2
