Mathematics Olympiad Test Questions
1.
On simplifying
999813 × 999815 + 1
(999814)2
4.
,
we get _______.
2.
(a) 1
(b) 2
(c) 3
(d) 4
2n+4
2(2n )
2(2
n+3
n+1
(a) 2
)
= __________.
5.
1
8
– n (c) 1 – 2
3.
If
x+
1
=a+b
x
(b) –2
(d)
n+1
7
8
and
x
1
=a
x
then
(a) ab = 1
(b) a = b
(c) ab = 2
(d) a + b = 0
b,
6.
The average of eleven-members cricket team reduces by 2 when two players of ages 30 and 32 leave the team and two new players of equal age join it. The age of each of the newcomers is _______.
(a) 20
(b) 62
(c) 12
(d) 22
Which equation satisfies the data in the table ?
x
-1
0
1
2
y
-3
-1
1
3
(a) y = x – 2
(b) y = 2x – 1
(c) y = 3x – 3
(d) y = x + 1
The ABC and BDC are right angles. If AD =
9 cm, DC = 16 cm and
AB = 15 cm, then the length of BD is ________.
D
B
(a) 12 cm
(b) 16 cm
(c) 15 cm
(d) 25 cm
Space for Rough Work
–2–
A
C
7.
xl
l +m
2
xm
8.
9.
The value of
2
.
m +n
xm xn 2
2
.
n+ l
(a) x
(b) –1
(c) 1
(d) 0
xn xl 2
2
= ____.
All the three quadrilaterals ADEC,
ABIH and BCGF are squares and
ABC = 90°. If the area of
2
2
ADEC = x and area of AHIB = y
2
2
(x > y ), then find the area of
BCGF ?
Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire rental of the car, then the share of each of the remaining persons is increased by
_______ of the original share.
(a) 1/9
(B) 1/8
(c) 1/7
(d) 7/8
10. Reena bought x pens at ` 2.60 each and y greeting cards at 80 paise each. If the pens cost ` 12 more than the cards, the equation involving x and y is ______.
(a) 13x – 4y = 6
(b) 13x – 4y = 60
(c) 260x – 8y = 100
(d) 260x – 8y = 12
11.
(a) x2 + y2
(b) 2y2
(c) 2x2
(d) x2 – y2
In a class, the number of boys is more than the number of girls by
12% of the total strength. The ratio of boys to girls is _______.
(a) 15 : 11
(b) 11 : 14
(c) 14 : 11
(d) 8 : 11
Space for Rough Work
–3–
12. Select a figure from
On simplifying
999813 × 999815 + 1
(999814)2
4.
,
we get _______.
2.
(a) 1
(b) 2
(c) 3
(d) 4
2n+4
2(2n )
2(2
n+3
n+1
(a) 2
)
= __________.
5.
1
8
– n (c) 1 – 2
3.
If
x+
1
=a+b
x
(b) –2
(d)
n+1
7
8
and
x
1
=a
x
then
(a) ab = 1
(b) a = b
(c) ab = 2
(d) a + b = 0
b,
6.
The average of eleven-members cricket team reduces by 2 when two players of ages 30 and 32 leave the team and two new players of equal age join it. The age of each of the newcomers is _______.
(a) 20
(b) 62
(c) 12
(d) 22
Which equation satisfies the data in the table ?
x
-1
0
1
2
y
-3
-1
1
3
(a) y = x – 2
(b) y = 2x – 1
(c) y = 3x – 3
(d) y = x + 1
The ABC and BDC are right angles. If AD =
9 cm, DC = 16 cm and
AB = 15 cm, then the length of BD is ________.
D
B
(a) 12 cm
(b) 16 cm
(c) 15 cm
(d) 25 cm
Space for Rough Work
–2–
A
C
7.
xl
l +m
2
xm
8.
9.
The value of
2
.
m +n
xm xn 2
2
.
n+ l
(a) x
(b) –1
(c) 1
(d) 0
xn xl 2
2
= ____.
All the three quadrilaterals ADEC,
ABIH and BCGF are squares and
ABC = 90°. If the area of
2
2
ADEC = x and area of AHIB = y
2
2
(x > y ), then find the area of
BCGF ?
Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire rental of the car, then the share of each of the remaining persons is increased by
_______ of the original share.
(a) 1/9
(B) 1/8
(c) 1/7
(d) 7/8
10. Reena bought x pens at ` 2.60 each and y greeting cards at 80 paise each. If the pens cost ` 12 more than the cards, the equation involving x and y is ______.
(a) 13x – 4y = 6
(b) 13x – 4y = 60
(c) 260x – 8y = 100
(d) 260x – 8y = 12
11.
(a) x2 + y2
(b) 2y2
(c) 2x2
(d) x2 – y2
In a class, the number of boys is more than the number of girls by
12% of the total strength. The ratio of boys to girls is _______.
(a) 15 : 11
(b) 11 : 14
(c) 14 : 11
(d) 8 : 11
Space for Rough Work
–3–
12. Select a figure from